• Syllabus

Topic 2 - Descriptive statistics

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Sub sections and their related questions

2.0

None

2.1

• 12M.2.sl.TZ2.3a: State if the data is discrete or continuous.
• 09M.1.sl.TZ2.3a: State whether the data is discrete, continuous or neither.
• 07M.1.sl.TZ0.2a: State which of the following sets of data are discrete. (i) Speeds of cars travelling along a...
• 08M.1.sl.TZ2.5a: State whether the data is discrete or continuous.
• 13N.1.sl.TZ0.1a: State whether the data is discrete or continuous.
• 14M.2.sl.TZ1.1a: State whether distance from the river bank is a continuous or discrete variable.
• 14N.1.sl.TZ0.3a: State whether these data are discrete or continuous.
• 17M.1.sl.TZ1.1a: Complete the following table.
• 17M.1.sl.TZ1.1b: State whether length of trout is a continuous or discrete variable.
• 17M.1.sl.TZ1.1c: Write down the modal class.
• 17M.1.sl.TZ1.1d: Any trout with length 40 cm or less is returned to the lake. Calculate the percentage of the...

2.2

• 11M.1.sl.TZ2.6a: Find the mean number of goals scored per match.
• 11M.1.sl.TZ2.6b: Find the median number of goals scored per match.
• 13M.1.sl.TZ2.4a: Write down the value of (i) t ; (ii) w .
• SPM.2.sl.TZ0.1a: Write down the mode.
• 08N.1.sl.TZ0.2a: Complete the following table for the grades obtained by the students.
• 14N.1.sl.TZ0.3a: State whether these data are discrete or continuous.
• 14N.1.sl.TZ0.3b: Write down (i)     the number of hens on the farm; (ii)     the modal number of eggs laid.
• 14N.1.sl.TZ0.3c: Calculate (i)     the mean number of eggs laid; (ii)     the standard deviation.
• 15M.1.sl.TZ2.4a: Write down the value of the median for these results.
• 15M.2.sl.TZ2.4a: Using your graphic display calculator, write down the value of (i)     the mean of the diameters...
• 17M.1.sl.TZ1.1a: Complete the following table.
• 17M.1.sl.TZ1.1b: State whether length of trout is a continuous or discrete variable.
• 17M.1.sl.TZ1.1c: Write down the modal class.
• 17M.1.sl.TZ1.1d: Any trout with length 40 cm or less is returned to the lake. Calculate the percentage of the...
• 17M.1.sl.TZ2.7a: Write down an equation, in terms of \(x\) and \(y\), for the total number of times the die was...
• 17M.1.sl.TZ2.7b: Using the mean score, write down a second equation in terms of \(x\) and \(y\).
• 17M.1.sl.TZ2.7c: Find the value of \(x\) and of \(y\).
• 18M.2.sl.TZ1.2a: State the alternative hypothesis.
• 18M.2.sl.TZ1.2b: Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.
• 18M.2.sl.TZ1.2c: Write down the number of degrees of freedom.
• 18M.2.sl.TZ1.2d.i: Write down the χ2 statistic.
• 18M.2.sl.TZ1.2d.ii: Write down the associated p-value.
• 18M.2.sl.TZ1.2e: State, with a reason, whether you would reject the null hypothesis.
• 18M.2.sl.TZ1.2f: Write down the probability that this flight arrived on time.
• 18M.2.sl.TZ1.2h: Two flights are chosen at random from those which were slightly delayed. Find the probability...
• 18M.1.sl.TZ2.7a: State the number of boys who answered questions in Portuguese.
• 18M.1.sl.TZ2.7b: Find the probability that the boy answered questions in Hindi.
• 18M.1.sl.TZ2.7c: Two girls are selected at random. Calculate the probability that one girl answered questions in...

2.3

• 10M.1.sl.TZ1.9a: Complete the grouped frequency table for the students.      
• 10M.1.sl.TZ1.9b: Write down the mid-interval value of the \(40 < x \leqslant 60\) interval.
• 11N.2.sl.TZ0.1a: Write down the midpoint of the \(60 < s \leqslant 70\) interval.
• 12N.1.sl.TZ0.11b: Write down the mid interval value for the class 6 ≤ x < 10 .
• 12M.2.sl.TZ2.3c: Write down the midpoint of the interval 10 < T ≤ 20 .
• 09M.2.sl.TZ1.1d, i: The times taken for the 2000 men were grouped as shown in the table below. Write down the...
• 07N.2.sl.TZ0.4i.c: On graph paper, draw a fully labelled histogram to represent the data.
• SPM.1.sl.TZ0.1a: Complete the frequency table for this distribution.
• SPM.1.sl.TZ0.1b: Write down the modal class.
• SPM.1.sl.TZ0.1c: Write down the mid interval value of the \(10 < t \leqslant 15\) class.
• SPM.1.sl.TZ0.1d: Use your graphic display calculator to find an estimate for the mean time.
• 07M.2.sl.TZ0.1a: Find the total number of fish in the net.
• 07M.2.sl.TZ0.1b: Find (i) the modal length interval, (ii) the interval containing the median length, (iii) an...
• 07N.2.sl.TZ0.4i.a: State the modal group.
• 07N.2.sl.TZ0.4i.b: Use your graphic display calculator to calculate approximate values of the mean and standard...
• 08N.1.sl.TZ0.6a: On the grid below draw a histogram to show the above weight distribution.
• 08N.1.sl.TZ0.6b: Write down the mid-interval value for the \(40 - 49\) interval.
• 08M.1.sl.TZ1.9a: Draw a histogram on the grid below for the data in this table.
• 08M.1.sl.TZ2.2b: Find the total number of chickens.
• 09M.2.sl.TZ1.1d, ii: The times taken for the 2000 men were grouped as shown in the table below. Write down the...
• 10N.1.sl.TZ0.7a: Write down the mid interval value for the interval \(50 \leqslant w \leqslant 60\).
• 14M.2.sl.TZ2.3a: Write down the total number of people who were surveyed.
• 14M.2.sl.TZ2.3b: Write down the mid-interval value for the \(10 < t \leqslant 15\) group.
• 14M.1.sl.TZ1.6b: Complete the following grouped frequency table for \(s\), the speed of the cars passing the...
• 14M.1.sl.TZ1.6c: Write down the mid-interval value of the \(50 < s \leqslant 70\) interval.
• 15M.2.sl.TZ1.3f: The table shows the speeds of these vehicles travelling past the hospital gate. Find the value...
• 15M.2.sl.TZ1.3g: The table shows the speeds of these vehicles travelling past the hospital gate. (i)     Write...
• 16M.1.sl.TZ2.14a: A group of students were asked how long they spend practising mathematics during the week. The...
• 16M.1.sl.TZ2.14b: For this group of students, the estimated mean number of hours spent practising mathematics is...
• 17M.1.sl.TZ1.1a: Complete the following table.
• 17M.1.sl.TZ1.1b: State whether length of trout is a continuous or discrete variable.
• 17M.1.sl.TZ1.1c: Write down the modal class.
• 17M.1.sl.TZ1.1d: Any trout with length 40 cm or less is returned to the lake. Calculate the percentage of the...
• 17N.2.sl.TZ0.1a: State whether \(N\) is a discrete or a continuous variable.
• 17N.2.sl.TZ0.1b.i: Write down, for \(N\), the modal class;
• 17N.2.sl.TZ0.1b.ii: Write down, for \(N\), the mid-interval value of the modal class.
• 17N.2.sl.TZ0.1c.i: Use your graphic display calculator to estimate the mean of \(N\);
• 17N.2.sl.TZ0.1c.ii: Use your graphic display calculator to estimate the standard deviation of \(N\).
• 17N.2.sl.TZ0.1d: Find the expected frequency of students choosing the Science category and obtaining 31 to 40...
• 17N.2.sl.TZ0.1e.i: Write down the null hypothesis for this test;
• 17N.2.sl.TZ0.1e.ii: Write down the number of degrees of freedom.
• 17N.2.sl.TZ0.1f.i: Write down the \(p\)-value for the test;
• 17N.2.sl.TZ0.1f.ii: Write down the \({\chi ^2}\) statistic.
• 17N.2.sl.TZ0.1g: State the result of the test. Give a reason for your answer.
• 18M.1.sl.TZ1.6a: Write down the median.
• 18M.1.sl.TZ1.6b: Complete the table.
• 18M.1.sl.TZ1.6c.i: Write down the mid-interval value for the 100 < x ≤ 150 group.
• 18M.1.sl.TZ1.6c.ii: Using the table, calculate an estimate for the mean number of people being followed on the social...
• 18M.1.sl.TZ2.12a: Write down the mid-interval value for 10 ≤ t < 15.
• 18M.1.sl.TZ2.12b.i: Write down the total number of customers in terms of k.
• 18M.1.sl.TZ2.12b.ii: Calculate the value of k.
• 18M.1.sl.TZ2.12c: Hence, complete the histogram.

2.4

• 10M.1.sl.TZ1.9a: Complete the grouped frequency table for the students.      
• 10M.1.sl.TZ2.3a: Write down the median waiting time.
• 10M.1.sl.TZ2.3c: Draw a box and whisker plot on the grid below to represent this information.
• 10N.1.sl.TZ0.5a.i: Write down the median mark.
• 10N.1.sl.TZ0.5b: Estimate the number of students who achieved a mark greater than 32.
• 12N.1.sl.TZ0.5a: Find the number of students who failed the examination.
• 12N.1.sl.TZ0.5b: Find the number of students who were awarded grade C or better.
• 12N.1.sl.TZ0.5c: The top 20 % of the students are eligible for further study. Find the lowest mark required to be...
• 11N.2.sl.TZ0.1c: Write down the number of vehicles whose speed is less than or equal to...
• 11N.2.sl.TZ0.1d: Consider the cumulative frequency table below. Write down the value of \(a\) , of \(b\) and of...
• 11N.2.sl.TZ0.1e: Consider the cumulative frequency table below. Draw a cumulative frequency graph for the...
• 11N.2.sl.TZ0.1f: Use your cumulative frequency graph to estimate (i)     the median speed of the...
• 12N.1.sl.TZ0.11d: Find the number of years for which the annual snowfall was at least 18 cm.
• 11N.2.sl.TZ0.1g: All drivers whose vehicle’s speed is greater than one standard deviation above the speed limit of...
• 12M.1.sl.TZ1.5a: Write down (i) the lowest daily rainfall; (ii) the highest daily rainfall.
• 12M.1.sl.TZ1.5b: State what the value of 12 mm represents on the given diagram.
• 12M.1.sl.TZ1.5c: Find the interquartile range.
• 12M.1.sl.TZ1.5d: Write down the percentage of the data which is less than the upper quartile.
• 12M.2.sl.TZ2.3e: The results are represented in the cumulative frequency table below, with upper class boundaries...
• 12M.2.sl.TZ2.3f: The results are represented in the cumulative frequency table below, with upper class boundaries...
• 12M.2.sl.TZ2.3g: Use your graph from part (f) to estimate (i) the median; (ii) the 90th percentile of the...
• 09N.1.sl.TZ0.5a: Write down the median height of the students.
• 09N.1.sl.TZ0.5b: Write down the 25th percentile.
• 09N.1.sl.TZ0.5c: Write down the 75th percentile.
• 09N.1.sl.TZ0.5d: The height of the tallest student is 195 cm and the height of the shortest student is 136...
• 11M.1.sl.TZ1.14a: Write down the median weight of the males.
• 11M.1.sl.TZ1.14b: Calculate the interquartile range.
• 11M.1.sl.TZ1.14c: Estimate the number of males who weigh between \(61\) kg and \(66\) kg.
• 11M.1.sl.TZ1.14d: Estimate the mean weight of the lightest \(40\) males.
• 09M.2.sl.TZ1.1a, i: Use the diagram to estimate the median time.
• 09M.2.sl.TZ1.1b: Find the number of men who take more than 11 seconds to perform the task.
• 09M.2.sl.TZ1.1c: 55 % of the men took less than p seconds to perform the task. Find p.
• 13M.1.sl.TZ2.4b: Indicate with a tick () whether the following statements are True or False.
• 07M.1.sl.TZ0.2b: The boxplot below shows the statistics for a set of data. For this data set write down the...
• 13M.1.sl.TZ1.4a: Write down the median height of the trees.
• 13M.1.sl.TZ1.4b: Write down the 75th percentile.
• 13M.1.sl.TZ1.4c: Find the interquartile range.
• 13M.1.sl.TZ1.4d: Estimate the number of trees that are more than 40 cm in height.
• 13M.1.sl.TZ1.8a: Write down the median weight of the females.
• 13M.1.sl.TZ1.8b: Calculate the range.
• 13M.1.sl.TZ1.8c: Estimate the probability that the weight of a randomly chosen female is more than 50 kg.
• 13M.1.sl.TZ1.8d: Use the box and whisker diagram to determine if the mean weight of the females is less than the...
• 13M.1.sl.TZ2.4a: Write down the value of (i) t ; (ii) w .
• SPM.2.sl.TZ0.1d: Draw a box and whisker diagram for this data, on graph paper, using a scale of \(1{\text{ cm}}\)...
• 08N.1.sl.TZ0.3a: Write down the median height of the trees.
• 08N.1.sl.TZ0.3b: Calculate the interquartile range of the heights of the trees.
• 08N.1.sl.TZ0.3c: Given that the smallest tree in the wood is \(3{\text{ m}}\) high and the tallest tree is...
• 08M.1.sl.TZ1.2c: Given that the youngest teacher is \(21\) years old and the oldest is \(72\) years old, represent...
• 08M.1.sl.TZ2.13a: Write down the median length of hair in the sample.
• 08M.1.sl.TZ2.13b: Find the interquartile range for the length of hair in the sample.
• 08M.1.sl.TZ2.13c: Given that the shortest length was \(6{\text{ cm}}\) and the longest \(47{\text{ cm}}\), draw and...
• 09M.2.sl.TZ1.1a, ii: Use the diagram to estimate the upper quartile and the lower quartile.
• 10N.1.sl.TZ0.5a.ii: Write down the 75th percentile mark.
• 10N.1.sl.TZ0.5a.iii: Write down the range of marks.
• 14M.1.sl.TZ2.5a: Write down the median rainfall.
• 14M.1.sl.TZ2.5b: Write down the minimum rainfall.
• 14M.1.sl.TZ2.5c: Find the interquartile range.
• 14M.1.sl.TZ2.5d: Write down the number of days the rainfall will be (i)     between 43 mm and 48 mm; (ii)    ...
• 14M.2.sl.TZ2.3d: The information above has been rewritten as a cumulative frequency table. Write down the value...
• 14M.2.sl.TZ2.3e: This information is shown in the following cumulative frequency graph. For the people who were...
• 13N.1.sl.TZ0.4a: Find the median distance travelled by the cars.
• 13N.1.sl.TZ0.4b: Calculate the interquartile range of the distance travelled by the cars.
• 13N.1.sl.TZ0.4c: Find the number of cars that travelled more than \(130\) km.
• 14M.1.sl.TZ1.6a: Write down the number of cars passing the camera with speed of less than or equal to 50...
• 14N.1.sl.TZ0.1a: Find (i)     the longest amount of time spent on homework per day; (ii)     the interquartile...
• 14N.1.sl.TZ0.1b: State the statistical term corresponding to the value of 140 minutes.
• 14N.1.sl.TZ0.1c: Find the percentage of students who spend (i)     between 100 and 140 minutes per day on their...
• 15M.1.sl.TZ2.4b: Draw a box-and-whisker diagram for these results on the following grid.
• 15M.1.sl.TZ2.4c: The results for the second group of 40 students are shown in the following box-and-whisker...
• 15M.2.sl.TZ1.3a: Estimate the minimum possible speed of one of these vehicles passing the hospital gate.
• 15M.2.sl.TZ1.3b: Find the median speed of the vehicles.
• 15M.2.sl.TZ1.3c: Write down the \({75^{{\text{th}}}}\) percentile.
• 15M.2.sl.TZ1.3d: Calculate the interquartile range.
• 15M.2.sl.TZ1.3e: The speed limit past the hospital gate is \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\). Find the...
• 15M.2.sl.TZ1.3i: It is proposed that the speed limit past the hospital gate is reduced to...
• 16M.1.sl.TZ1.3a: In a school 160 students sat a mathematics examination. Their scores, given as marks out of 90,...
• 16M.1.sl.TZ1.3b: The lower quartile of these scores is 40. Find the interquartile range.
• 16M.1.sl.TZ1.3c: The lowest score was 6 marks and the highest score was 90 marks. Draw a box-and-whisker diagram...
• 16N.1.sl.TZ0.2a: Giving your answer to one decimal place, write down the value of (i)     the median level of...
• 16N.1.sl.TZ0.2b: Draw a box-and-whisker diagram on the grid below to represent the Vitamin C content, in...
• 17M.1.sl.TZ2.6a: Write down the median length of these leaves.
• 17M.1.sl.TZ2.6b: Write down the number of leaves with a length less than or equal to 8 cm.
• 17M.1.sl.TZ2.6c.i: Use the graph to find the value of \(k\).
• 17M.1.sl.TZ2.6c.ii: Before measuring, the researcher estimated \(k\) to be approximately 9.5 cm. Find the percentage...
• 17N.1.sl.TZ0.1a.i: For the students in this group find the mean age;
• 17N.1.sl.TZ0.1a.ii: For the students in this group write down the median age.
• 17N.1.sl.TZ0.1b: Draw a box-and-whisker diagram, for these students’ ages, on the following grid.
• 18M.1.sl.TZ1.6a: Write down the median.
• 18M.1.sl.TZ1.6b: Complete the table.
• 18M.1.sl.TZ1.6c.i: Write down the mid-interval value for the 100 < x ≤ 150 group.
• 18M.1.sl.TZ1.6c.ii: Using the table, calculate an estimate for the mean number of people being followed on the social...
• 18M.2.sl.TZ2.2a: Find the number of buses that travelled a distance between 15000 and 20000 kilometres.
• 18M.2.sl.TZ2.2b.i: Use the cumulative frequency curve to find the median distance.
• 18M.2.sl.TZ2.2b.ii: Use the cumulative frequency curve to find the lower quartile.
• 18M.2.sl.TZ2.2b.iii: Use the cumulative frequency curve to find the upper quartile.
• 18M.2.sl.TZ2.2c: Hence write down the interquartile range.
• 18M.2.sl.TZ2.2d: Write down the percentage of buses that travelled a distance greater than the upper quartile.
• 18M.2.sl.TZ2.2e: Find the number of buses that travelled a distance less than or equal to 12 000 km.
• 18M.2.sl.TZ2.2f: Find the value of m.
• 18M.2.sl.TZ2.2g: The smallest distance travelled by one of the buses was 2500 km.The longest distance travelled by...

2.5

• 10M.1.sl.TZ1.9c: Calculate an estimate of the mean examination score of the students.
• 10M.1.sl.TZ2.5a: Write down an equation in terms of p and q.
• 10M.1.sl.TZ2.5b.i: The mode of these ten numbers is five and p is less than q. Write down the value of p.
• 10M.1.sl.TZ2.5c: Find the median of the ten numbers.
• 10M.2.sl.TZ1.1c.i: Use your graphic display calculator to write down \(\bar x\), the mean of the distances from the...
• 11N.1.sl.TZ0.2a: Write down the modal grade.
• 11N.1.sl.TZ0.2b: Find the mean grade.
• 10N.1.sl.TZ0.5a.i: Write down the median mark.
• 10N.1.sl.TZ0.7b.i: Use your graphic display calculator to find an estimate for the mean weight.
• 12N.1.sl.TZ0.3a: Calculate the exact value of the mean length.
• 11N.2.sl.TZ0.1b: Use your graphic display calculator to find an estimate for (i)     the mean speed of the...
• 12N.1.sl.TZ0.11a: Write down the modal class.
• 12N.1.sl.TZ0.11c: Calculate an estimate of the mean annual snowfall.
• 12N.2.sl.TZ0.1a: (i) Write down the mean score in Round 1. (ii) Write down the standard deviation in Round...
• 12M.1.sl.TZ1.1a: Find x ;
• 12M.1.sl.TZ1.1b: Find y ;
• 12M.1.sl.TZ1.1c: Find z .
• 12M.1.sl.TZ1.5b: State what the value of 12 mm represents on the given diagram.
• 10M.2.sl.TZ2.2b.i: Write down for this set of data the mean time, \(\bar t\).
• 12M.1.sl.TZ2.10a: Find the median resting pulse rate of the students.
• 12M.1.sl.TZ2.10b: Find the mean resting pulse rate of the students.
• 12M.1.sl.TZ2.10c: A new student joins the class and the mean resting pulse rate of the group of 11 students becomes...
• 12M.2.sl.TZ2.3b: State the modal group.
• 12M.2.sl.TZ2.3d: Use your graphic display calculator to find an estimate for (i) the mean; (ii) the standard...
• 09N.1.sl.TZ0.1a: Find the value of T.
• 09N.1.sl.TZ0.1b: Write down the mode.
• 09N.1.sl.TZ0.1c: Find the median.
• 11M.1.sl.TZ1.2b: Use your graphic display calculator to find(i)     the mean number of fillings;(ii)    the median...
• 09N.2.sl.TZ0.4A, a, i: Use your graphic display calculator to find the mean number of trees.
• 09M.1.sl.TZ1.1a, i: The mean is \(5\).
• 11M.1.sl.TZ1.14d: Estimate the mean weight of the lightest \(40\) males.
• 09M.2.sl.TZ1.1a, i: Use the diagram to estimate the median time.
• 09M.2.sl.TZ1.1e, i: Use your graphic display calculator to find an estimate of the mean time.
• 09M.2.sl.TZ1.1f: Everyone who performs the task in less than one standard deviation below the mean will receive a...
• 11M.2.sl.TZ1.1b: Write down(i)     the mean percentage moisture content, \(\bar x\) ;(ii)    the mean heat output,...
• 07M.1.sl.TZ0.2b: The boxplot below shows the statistics for a set of data. For this data set write down the...
• 09M.1.sl.TZ2.3b: Find the mean number of errors per page.
• 09M.1.sl.TZ2.3c: Find the median number of errors per page.
• 09M.1.sl.TZ2.3d: Write down the mode.
• 11M.1.sl.TZ2.6a: Find the mean number of goals scored per match.
• 11M.1.sl.TZ2.6b: Find the median number of goals scored per match.
• 13M.1.sl.TZ1.8a: Write down the median weight of the females.
• 13M.1.sl.TZ1.8d: Use the box and whisker diagram to determine if the mean weight of the females is less than the...
• 11M.2.sl.TZ2.1B.b: Use your graphic calculator to find (i)     \({\bar S}\), the mean of \(S\) ; (ii)   ...
• 13M.1.sl.TZ2.14a: Calculate the value of p.
• 13M.1.sl.TZ2.14b: Find the median number of passengers per carriage.
• 13M.1.sl.TZ2.14c: If the passengers in the eleventh carriage are also included, the mean number of passengers per...
• 13M.2.sl.TZ2.2b: Write down for this set of data (i) the mean mass, \(\bar m\) ; (ii) the mean cooking time,...
• SPM.1.sl.TZ0.1b: Write down the modal class.
• SPM.1.sl.TZ0.1d: Use your graphic display calculator to find an estimate for the mean time.
• 07M.1.sl.TZ0.1a: (i) Find the mean of the contractor’s measurements. (ii) Calculate the percentage error between...
• 07M.1.sl.TZ0.2c: Write down three different integers whose mean is 10.
• 07M.1.sl.TZ0.6b: Write down the median of the numbers in part (a).
• SPM.1.sl.TZ0.4a: Write down the coordinates of the mean point \((\bar x{\text{, }}\bar y)\).
• SPM.2.sl.TZ0.1a: Write down the mode.
• SPM.2.sl.TZ0.1b: Using your graphic display calculator, write down the value of(i)     the mean;(ii)    the...
• 07M.2.sl.TZ0.1b: Find (i) the modal length interval, (ii) the interval containing the median length, (iii) an...
• 07N.2.sl.TZ0.4i.a: State the modal group.
• 08N.1.sl.TZ0.2b: Write down the modal grade obtained by the students.
• 08N.1.sl.TZ0.2c: Calculate the median grade obtained by the students.
• 08N.1.sl.TZ0.6c: Find an estimate of the mean weight of the members of the club.
• 08M.1.sl.TZ1.2a: Write down the median age.
• 08M.1.sl.TZ1.4a: Complete the following table of values for the height and weight of seven students.
• 08M.1.sl.TZ1.9b: Write down the modal group.
• 08M.2.sl.TZ1.3a: Write down (i)     the mean temperature; (ii)    the standard deviation of the temperatures.
• 08M.1.sl.TZ2.2c: Write down the modal group.
• 08M.1.sl.TZ2.5b: Write down the mean number of bedrooms per house.
• 08M.1.sl.TZ2.5d: Find how many houses have a number of bedrooms greater than one standard deviation above the mean.
• 09M.1.sl.TZ1.1a, ii: The range is \(4\).
• 09M.1.sl.TZ1.1a, iii: The mode is \(6\).
• 09N.2.sl.TZ0.4A, a, iii: Use your graphic display calculator to find the mean depth of snow.
• 10M.2.sl.TZ1.1c.ii: Use your graphic display calculator to write down \(\bar y\), the mean number of plant species.
• 10M.1.sl.TZ2.5b.ii: The mode of these ten numbers is five and p is less than q. Write down the value of q.
• 10M.2.sl.TZ2.2b.ii: Write down for this set of data the mean distance, \(\bar d\).
• 14M.1.sl.TZ2.5a: Write down the median rainfall.
• 14M.2.sl.TZ2.3c: Find an estimate of the mean time people took to drink their coffee.
• 13N.1.sl.TZ0.1b: Write down the mode.
• 13N.1.sl.TZ0.1c: Use your graphic display calculator to find (i)     the mean number of passengers per car; (ii)...
• 13N.2.sl.TZ0.1b: Use your graphic display calculator to find (i)     \(\bar x\), the mean of the distances; (ii)...
• 14M.1.sl.TZ1.2a: For these grades, find the mode;
• 14M.1.sl.TZ1.2b: For these grades, find the median;
• 14M.1.sl.TZ1.6d: Use your graphic display calculator to find an estimate of (i)     the mean speed of the cars...
• 14M.2.sl.TZ1.1c: Write down (i)     the mean distance, \(\bar x\), of the trees from the river bank; (ii)    ...
• 14N.1.sl.TZ0.1b: State the statistical term corresponding to the value of 140 minutes.
• 14N.1.sl.TZ0.3b: Write down (i)     the number of hens on the farm; (ii)     the modal number of eggs laid.
• 14N.1.sl.TZ0.3c: Calculate (i)     the mean number of eggs laid; (ii)     the standard deviation.
• 15M.1.sl.TZ1.2a: Find the median grade.
• 15M.1.sl.TZ2.4a: Write down the value of the median for these results.
• 15M.2.sl.TZ1.3g: The table shows the speeds of these vehicles travelling past the hospital gate. (i)     Write...
• 15M.2.sl.TZ1.3h: The table shows the speeds of these vehicles travelling past the hospital gate. Use your...
• 15M.2.sl.TZ2.4a: Using your graphic display calculator, write down the value of (i)     the mean of the diameters...
• 16M.1.sl.TZ1.3a: In a school 160 students sat a mathematics examination. Their scores, given as marks out of 90,...
• 16M.1.sl.TZ1.3b: The lower quartile of these scores is 40. Find the interquartile range.
• 16M.2.sl.TZ1.1a: For an ecological study, Ernesto measured the average concentration \((y)\) of the fine...
• 16M.2.sl.TZ1.1b: Calculate i)      \({\bar x}\) , the mean distance from the power plant; ii)     \({\bar y}\) ,...
• 16M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\) .
• 16M.2.sl.TZ1.1d: Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of...
• 16N.1.sl.TZ0.2a: Giving your answer to one decimal place, write down the value of (i)     the median level of...
• 16M.1.sl.TZ2.14a: A group of students were asked how long they spend practising mathematics during the week. The...
• 16M.1.sl.TZ2.14b: For this group of students, the estimated mean number of hours spent practising mathematics is...
• 16N.2.sl.TZ0.1a: On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours...
• 16N.2.sl.TZ0.1b: (i)     \({\bar x}\), the mean number of hours spent on social media; (ii)     \({\bar y}\), the...
• 16N.2.sl.TZ0.1c: Plot the point \((\bar x,{\text{ }}\bar y)\) on your scatter diagram and label this point M.
• 16N.2.sl.TZ0.1d: Write down the value of \(r\), the Pearson’s product–moment correlation coefficient, for these data.
• 16N.2.sl.TZ0.1h: Write down a reason why this estimate is not reliable.
• 17M.1.sl.TZ2.7a: Write down an equation, in terms of \(x\) and \(y\), for the total number of times the die was...
• 17M.1.sl.TZ2.7b: Using the mean score, write down a second equation in terms of \(x\) and \(y\).
• 17M.1.sl.TZ2.7c: Find the value of \(x\) and of \(y\).
• 17M.2.sl.TZ1.5a.i: Calculate the mean test grade of the students;
• 17M.2.sl.TZ1.5b: Find the median test grade of the students.
• 17M.2.sl.TZ1.5c: Find the interquartile range.
• 17M.2.sl.TZ1.5d: Find the probability that this student scored a grade 5 or higher.
• 17M.2.sl.TZ1.5e: Given that the first student chosen at random scored a grade 5 or higher, find the probability...
• 17M.2.sl.TZ1.5f.i: Calculate the probability that a student chosen at random spent at least 90 minutes preparing for...
• 17M.2.sl.TZ1.5f.ii: Calculate the expected number of students that spent at least 90 minutes preparing for the test.
• 17M.2.sl.TZ1.5a.ii: Calculate the standard deviation.
• 17N.1.sl.TZ0.1a.i: For the students in this group find the mean age;
• 17N.1.sl.TZ0.1a.ii: For the students in this group write down the median age.
• 17N.1.sl.TZ0.1b: Draw a box-and-whisker diagram, for these students’ ages, on the following grid.
• 17N.2.sl.TZ0.1a: State whether \(N\) is a discrete or a continuous variable.
• 17N.2.sl.TZ0.1b.i: Write down, for \(N\), the modal class;
• 17N.2.sl.TZ0.1b.ii: Write down, for \(N\), the mid-interval value of the modal class.
• 17N.2.sl.TZ0.1c.i: Use your graphic display calculator to estimate the mean of \(N\);
• 17N.2.sl.TZ0.1c.ii: Use your graphic display calculator to estimate the standard deviation of \(N\).
• 17N.2.sl.TZ0.1d: Find the expected frequency of students choosing the Science category and obtaining 31 to 40...
• 17N.2.sl.TZ0.1e.i: Write down the null hypothesis for this test;
• 17N.2.sl.TZ0.1e.ii: Write down the number of degrees of freedom.
• 17N.2.sl.TZ0.1f.i: Write down the \(p\)-value for the test;
• 17N.2.sl.TZ0.1f.ii: Write down the \({\chi ^2}\) statistic.
• 17N.2.sl.TZ0.1g: State the result of the test. Give a reason for your answer.
• 18M.1.sl.TZ1.2a: Find the value of x.
• 18M.1.sl.TZ1.2b.i: Find the standard deviation
• 18M.1.sl.TZ1.2b.ii: Find the interquartile range.
• 18M.1.sl.TZ1.6a: Write down the median.
• 18M.1.sl.TZ1.6b: Complete the table.
• 18M.1.sl.TZ1.6c.i: Write down the mid-interval value for the 100 < x ≤ 150 group.
• 18M.1.sl.TZ1.6c.ii: Using the table, calculate an estimate for the mean number of people being followed on the social...
• 18M.2.sl.TZ1.2g: Given that this flight was not heavily delayed, find the probability that it travelled between...
• 18M.1.sl.TZ2.12a: Write down the mid-interval value for 10 ≤ t < 15.
• 18M.1.sl.TZ2.12b.i: Write down the total number of customers in terms of k.
• 18M.1.sl.TZ2.12b.ii: Calculate the value of k.
• 18M.1.sl.TZ2.12c: Hence, complete the histogram.
• 18M.2.sl.TZ2.2a: Find the number of buses that travelled a distance between 15000 and 20000 kilometres.
• 18M.2.sl.TZ2.2b.i: Use the cumulative frequency curve to find the median distance.
• 18M.2.sl.TZ2.2b.ii: Use the cumulative frequency curve to find the lower quartile.
• 18M.2.sl.TZ2.2b.iii: Use the cumulative frequency curve to find the upper quartile.
• 18M.2.sl.TZ2.2c: Hence write down the interquartile range.
• 18M.2.sl.TZ2.2d: Write down the percentage of buses that travelled a distance greater than the upper quartile.
• 18M.2.sl.TZ2.2e: Find the number of buses that travelled a distance less than or equal to 12 000 km.
• 18M.2.sl.TZ2.2f: Find the value of m.
• 18M.2.sl.TZ2.2g: The smallest distance travelled by one of the buses was 2500 km.The longest distance travelled by...

2.6

• 10M.1.sl.TZ2.3b: Find the interquartile range for the waiting time.
• 11N.1.sl.TZ0.2c: Write down the standard deviation.
• 11N.1.sl.TZ0.2d: Find the interquartile range.
• 10N.1.sl.TZ0.7b.ii: Use your graphic display calculator to find an estimate for the standard deviation.
• 10N.1.sl.TZ0.7c: Find the weight that is 3 standard deviations below the mean.
• 11N.2.sl.TZ0.1b: Use your graphic display calculator to find an estimate for (i)     the mean speed of the...
• 11N.2.sl.TZ0.1g: All drivers whose vehicle’s speed is greater than one standard deviation above the speed limit of...
• 12N.2.sl.TZ0.1a: (i) Write down the mean score in Round 1. (ii) Write down the standard deviation in Round...
• 12M.1.sl.TZ1.5c: Find the interquartile range.
• 12M.2.sl.TZ2.3d: Use your graphic display calculator to find an estimate for (i) the mean; (ii) the standard...
• 11M.1.sl.TZ1.2b: Use your graphic display calculator to find(i)     the mean number of fillings;(ii)    the median...
• 09N.2.sl.TZ0.4A, a, i: Use your graphic display calculator to find the mean number of trees.
• 09M.1.sl.TZ1.1b: Calculate the interquartile range for the number of inhabitants per house.
• 11M.1.sl.TZ1.14b: Calculate the interquartile range.
• 11M.1.sl.TZ1.14c: Estimate the number of males who weigh between \(61\) kg and \(66\) kg.
• 09M.2.sl.TZ1.1f: Everyone who performs the task in less than one standard deviation below the mean will receive a...
• 13M.1.sl.TZ1.4c: Find the interquartile range.
• 13M.1.sl.TZ1.8b: Calculate the range.
• SPM.2.sl.TZ0.1b: Using your graphic display calculator, write down the value of(i)     the mean;(ii)    the...
• SPM.2.sl.TZ0.1c: Find the interquartile range.
• 07M.2.sl.TZ0.1c: (i) Write down an estimate for the standard deviation of the lengths. (ii) How many fish (if...
• 08N.1.sl.TZ0.3b: Calculate the interquartile range of the heights of the trees.
• 08N.1.sl.TZ0.6d: Write down an estimate of the standard deviation of their weights.
• 08M.1.sl.TZ1.2b: Find the interquartile range for the ages.
• 08M.1.sl.TZ1.4a: Complete the following table of values for the height and weight of seven students.
• 08M.2.sl.TZ1.3a: Write down (i)     the mean temperature; (ii)    the standard deviation of the temperatures.
• 08M.1.sl.TZ2.5c: Write down the standard deviation of the number of bedrooms per house.
• 08M.1.sl.TZ2.5d: Find how many houses have a number of bedrooms greater than one standard deviation above the mean.
• 08M.1.sl.TZ2.13b: Find the interquartile range for the length of hair in the sample.
• 09M.1.sl.TZ1.1a, iv: The standard deviation is \(1.4\) correct to \(2\) significant figures.
• 09M.2.sl.TZ1.1a, iii: Use the diagram to estimate the interquartile range.
• 09M.2.sl.TZ1.1e, ii: Use your graphic display calculator to find an estimate of the standard deviation of the time.
• 09N.2.sl.TZ0.1A, a, ii: Use your graphic display calculator to find the standard deviation of the number of trees.
• 09N.2.sl.TZ0.4A, a, iv: Use your graphic display calculator to find the standard deviation of the depth of snow.
• 10N.1.sl.TZ0.5a.iii: Write down the range of marks.
• 14M.1.sl.TZ2.5c: Find the interquartile range.
• 13N.1.sl.TZ0.1c: Use your graphic display calculator to find (i)     the mean number of passengers per car; (ii)...
• 13N.1.sl.TZ0.4b: Calculate the interquartile range of the distance travelled by the cars.
• 14M.1.sl.TZ1.2c: For these grades, find the upper quartile;
• 14M.1.sl.TZ1.2d: For these grades, find the interquartile range.
• 14M.1.sl.TZ1.6d: Use your graphic display calculator to find an estimate of (i)     the mean speed of the cars...
• 14N.1.sl.TZ0.1a: Find (i)     the longest amount of time spent on homework per day; (ii)     the interquartile...
• 14N.1.sl.TZ0.3c: Calculate (i)     the mean number of eggs laid; (ii)     the standard deviation.
• 15M.1.sl.TZ1.2b: Calculate the interquartile range.
• 15M.2.sl.TZ1.3d: Calculate the interquartile range.
• 15M.2.sl.TZ1.3h: The table shows the speeds of these vehicles travelling past the hospital gate. Use your...
• 15M.2.sl.TZ2.4a: Using your graphic display calculator, write down the value of (i)     the mean of the diameters...
• 16M.1.sl.TZ1.3a: In a school 160 students sat a mathematics examination. Their scores, given as marks out of 90,...
• 16M.1.sl.TZ1.3b: The lower quartile of these scores is 40. Find the interquartile range.
• 16N.1.sl.TZ0.2a: Giving your answer to one decimal place, write down the value of (i)     the median level of...
• 17M.2.sl.TZ1.5a.i: Calculate the mean test grade of the students;
• 17M.2.sl.TZ1.5b: Find the median test grade of the students.
• 17M.2.sl.TZ1.5c: Find the interquartile range.
• 17M.2.sl.TZ1.5d: Find the probability that this student scored a grade 5 or higher.
• 17M.2.sl.TZ1.5e: Given that the first student chosen at random scored a grade 5 or higher, find the probability...
• 17M.2.sl.TZ1.5f.i: Calculate the probability that a student chosen at random spent at least 90 minutes preparing for...
• 17M.2.sl.TZ1.5f.ii: Calculate the expected number of students that spent at least 90 minutes preparing for the test.
• 17M.2.sl.TZ1.5a.ii: Calculate the standard deviation.
• 17N.1.sl.TZ0.1a.i: For the students in this group find the mean age;
• 17N.1.sl.TZ0.1a.ii: For the students in this group write down the median age.
• 17N.1.sl.TZ0.1b: Draw a box-and-whisker diagram, for these students’ ages, on the following grid.
• 17N.2.sl.TZ0.1a: State whether \(N\) is a discrete or a continuous variable.
• 17N.2.sl.TZ0.1b.i: Write down, for \(N\), the modal class;
• 17N.2.sl.TZ0.1b.ii: Write down, for \(N\), the mid-interval value of the modal class.
• 17N.2.sl.TZ0.1c.i: Use your graphic display calculator to estimate the mean of \(N\);
• 17N.2.sl.TZ0.1c.ii: Use your graphic display calculator to estimate the standard deviation of \(N\).
• 17N.2.sl.TZ0.1d: Find the expected frequency of students choosing the Science category and obtaining 31 to 40...
• 17N.2.sl.TZ0.1e.i: Write down the null hypothesis for this test;
• 17N.2.sl.TZ0.1e.ii: Write down the number of degrees of freedom.
• 17N.2.sl.TZ0.1f.i: Write down the \(p\)-value for the test;
• 17N.2.sl.TZ0.1f.ii: Write down the \({\chi ^2}\) statistic.
• 17N.2.sl.TZ0.1g: State the result of the test. Give a reason for your answer.
• 18M.1.sl.TZ1.2a: Find the value of x.
• 18M.1.sl.TZ1.2b.i: Find the standard deviation
• 18M.1.sl.TZ1.2b.ii: Find the interquartile range.
• 18M.2.sl.TZ1.2g: Given that this flight was not heavily delayed, find the probability that it travelled between...
• 18M.2.sl.TZ2.2a: Find the number of buses that travelled a distance between 15000 and 20000 kilometres.
• 18M.2.sl.TZ2.2b.i: Use the cumulative frequency curve to find the median distance.
• 18M.2.sl.TZ2.2b.ii: Use the cumulative frequency curve to find the lower quartile.
• 18M.2.sl.TZ2.2b.iii: Use the cumulative frequency curve to find the upper quartile.
• 18M.2.sl.TZ2.2c: Hence write down the interquartile range.
• 18M.2.sl.TZ2.2d: Write down the percentage of buses that travelled a distance greater than the upper quartile.
• 18M.2.sl.TZ2.2e: Find the number of buses that travelled a distance less than or equal to 12 000 km.
• 18M.2.sl.TZ2.2f: Find the value of m.
• 18M.2.sl.TZ2.2g: The smallest distance travelled by one of the buses was 2500 km.The longest distance travelled by...