| Date | May 2018 | Marks available | 2 | Reference code | 18M.1.sl.TZ1.2 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Each month the number of days of rain in Cardiff is recorded.
The following data was collected over a period of 10 months.
11 13 8 11 8 7 8 14 x 15
For these data the median number of days of rain per month is 10.
Find the value of x.
[2]
a.
Find the standard deviation
[2]
b.i.
Find the interquartile range.
[2]
b.ii.
Markscheme
\(\frac{{x + 11}}{2} = 10\) (M1)
Note: Award (M1) for correct substitution into median formula or for arranging all 9 values into ascending/descending order.
\(\left( {x = } \right)\,\,9\) (A1) (C2)
[2 marks]
a.
2.69 (2.69072…) (A2)(ft)
Note: Follow through from part (a).
[2 marks]
b.i.
13 − 8 (M1)
Note: Award (M1) for 13 and 8 seen.
= 5 (A1)(ft) (C4)
Note: Follow through from part (a).
[2 marks]
b.ii.
Examiners report
[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
Syllabus sections
Show 150 related questions
- 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.
- 12M.1.sl.TZ2.10b: Find the mean resting pulse rate of the students.
- 11M.2.sl.TZ2.1B.b: Use your graphic calculator to find (i) \({\bar S}\), the mean of \(S\) ; (ii) ...
- SPM.2.sl.TZ0.1b: Using your graphic display calculator, write down the value of(i) the mean;(ii) the...
- 09M.1.sl.TZ1.1a, ii: The range is \(4\).
- 10M.2.sl.TZ1.1c.ii: Use your graphic display calculator to write down \(\bar y\), the mean number of plant species.
- 13N.1.sl.TZ0.1b: Write down the mode.
- 16M.2.sl.TZ1.1b: Calculate i) \({\bar x}\) , the mean distance from the power plant; ii) ...
- 17N.1.sl.TZ0.1b: Draw a box-and-whisker diagram, for these students’ ages, on the following grid.
- 17N.2.sl.TZ0.1e.ii: Write down the number of degrees of freedom.
- 18M.1.sl.TZ1.6a: Write down the median.
- 18M.1.sl.TZ2.12b.ii: Calculate the value of k.
- 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.TZ2.2b.i: Use the cumulative frequency curve to find the median distance.
- 11N.1.sl.TZ0.2b: Find the mean grade.
- 12M.1.sl.TZ1.1a: Find x ;
- 10M.2.sl.TZ2.2b.i: Write down for this set of data the mean time, \(\bar t\).
- 11M.1.sl.TZ1.14d: Estimate the mean weight of the lightest \(40\) males.
- 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...
- 09M.1.sl.TZ2.3d: Write down the mode.
- 12M.2.sl.TZ2.3d: Use your graphic display calculator to find an estimate for (i) the mean; (ii) the standard...
- 08M.1.sl.TZ1.9b: Write down the modal group.
- 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.
- 14M.1.sl.TZ2.5a: Write down the median rainfall.
- 14M.1.sl.TZ1.6d: Use your graphic display calculator to find an estimate of (i) the mean speed of the...
- 16M.2.sl.TZ1.1d: Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of...
- 17M.2.sl.TZ1.5b: Find the median test grade of the students.
- 17M.1.sl.TZ2.7a: Write down an equation, in terms of \(x\) and \(y\), for the total number of times the die...
- 16N.2.sl.TZ0.1b: (i) \({\bar x}\), the mean number of hours spent on social media; (ii) \({\bar y}\),...
- 17N.2.sl.TZ0.1b.ii: Write down, for \(N\), the mid-interval value of the modal class.
- 17N.2.sl.TZ0.1c.ii: Use your graphic display calculator to estimate the standard deviation of \(N\).
- 18M.1.sl.TZ1.2b.i: Find the standard deviation
- 18M.2.sl.TZ2.2c: Hence write down the interquartile range.
- 18M.2.sl.TZ2.2b.iii: Use the cumulative frequency curve to find the upper quartile.
- 12M.1.sl.TZ2.10a: Find the median resting pulse rate of the students.
- 09N.1.sl.TZ0.1b: Write down the mode.
- 11M.1.sl.TZ1.2b: Use your graphic display calculator to find(i) the mean number of fillings;(ii) the...
- 11M.1.sl.TZ2.6a: Find the mean number of goals scored per match.
- 14M.2.sl.TZ2.3c: Find an estimate of the mean time people took to drink their coffee.
- 14M.1.sl.TZ1.2a: For these grades, find the mode;
- 14M.1.sl.TZ1.2b: For these grades, find the median;
- 15M.2.sl.TZ1.3h: The table shows the speeds of these vehicles travelling past the hospital gate. Use your...
- 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.
- 17M.2.sl.TZ1.5e: Given that the first student chosen at random scored a grade 5 or higher, find the...
- 17N.1.sl.TZ0.1a.i: For the students in this group find the mean age;
- 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;
- 18M.2.sl.TZ1.2g: Given that this flight was not heavily delayed, find the probability that it travelled...
- 10M.2.sl.TZ1.1c.i: Use your graphic display calculator to write down \(\bar x\), the mean of the distances from...
- 10N.1.sl.TZ0.5a.i: Write down the median mark.
- 12N.1.sl.TZ0.3a: Calculate the exact value of the mean length.
- 12N.1.sl.TZ0.11c: Calculate an estimate of the mean annual snowfall.
- 12M.1.sl.TZ2.10c: A new student joins the class and the mean resting pulse rate of the group of 11 students...
- 09M.1.sl.TZ2.3c: Find the median number of errors per page.
- 13M.1.sl.TZ1.8a: Write down the median weight of the females.
- 13M.2.sl.TZ2.2b: Write down for this set of data (i) the mean mass, \(\bar m\) ; (ii) the mean cooking time,...
- 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).
- 08N.1.sl.TZ0.2c: Calculate the median grade obtained by the students.
- 08M.1.sl.TZ2.2c: Write down the modal group.
- 15M.1.sl.TZ2.4a: Write down the value of the median for these results.
- 14N.1.sl.TZ0.1b: State the statistical term corresponding to the value of 140 minutes.
- 16M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\) .
- 16M.1.sl.TZ1.3a: In a school 160 students sat a mathematics examination. Their scores, given as marks out of...
- 17M.2.sl.TZ1.5a.i: Calculate the mean test grade of the students;
- 17M.2.sl.TZ1.5f.ii: Calculate the expected number of students that spent at least 90 minutes preparing for the test.
- 17M.1.sl.TZ2.7c: Find the value of \(x\) and of \(y\).
- 16N.2.sl.TZ0.1a: On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5...
- 16N.2.sl.TZ0.1h: Write down a reason why this estimate is not reliable.
- 17N.2.sl.TZ0.1f.ii: Write down the \({\chi ^2}\) statistic.
- 18M.1.sl.TZ1.6b: Complete the table.
- 18M.1.sl.TZ2.12b.i: Write down the total number of customers in terms of k.
- 18M.2.sl.TZ2.2d: Write down the percentage of buses that travelled a distance greater than the upper quartile.
- 18M.2.sl.TZ2.2a: Find the number of buses that travelled a distance between 15000 and 20000 kilometres.
- 12M.1.sl.TZ1.1c: Find z .
- 12M.1.sl.TZ1.5b: State what the value of 12 mm represents on the given diagram.
- 09M.1.sl.TZ1.1a, i: The mean is \(5\).
- 09M.2.sl.TZ1.1a, i: Use the diagram to estimate the median time.
- 09M.1.sl.TZ2.3b: Find the mean number of errors per page.
- 13M.1.sl.TZ2.14b: Find the median number of passengers per carriage.
- SPM.2.sl.TZ0.1a: Write down the mode.
- 08M.1.sl.TZ1.4a: Complete the following table of values for the height and weight of seven students.
- 09M.1.sl.TZ1.1a, iii: The mode is \(6\).
- 16M.1.sl.TZ1.3b: The lower quartile of these scores is 40. Find the interquartile range.
- 17M.2.sl.TZ1.5d: Find the probability that this student scored a grade 5 or higher.
- 16N.2.sl.TZ0.1d: Write down the value of \(r\), the Pearson’s product–moment correlation coefficient, for...
- 18M.1.sl.TZ1.6c.ii: Using the table, calculate an estimate for the mean number of people being followed on the...
- 18M.1.sl.TZ1.6c.i: Write down the mid-interval value for the 100 < x ≤ 150 group.
- 18M.1.sl.TZ2.12c: Hence, complete the histogram.
- 18M.2.sl.TZ2.2g: The smallest distance travelled by one of the buses was 2500 km.The longest distance...
- 10M.1.sl.TZ1.9c: Calculate an estimate of the mean examination score of the students.
- 11M.1.sl.TZ2.6b: Find the median number of goals scored per match.
- 13M.1.sl.TZ1.8d: Use the box and whisker diagram to determine if the mean weight of the females is less than...
- 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...
- 07M.2.sl.TZ0.1b: Find (i) the modal length interval, (ii) the interval containing the median length, (iii)...
- 08M.1.sl.TZ2.5b: Write down the mean number of bedrooms per house.
- 14M.2.sl.TZ1.1c: Write down (i) the mean distance, \(\bar x\), of the trees from the river bank; (ii) ...
- 17M.2.sl.TZ1.5f.i: Calculate the probability that a student chosen at random spent at least 90 minutes preparing...
- 17M.1.sl.TZ2.7b: Using the mean score, write down a second equation in terms of \(x\) and \(y\).
- 17N.1.sl.TZ0.1a.ii: For the students in this group write down the median age.
- 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.TZ0.1c.i: Use your graphic display calculator to estimate the mean of \(N\);
- 10M.1.sl.TZ2.5a: Write down an equation in terms of p and q.
- 10N.1.sl.TZ0.7b.i: Use your graphic display calculator to find an estimate for the mean weight.
- 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.2.sl.TZ0.1a: (i) Write down the mean score in Round 1. (ii) Write down the standard deviation in Round...
- 12M.1.sl.TZ1.1b: Find y ;
- 12M.2.sl.TZ2.3b: State the modal group.
- 09N.1.sl.TZ0.1c: Find the median.
- 09N.2.sl.TZ0.4A, a, i: Use your graphic display calculator to find the mean number of trees.
- 13M.1.sl.TZ2.14a: Calculate the value of p.
- 13M.1.sl.TZ2.14c: If the passengers in the eleventh carriage are also included, the mean number of passengers...
- SPM.1.sl.TZ0.1b: Write down the modal class.
- 07M.1.sl.TZ0.2b: The boxplot below shows the statistics for a set of data. For this data set write down the...
- SPM.1.sl.TZ0.4a: Write down the coordinates of the mean point \((\bar x{\text{, }}\bar y)\).
- 07N.2.sl.TZ0.4i.a: State the modal group.
- 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.TZ2.5d: Find how many houses have a number of bedrooms greater than one standard deviation above the...
- 13N.1.sl.TZ0.1c: Use your graphic display calculator to find (i) the mean number of passengers per...
- 15M.2.sl.TZ1.3g: The table shows the speeds of these vehicles travelling past the hospital gate. (i) ...
- 15M.2.sl.TZ2.4a: Using your graphic display calculator, write down the value of (i) the mean of the...
- 16N.1.sl.TZ0.2a: Giving your answer to one decimal place, write down the value of (i) the median level of...
- 16M.2.sl.TZ1.1a: For an ecological study, Ernesto measured the average concentration \((y)\) of the fine...
- 16M.1.sl.TZ2.14a: A group of students were asked how long they spend practising mathematics during the week....
- 17N.2.sl.TZ0.1f.i: Write down the \(p\)-value for the test;
- 18M.2.sl.TZ2.2b.ii: Use the cumulative frequency curve to find the lower quartile.
- 11N.1.sl.TZ0.2a: Write down the modal grade.
- 09N.1.sl.TZ0.1a: Find the value of T.
- 11M.2.sl.TZ1.1b: Write down(i) the mean percentage moisture content, \(\bar x\) ;(ii) the mean heat...
- 08N.1.sl.TZ0.2b: Write down the modal grade obtained by the students.
- 08M.2.sl.TZ1.3a: Write down (i) the mean temperature; (ii) the standard deviation of the temperatures.
- 09N.2.sl.TZ0.4A, a, iii: Use your graphic display calculator to find the mean depth of snow.
- 10M.2.sl.TZ2.2b.ii: Write down for this set of data the mean distance, \(\bar d\).
- 13N.2.sl.TZ0.1b: Use your graphic display calculator to find (i) \(\bar x\), the mean of the...
- 15M.1.sl.TZ1.2a: Find the median grade.
- 16M.1.sl.TZ2.14b: For this group of students, the estimated mean number of hours spent practising mathematics...
- 17M.2.sl.TZ1.5c: Find the interquartile range.
- 17M.2.sl.TZ1.5a.ii: Calculate the standard deviation.
- 16N.2.sl.TZ0.1c: Plot the point \((\bar x,{\text{ }}\bar y)\) on your scatter diagram and label this point M.
- 17N.2.sl.TZ0.1g: State the result of the test. Give a reason for your answer.
- 18M.1.sl.TZ1.2b.ii: Find the interquartile range.
- 18M.1.sl.TZ2.12a: Write down the mid-interval value for 10 ≤ t < 15.
- 18M.2.sl.TZ2.2f: Find the value of m.
