DP Mathematics: Analysis and Approaches Questionbank

Find the value of $a$.

Write down the value of the median distance in kilometres (km).

Find the value of $b$.

Find $m$.

The first $150$ athletes that completed the race won a prize.

Given that an athlete took between $22$ and $m$ minutes to complete the $5 \text{km}$ race, calculate the probability that they won a prize.

Write down the modal group for these data.

Use your graphic display calculator to find an estimate of the standard deviation of the weights of mangoes from this harvest.

On the grid below, draw a histogram for the data in the table.

Find the minimum possible value of $U$.

Hence, find the minimum possible value of $L$.

Find the median number of hours per week these Year 12 students spend doing homework.

Given that $10\%$ of these Year 12 students spend more than $k$ hours per week doing homework, find the value of $k$.

Estimate the number of Year 12 students that spend more than $15$ hours each week doing homework.

Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.

Find the value of $p$ and the value of $q$.

Suggest a more appropriate sampling method.

Find the largest value of $c$ that would not be considered an outlier.

State why it appears that the mean reaction time is greater than the median reaction time.

State the median reaction time after sleeping well.

Now consider the two box and whisker diagrams.

Comment on whether these box and whisker diagrams provide any evidence that might suggest that not sleeping well causes an increase in reaction time.

Find the number of employees whose travelling time is within 15 minutes of the median.

Travelling times of less than $p$ minutes are considered outliers.

Find the value of $p$.

Find the median number of minutes spent traveling to work.

Hence, find the interquartile range.

Write down the value of $b$.

Find the value of $k$.

Find the value of $a$.

Write down the value of $a$ and of $b$.

Use this regression line to estimate the monthly honey production from a hive that has 270 bees.

Write down the number of low production hives.

Find the value of $k$;

Find the number of hives that have a high production.

Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.

Find the median number of hours worked by the employees.

Write down the number of employees who worked 50 hours or less.

Find the amount of money an employee earned for working 40 hours;

Find the amount of money an employee earned for working 43 hours.

Find the number of employees who earned £200 or less.

Only 10 employees earned more than £$k$. Find the value of $k$.

Complete the following table.

State whether length of trout is a continuous or discrete variable.

Write down the modal class.

Any trout with length 40 cm or less is returned to the lake.

Calculate the percentage of the fisherman’s catch that is returned to the lake.

State whether speed is a continuous or discrete variable.

Write down the median speed for these animals.

Write down the range of the animal speeds.

For these eight animals find the mean speed.

For these eight animals write down the standard deviation.

State the alternative hypothesis.

Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.

Write down the number of degrees of freedom.

Write down the χ² statistic.

Write down the associated p-value.

State, with a reason, whether you would reject the null hypothesis.

Write down the probability that this flight arrived on time.

Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.

Two flights are chosen at random from those which were slightly delayed.

Find the probability that each of these flights travelled at least 5000 km.

State the number of boys who answered questions in Portuguese.

Find the probability that the boy answered questions in Hindi.

Two girls are selected at random.

Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.

Write down an equation, in terms of $x$ and $y$, for the total number of times the die was rolled.

Using the mean score, write down a second equation in terms of $x$ and $y$.

Find the value of $x$ and of $y$.

Write down the modal length of the rods.

Find the median length of the rods.

Calculate the lower quartile.

Calculate the interquartile range.

Complete the cumulative frequency table.

Write down the probability that a bouquet of roses sold is not small.

A customer buys a large bouquet.

Find the probability that there are 12 roses in this bouquet.

Write down the median.

Complete the table.

Write down the mid-interval value for the 100 < x ≤ 150 group.

Using the table, calculate an estimate for the mean number of people being followed on the social media website by these 160 students.

Write down the mid-interval value for 10 ≤ t < 15.

Write down the total number of customers in terms of k.

Calculate the value of k.

Hence, complete the histogram.

State whether $N$ is a discrete or a continuous variable.

Write down, for $N$, the modal class;

Write down, for $N$, the mid-interval value of the modal class.

Use your graphic display calculator to estimate the mean of $N$;

Use your graphic display calculator to estimate the standard deviation of $N$.

Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.

Write down the null hypothesis for this test;

Write down the number of degrees of freedom.

Write down the $p$-value for the test;

Write down the ${\chi }^2$ statistic.

State the result of the test. Give a reason for your answer.

Find the median of the examination results.

Find the interquartile range.

Find the final examination result required to obtain the highest possible grade.

Write down the modal class.

Write down the mid-interval value of the modal class.

Calculate an estimate of the mean examination result.

Calculate an estimate of the standard deviation, giving your answer correct to three decimal places.

The teacher sets a grade boundary that is one standard deviation below the mean.

Use the cumulative frequency graph to estimate the number of students whose final examination result was below this grade boundary.

$p$.

$q$.

On the same grid, complete the cumulative frequency curve for these data.

Use the cumulative frequency curve to find an estimate for the number of students who worked at most 35 hours per month.

For the students in this group find the mean age;

For the students in this group write down the median age.

Draw a box-and-whisker diagram, for these students’ ages, on the following grid.

Find the number of buses that travelled a distance between 15000 and 20000 kilometres.

Use the cumulative frequency curve to find the median distance.

Use the cumulative frequency curve to find the lower quartile.

Use the cumulative frequency curve to find the upper quartile.

Hence write down the interquartile range.

Write down the percentage of buses that travelled a distance greater than the upper quartile.

Find the number of buses that travelled a distance less than or equal to 12 000 km.

Find the value of m.

The smallest distance travelled by one of the buses was 2500 km.
The longest distance travelled by one of the buses was 23 000 km.

On graph paper, draw a box-and-whisker diagram for these data. Use a scale of 2 cm to represent 5000 km.

Write down the median length of these leaves.

Write down the number of leaves with a length less than or equal to 8 cm.

Use the graph to find the value of $k$.

Before measuring, the researcher estimated $k$ to be approximately 9.5 cm. Find the percentage error in her estimate.

State what 13 represents in the given diagram.

Write down the interquartile range for this data.

Write down the approximate number of snacks whose amount of sugar ranges from 18 to 20 grams.

The health inspector visits two school cafeterias. She inspects the same number of meals at each cafeteria. The data is shown in the following box-and-whisker diagrams.

Meals prepared in the school cafeterias are required to have less than 10 grams of sugar.

State, giving a reason, which school cafeteria has more meals that do not meet the requirement.

Giving your answer to one decimal place, write down the value of

(i)     the median level of Vitamin C content of the oranges in the sample;

(ii)     the lower quartile;

(iii)     the upper quartile.

Draw a box-and-whisker diagram on the grid below to represent the Vitamin C content, in milligrams, for this sample.