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.

Find the probability that it will take Fiona between $15$ minutes and $30$ minutes to walk to the bus stop.

Find $\sigma$.

Find the probability that the bus journey takes less than $45$ minutes.

Find the probability that Fiona will arrive on time.

This year, Fiona will go to school on $183$ days.

Calculate the number of days Fiona is expected to arrive on time.

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 height of Flower null.

Using this information, write down an equation in $p$ and $q$.

Write down a second equation in $p$ and $q$.

Using your answers to parts (b) and (c), find the height of Flower $\text{A}$.

Using your answers to parts (b) and (c), find the height of Flower $\text{D}$.

A data set consisting of $16$ test scores has mean $14.5$ . One test score of $9$ requires a second marking and is removed from the data set.

Find the mean of the remaining $15$ test scores.

Find the value of $x$.

Find the standard deviation.

One of the adults surveyed is $42$ years old. Estimate the age of their eldest child.

Find the mean age of all the adults surveyed.

Find the value of p.

Find μ, the expected value of X.

Find P(X > μ).

Find the mean.

Find the standard deviation.

the mean.

the standard deviation.

A ninth student also takes the test.

Explain why the median is unchanged.

Find the value of the interquartile range.

One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.

Write down the mode.

Find the value of the range.

Find the mean.

Find the variance.

For these data, find the mean distance from a student’s home to school.

Find the value of $p$.

Find the interquartile range.

The range of the data is 16. Find the value of $a$.

Find the value of the interquartile range.

Find the mean number of hours that the girls in this group spent watching television that week.

Find the total number of hours the group of boys spent watching television that week.

Find the mean number of hours that all 30 girls and boys spent watching television that week.

the mean number of hours that the group of boys spent watching television.

Find n.

Write down the value of the new mean.

Find the value of the new variance.

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 $k$.

Find the mean number of hours spent browsing the Internet.

During week 2, the students worked on a major project and they each spent an additional five hours browsing the Internet. For week 2, write down

(i)     the mean;

(ii)     the standard deviation.

During week 3 each student spent 5% less time browsing the Internet than during week 1. For week 3, find

(i)     the median;

(ii)     the variance.

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 value of x.

Find the standard deviation

Find the interquartile range.

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.

On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the $x$-axis and 2 cm to represent 10 points on the $y$-axis.

(i)     $\overline{x}$, the mean number of hours spent on social media;

(ii)     $\overline{y}$, the mean number of IB Diploma points.

Plot the point $(\overline{x},\overline{y})$ on your scatter diagram and label this point M.

Write down the value of $r$, the Pearson’s product–moment correlation coefficient, for these data.

Write down the equation of the regression line $y$ on $x$ for these eight male students.

Draw the regression line, from part (e), on your scatter diagram.

Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.

Write down a reason why this estimate is not reliable.

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.

Calculate the mean test grade of the students;

Calculate the standard deviation.

Find the median test grade of the students.

Find the interquartile range.

Find the probability that this student scored a grade 5 or higher.

Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.

Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.

Calculate the expected number of students that spent at least 90 minutes preparing for the test.

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.

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.

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.

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 total number of people, from this group, who are pet owners.

Write down the modal number of pets.

For these data, write down the median number of pets.

For these data, write down the lower quartile.

For these data, write down the upper quartile.

Write down the ratio of teenagers to non-teenagers in its simplest form.

State the null hypothesis.

State the alternative hypothesis.

Write down the number of degrees of freedom for this test.

Calculate the expected number of teenagers that prefer cats.

Use your graphic display calculator to find the $p$-value for this test.

State the conclusion for this test. Give a reason for your answer.

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.

Find the price that is two standard deviations above the mean price.

Find the probability that the price of a kilogram of tomatoes, chosen at random, will be between 2.00 and 3.00 euro.

To stimulate reasonable pricing, the city offers a free permit to the sellers whose price of a kilogram of tomatoes is in the lowest 20 %.

Find the highest price that a seller can charge and still receive a free permit.

Write down the modal length of the rods.

Find the median length of the rods.

Calculate the lower quartile.

Calculate the interquartile range.

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.

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.

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.

One of the players is chosen at random. Find the probability that this player’s score was 5 or more.

Calculate the mean score.