Statistics Toolkit (DP IB Applications & Interpretation (AI): SL): Exam Questions

The following cumulative frequency curve shows the distances, in kilometres, travelled to work by 160 people in Cape Town, South Africa, during 2021.

Use the cumulative frequency curve to estimate

(i) the median distance;

(ii) the lower quartile;

(iii) the upper quartile.

Draw a box and whisker diagram to represent these data.

An outlier is a value that is less than $Q_1-1.5\times \text{IQR}$ or greater than $Q_3+1.5\times \text{IQR}$.

Find the largest distance travelled to work that would not be considered an outlier.

The following cumulative frequency curve shows the number of hours spent gaming per week by 120 high school students.

Find the

(i) median

(ii) interquartile range.

Find the percentage of the students who spent less than 17 hours gaming per week.

The 120 students were chosen at random by sampling 60 senior students and 60 junior students. The school has the same number of senior students as junior students.

State the sampling method used.

The histogram below shows the weights of kiwifruit, each measured to the nearest gram.

Write down the modal weight of the kiwifruits.

Find the median weight of the kiwifruits.

An outlier is a value that is less than $Q_1-1.5\times \text{IQR}$ or greater than $Q_3+1.5\times \text{IQR}$.

Find the weights, $w$ grams, of kiwifruit that would be considered outliers.

A group of people who use a gym took part in a survey, and the ages of the participants were recorded in the following table.

It is known that $34<x<40$.

Write down the mid-interval value of the class $18\le a<30$.

Determine the class in which the lower quartile lies.

Use the mid-interval values to find an estimate of the mean age of the participants aged 30 or over.

The participants in this survey were chosen by selecting every person who entered the gym who was not wearing headphones.

State the sampling method used.

The table below shows the number of deliveries made by each of a group of food delivery drivers on one working day in Berlin.

Find

(i) the mean number of deliveries;

(ii) the standard deviation;

(iii) the median;

(iv) the interquartile range.

An outlier is a value that is less than $Q_1-1.5\times \text{IQR}$ or greater than $Q_3+1.5\times \text{IQR}$.

Determine whether a driver who made 4 deliveries is an outlier.

The delivery drivers were selected for the survey by listing their names alphabetically and then selecting every 20th name.

State the sampling method used.

The following table shows the number of passes made by each of the 11 players in a rugby team during a match.

Find

(i) the mean;

(ii) the median;

(iii) the mode.

Find the interquartile range.

An outlier is a value that is less than $Q_1-1.5\times \text{IQR}$ or greater than $Q_3+1.5\times \text{IQR}$.

Show that none of the players' numbers of passes is an outlier.

The table below shows the number of TVs in the homes of a group of school students.

Find

(i) the mean;

(ii) the standard deviation;

(iii) the median;

(iv) the interquartile range.

An outlier is a value that is less than $Q_1-1.5\times \text{IQR}$ or greater than $Q_3+1.5\times \text{IQR}$.

Show that a student who has seven TVs would be considered an outlier.

The students were selected for the survey by using a random number generator to choose student ID numbers.

State the sampling method used.

The number of days off taken by employees in a company during a two-year period was recorded. The data was organised into a box and whisker diagram as shown below:

For this data, write down

(i) the maximum number of days off by an employee during the two years.

(ii) the median.

(iii) the interquartile range.

Steven claims that this box and whisker diagram can be used to infer that the percentage of employees who took between 13 and 30 days off is greater than the percentage of employees who took 25 days or more off.

State whether Steven is correct. Justify your answer.

A medium rare steak should have an internal temperature of $55°\mathrm{C}$ to $56°\mathrm{C}$. Max visits 10 different steak houses. At each one he measures the internal temperature of a medium rare steak, and records the following temperatures, in ${}^{\circ }\mathrm{C}$.

51.0, 52.1, 62.9, 49.0, 59.8, 50.2, 54.3, 47.7, 48.6, 65.4

Find the mean internal temperature of Max's recordings.

Max visits 5 more steak houses. He calculates the mean internal temperature of the steaks from all 15 steak houses to be $55.2°\mathrm{C}$.

Calculate the mean internal temperature of the steaks from the 5 additional steak houses.

Max records one final steak, which has an internal temperature of $T°\mathrm{C}$.

Find the range of values of $T$ for which the mean internal temperature of all 16 steaks is within the range for a medium rare steak.

The following table shows the percentage change in the value of an investor's portfolio in each of 12 months.

Find

(i) the mean;

(ii) the standard deviation.

State which statistical measure, calculated in part (a), gives an indication of the volatility of the investor’s portfolio.

The value of the investor's portfolio at the beginning of the 12 months was 6000 dollars.

Find the value of the portfolio at the end of the 12 months. Give your answer correct to two decimal places.

A data set has a mean of 22 and a standard deviation of 6.

Each element of the data set has 4 subtracted from it.

Find the value of

(i) the new mean

(ii) the new standard deviation.

After each element has 4 subtracted from it, each element is divided by  $\frac{2}{3}$ .

Find the value of

(i) the new mean

(ii) the new variance.

At a swimming competition, the mean time of the first four swimmers, in order of finish, is 28.2 seconds. The times of the fifth and sixth swimmers are then recorded, and the mean time of the first six swimmers is 29.8 seconds. The difference between the fifth and sixth swimmers' times is 0.4 seconds.

Find the time achieved by

(i) the fifth swimmer;

(ii) the sixth swimmer.

The first swimmer's time is 25.7 seconds.

Find the range of the six times.

A group of Netflix subscribers took part in a survey, and the ages of the participants were recorded in the following table.

It is known that $56<x<62$.

Write down

(i) the modal class;

(ii) the mid-interval value of the modal class.

Determine the class in which the upper quartile lies.

Using the mid-interval values the mean of the data can be estimated to be 39.95.

Find the value of $x$.

The participants in this survey were chosen by randomly selecting people entering a supermarket. However, to be more efficient, the surveyor only selected people who were in groups of at least 3.

State the sampling method used.

The following box and whisker diagram shows the number of social media posts made by a group of content creators over a week.

State whether the data is discrete or continuous.

It is given that $7a=4b$ and $a+b=22$.

Calculate the value of

(i) $a$

(ii) $b$

An outlier is a value that is less than $Q_1-1.5\times \text{IQR}$ or greater than $Q_3+1.5\times \text{IQR}$.

A content creator made $k$ posts, where $k<a$. The number of posts, $k$, is an outlier.

Find the largest possible value of $k$.

The table below shows the average temperature, $T°C$, in a city over a normal year (not a leap year).

It is given that $p=11q$.

Calculate the values of

(i) $p$

(ii) $q$

Using your GDC, estimate the value of

(i) the mean

(ii) the standard deviation.

It Is given that the mean temperature of the city over the year is $14.2°\mathrm{C}$.

Calculate the percentage error between your estimate of the mean temperature, found in part (b) (i), and the actual mean temperature.