Statistics – Averages and Analysis — Free IB MYP2 Mathematics Questions

1QuestionCalculating Midpoints for IntervalsConcept Practice

2 marks~3 minCriterion B

A grouped frequency table shows the masses of several parcels.

Mass (kg)	0–10	10–20	20–30	30–40
Midpoint (kg)	5	15	?	?

a

Calculate the midpoints for the intervals 20–30 kg and 30–40 kg. [1]

Midpoint for 20–30 kg: ___
Midpoint for 30–40 kg: ___

b

Describe the pattern in the midpoint values across all four intervals. [1]

Solutions

2QuestionFinding the Modal ClassConcept Practice

2 marks~3 minCriterion A

The bar chart below shows the number of students in each height interval.

Height interval (cm)	$140$ – $150$	$150$ – $160$	$160$ – $170$	$170$ – $180$
Number of students	$5$	$12$	$8$	$3$

a

Identify the modal class — the height interval with the greatest number of students. [1]

b

Explain how you know this interval is the modal class. [1]

Solutions

3QuestionSolving Problems with Given Total and FrequencyConcept Practice

2 marks~3 minCriterion A

Four rectangles have the following side lengths:

Rectangle A:

5

cm and

3

cm
Rectangle B:

7

cm and

2

cm
Rectangle C:

4

cm and

6

cm
Rectangle D:

x

cm and

5

cm

The mean of all eight side lengths is

4.5

cm.

a

State the total sum of all eight side lengths. [1]

b

Calculate the value of

x

. [1]

Solutions

4QuestionCalculating and Interpreting the Interquartile RangeConcept Practice

3 marks~5 minCriterion A

The box plots below show the test scores of Class A and Class B.

Class A	$Q_1 = 55$	$Q_3 = 75$
Class B	$Q_1 = 60$	$Q_3 = 80$

The interquartile range (IQR) measures the spread of the middle 50% of scores:

IQR = Q_3 - Q_1

a

State the

Q_1

and

Q_3

values for Class B. [1]

b

Calculate the IQR for each class. [1]

c

Compare the consistency of the two classes. Refer to your IQR values in your answer. [1]

Solutions

5QuestionComparing Data Sets Using Box PlotsConcept Practice

2 marks~3 minCriterion B

Three box plots show test scores for Class A, Class B, and Class C. All three classes have a median of

75

.

Class A:

\text{IQR} = 10

— Class B:

\text{IQR} = 20

— Class C:

\text{IQR} = 30

a

Identify which class has the most spread in the middle 50% of scores. [1]

b

Describe the relationship between the IQR and how clustered the middle 50% of scores are, using all three classes as evidence. [1]

Solutions

6QuestionCalculating the Range and Interpreting ItConcept Practice

2 marks~3 minCriterion B

Three data sets follow a pattern:

Set A:

2, 5

Set B:

2, 5, 8

Set C:

2, 5, 8, 11

a

Calculate the range of each data set. [1]

b

Describe the pattern in the ranges as each new term is added, and predict the range of Set D:

2, 5, 8, 11, 14

. [1]

Solutions

7QuestionCalculating the Range and Interpreting ItConcept Practice

2 marks~3 minCriterion A

Five line segments have the following lengths in centimetres:

Lengths (cm): 2, 3, 5, 7, 9

a

Calculate the range of these lengths. [1]

b

Explain what the range tells you about the variation in the lengths of these line segments. [1]

Solutions

8QuestionFinding the Mean of a Data SetConcept Practice

4 marks~6 minCriterion C

A teacher records the number of books read by 5 students in one month:

4, \quad 5, \quad 6, \quad 7, \quad 28

a

Calculate the mean number of books read. [2]

b

The value 28 is an outlier (a value much larger or smaller than the rest). Explain whether the mean is a good representation of the typical number of books read, and identify one alternative measure that would better represent the group. [2]

Solutions

9QuestionAnalyzing Real-Life Data with AveragesConcept Practice

2 marks~3 minCriterion A

The ages (in years) of seven students in a sports club are listed below.

Age (years): 8, 10, 9, 11, 12, 10, 9

a

Identify the median age of the students. [1]

b

Explain how you found the median, showing your ordered list. [1]

Solutions

10QuestionFinding the Modal ClassAssessment Practice

5 marks~8 minCriterion C

A school librarian records the number of books borrowed per student in one month.

Books borrowed	0–4	5–9	10–14	15–19	20 or more
Number of students	15	22	18	8	5

The mean number of books borrowed is 9.6.

a

Identify the modal class. [1]

b

Explain whether the modal class is a good measure of typical borrowing for this group. Use the mean in your answer. [2]

c

Describe one limitation of using only the modal class to summarise the borrowing data. [2]

Solutions

11QuestionGrouping Data into Class IntervalsAssessment Practice

6 marks~9 minCriterion D

A fitness centre records how long 20 members spend on a treadmill. Each time is rounded to the nearest 5 minutes. The recorded times (in minutes) are:

10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 25, 25, 30, 30, 30, 30, 35, 35, 40, 45

a

Complete a frequency table using class intervals of width 10 minutes: 10–19, 20–29, 30–39, 40–49. State the frequency for each interval. [2]

b

Calculate the mean time using the midpoint of each class interval. Show your working. [2]

c

The times were rounded before grouping. Explain how this affects the accuracy of the mean you calculated, and identify one way this grouped data could mislead the fitness centre's planning. [2]

Solutions

12QuestionCreating Balanced Data SetsAssessment Practice

4 marks~6 minCriterion B

Each set of five numbers has one missing value. The mean (average) of a data set is the sum of all values divided by how many there are.

Set A: $3, 7, 5, 9, ?$	Mean $= 6$
Set B: $12, 8, 15, 10, ?$	Mean $= 11$
Set C: $20, 25, 15, 30, ?$	Mean $= 22$
Set D: $4, 9, 6, 11, ?$	Mean $= 7$

a

Calculate the missing value for each set. Show your working. [1]

b

Describe the relationship between the sum of the known values and the missing value. State a general rule for finding the missing value when the mean and total count are given. [2]

c

A set of five numbers has a known sum of 40 and a target mean of 10. Use your rule to find the missing value, then verify your answer by checking the mean. [1]

Solutions

13QuestionCreating Balanced Data SetsAssessment Practice

4 marks~6 minCriterion C

A sports coach records fitness scores for 8 players: 2, 5, 8, 9, 11, 14,

x

, and

y

. The coach wants the mean score to be exactly 8.

a

Calculate one possible pair of whole-number values for

x

and

y

, where each value is between 1 and 20. [2]

b

The coach claims the team is "balanced" because the mean is 8. Explain whether this claim is valid, referring to the spread of scores. [2]

Solutions

14QuestionCreating Balanced Data SetsAssessment Practice

6 marks~9 minCriterion D

A school uses the mean of five test scores to decide if a student qualifies for a gifted programme. A student scored 78, 85, 92, and 90 on the first four tests.

a

Calculate the score the student needs on the fifth test to achieve a mean of exactly 88. [2]

b

Explain one reason why using only the mean may be unfair for this decision. [2]

c

Suggest one change to the school's method and explain how it makes the decision fairer. [2]

Solutions

15QuestionCalculating and Interpreting the Interquartile RangeAssessment Practice

6 marks~9 minCriterion D

A school records the weekly homework time (in minutes) for 7 students:

45, \quad 50, \quad 55, \quad 60, \quad 65, \quad 70, \quad 200

a

Calculate the range and the interquartile range (IQR) for this data set. [2]

b

Identify which value is an outlier (a value far outside the rest of the data) and explain how it affects the range. [2]

c

Compare the range and the IQR as measures of spread. State which better represents the typical homework time for most students, and why. [2]

Solutions

16QuestionFinding the Five-Number SummaryAssessment Practice

5 marks~8 minCriterion C

A student records the ages (in years) of six participants at a community sports event:

8, \quad 9, \quad 10, \quad 11, \quad 12, \quad 45

a

State the five-number summary (minimum,

Q_1

, median,

Q_3

, maximum) for this data set. [2]

b

Calculate the interquartile range (IQR), where

\text{IQR} = Q_3 - Q_1

. [1]

c

Compare how well the median and IQR represent the typical age of participants, and identify one limitation of the five-number summary for this data set. [2]

Solutions

17QuestionDetermining the Mode in a Data SetAssessment Practice

4 marks~6 minCriterion D

A shop owner records the number of customers per day over two weeks:

3, \ 5, \ 5, \ 5, \ 7, \ 8, \ 12, \ 15, \ 15, \ 15, \ 15, \ 15, \ 42, \ 45

a

State the mode of this data set. [1]

b

Identify two values in the data set that are outliers (values far outside the typical range) and explain why they make the mode less reliable. [2]

c

Compare the mode with one other measure of central tendency to explain whether the owner should use the mode alone to plan staffing. [1]

Solutions

18QuestionAnalyzing Real-Life Data with AveragesAssessment Practice

8 marks~12 minCriterion B

A city records daily temperatures (°C) during January.

Week 1 (4 days): 12, 15, 13, 14
Week 2 (8 days): 12, 15, 13, 14, 11, 16, 12, 15
Week 3 (12 days): 12, 15, 13, 14, 11, 16, 12, 15, 10, 17, 13, 14

a

Calculate the mean temperature for each week. [3]

b

The pattern in the weekly means suggests a value for the monthly mean. State what that value is and explain what the pattern shows. [2]

c

All 24 recorded values are listed below.

12, 15, 13, 14, 11, 16, 12, 15, 10, 17, 13, 14, 12, 15, 13, 14, 11, 16, 12, 15, 10, 17, 13, 14

Calculate the mean of these 24 values. Compare this result with your answer from part (b) and explain how a larger sample size affects the reliability of a mean. [3]

Solutions

19QuestionComparing Mean Median and Mode in ContextAssessment Practice

5 marks~8 minCriterion D

The number of books read by 15 students in one month is shown below.

Student 1: 3	Student 2: 4	Student 3: 5	Student 4: 4	Student 5: 6
Student 6: 4	Student 7: 5	Student 8: 3	Student 9: 4	Student 10: 5
Student 11: 4	Student 12: 12	Student 13: 4	Student 14: 5	Student 15: 3

a

Identify the mode of the data. [1]

b

Calculate the mean number of books read. Show your working. [2]

c

The value 12 is an outlier — a value much higher than the rest. Compare the mean and the median, and explain which better represents the typical number of books read. [2]

Solutions

20QuestionComparing Mean Median and Mode in ContextAssessment Practice

8 marks~12 minCriterion C

A bakery records croissant sales (number sold) over 10 days:

12, 15, 18, 20, 22, 25, 28, 30, 35, 120

The owner wants to report a "typical daily sale" to a bank.

a

Calculate the mean and median of the daily sales. [4]

b

Explain which average better represents a typical day. [2]

c

Compare what is gained and lost by choosing the median over the mean in this context. [2]

Solutions

Statistics – Averages and Analysis — Free MYP2 Mathematics Practice Questions