Statistics – Averages and Analysis — Free IB MYP1 Mathematics Questions

1QuestionCalculating Midpoints for IntervalsConcept Practice

4 marks~6 minCriterion B

A community event records the ages of 75 visitors in a grouped frequency table.

Age interval (years)	0–4	5–9	10–14
Frequency	12	18	22

a

State the midpoint formula used to find the middle value of an age interval. [1]

b

Calculate the midpoint of the age interval 5–9. [1]

c

The interval 0–4 has a midpoint of 2 and the interval 10–14 has a midpoint of 12. Describe what you notice about how the midpoints change across the three intervals. [2]

Solutions

2QuestionGrouping Data into Class IntervalsConcept Practice

2 marks~3 minCriterion C

A school librarian tracks the number of books borrowed by students each week, with recorded values such as 3, 4, 7, 12, 15, and 18.

1

Explain one reason why the librarian might choose to group this data into class intervals, such as 0-4, 5-9, 10-14, and 15-19.

2

Discuss one limitation of using this method to group the data.

Solutions

3QuestionFinding the Modal ClassConcept Practice

2 marks~3 minCriterion D

A shop owner records how many customers visit each hour. The modal class is 30–39 customers per hour.

a

Identify one way the shop owner could use this information to plan their day. [1]

b

Describe one reason why grouped data does not show the exact busiest hour. [1]

Solutions

4QuestionEstimating Mean from Grouped DataConcept Practice

2 marks~3 minCriterion A

A gardener measures the heights of 20 plants. The results are shown below.

Height (cm)	0–5	5–10	10–15	15–20
Frequency	2	8	6	4

Calculate the midpoint of the class interval 10–15 cm. [2]

Solutions

5QuestionCreating Balanced Data SetsConcept Practice

2 marks~3 minCriterion B

Each data set below has three numbers. In every set, the mean equals the middle number.

Set A:

2, \ 4, \ ?

Set B:

5, \ 7, \ ?

Set C:

1, \ 9, \ ?

a

Calculate the missing number in one of the sets above. [1]

b

Describe the rule that connects the missing number to the other two numbers in the set. [1]

Solutions

6QuestionWord Problems Involving Unknowns in Data SetsConcept Practice

2 marks~3 minCriterion C

The mean of the four numbers 4, 7,

x

, and 10 is 7.

a

Write an equation using algebra to show this. [1]

b

In one sentence, describe what each part of your equation means. [1]

Solutions

7QuestionUsing the Mean to Find a Missing ValueConcept Practice

2 marks~3 minCriterion A

Three rectangles have a mean perimeter of 24 cm. Two of the rectangles have perimeters of 20 cm and 26 cm. The third rectangle has a width of 5 cm.

a

Calculate the perimeter of the third rectangle. [1]

b

Calculate the length of the third rectangle. [1]

Solutions

8QuestionSolving Problems with Given Total and FrequencyConcept Practice

2 marks~3 minCriterion D

A teacher recorded how many students came to class each day for 5 days. The total number of students present across all 5 days was 120. On one of those days, almost everyone was on a field trip and only 10 students were in class.

a

Identify one reason why a school might want to know the mean daily attendance. [1]

b

Describe how the field trip day affects the mean, and why this makes the mean less useful for planning. [1]

Solutions

9QuestionCalculating and Interpreting the Interquartile RangeConcept Practice

2 marks~3 minCriterion B

Here are two sets of numbers:

Set A	2	4	6	8	10
Set B	2	4	6	8	16

a

Calculate the interquartile range (IQR) for Set B. [1]

b

Describe what happens to the IQR when the largest value increases. [1]

Solutions

10QuestionDrawing Box Plots from Data SetsConcept Practice

2 marks~3 minCriterion A

The box plot below shows the test scores of a class.

Identify the median score shown on the box plot. [1]

Describe what the median tells you about the class's test scores. [1]

Solutions

11QuestionComparing Data Sets Using Box PlotsConcept Practice

2 marks~3 minCriterion C

Two Year 7 classes took the same test. Their results are shown in the box plots below.

Class A	minimum 40	$Q_1$ = 55	median = 65	$Q_3$ = 75	maximum 95
Class B	minimum 50	$Q_1$ = 60	median = 70	$Q_3$ = 80	maximum 90

a

Identify one way a teacher could use these box plots to compare the two classes. [1]

b

Describe one thing the box plots do not tell the teacher about the students' scores. [1]

Solutions

12QuestionComparing Data Sets Using Box PlotsConcept Practice

2 marks~3 minCriterion A

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

Class A	minimum 40	lower quartile 55	median 65	upper quartile 75	maximum 90
Class B	minimum 35	lower quartile 50	median 60	upper quartile 70	maximum 85

a

State the median score for each class. [1]

b

Identify which class has the higher median score and give its value. [1]

Solutions

13QuestionIdentifying the Median ValueConcept Practice

3 marks~5 minCriterion C

A weather station recorded the highest temperature each day for five days:

22°C

,

18°C

,

25°C

,

20°C

, and

23°C

.

a

List the five temperatures in order from smallest to largest. [1]

b

Identify the median temperature. [1]

c

The weather station says: "Most of our recorded temperatures were above the median." State whether this is correct and describe what you notice about how the temperatures are spread around the median. [1]

Solutions

14QuestionCalculating the Range and Interpreting ItConcept Practice

2 marks~3 minCriterion B

Five friends recorded how many books they read last month: 3, 7, 10, 12, 15.

a

Calculate the range of this data set. [1]

b

Each friend reads 4 more books the following month, giving the new data set: 7, 11, 14, 16, 19. Describe what happens to the range. [1]

Solutions

15QuestionCalculating the Range and Interpreting ItConcept Practice

2 marks~3 minCriterion A

Five bars are shown in the diagram, with the following lengths:

Bar A: 3 cm Bar B: 7 cm Bar C: 5 cm Bar D: 9 cm Bar E: 4 cm

a

Identify the longest and shortest bars. [1]

b

Calculate the range of the bar lengths. [1]

Solutions

16QuestionDetermining the Mode in a Data SetConcept Practice

2 marks~3 minCriterion D

A shoe shop owner records the sizes of all shoes sold in one week.

a

Identify what the mode of the shoe sizes tells the shop owner. [1]

b

Describe one piece of information the mode does not tell the shop owner. [1]

Solutions

17QuestionAnalyzing Real-Life Data with AveragesConcept Practice

2 marks~3 minCriterion B

The mean ages of students in four classes are shown below.

Class A:

11.5

years
Class B:

12.5

years
Class C:

13.5

years
Class D:

14.5

years

a

Identify the pattern in the mean ages. [1]

b

Using your answer to part (a), state the mean age you would expect for Class E. [1]

Solutions

18QuestionAnalyzing Real-Life Data with AveragesConcept Practice

3 marks~5 minCriterion C

A class voted for their favourite pet. The bar chart shows the results.

Cats: 8 students
Dogs: 12 students
Fish: 5 students
Hamsters: 3 students

a

Name the most popular pet. [1]

b

Identify which measure — mode, median, or mean — tells you which pet was chosen most often. [1]

c

Describe why the other two measures are not useful for finding the most popular pet. [1]

Solutions

19QuestionComparing Mean Median and Mode in ContextConcept Practice

2 marks~3 minCriterion A

A class voted for their favourite fruit. The bar chart shows how many students chose each fruit.

Apple: 5, Banana: 3, Orange: 2, Grape: 4

a

Name the mode of this data set. [1]

b

Describe how the bar chart shows which fruit is the mode. [1]

Solutions

20QuestionChoosing the Most Appropriate AverageConcept Practice

3 marks~5 minCriterion D

Five students recorded how many books they read in one month.

Student A: 2 — Student B: 2 — Student C: 2 — Student D: 5 — Student E: 9

a

Identify the mode. [1]

b

Calculate the mean. [1]

c

Describe why the mode is a better average than the mean for this data. [1]

Solutions

Statistics – Averages and Analysis — Free MYP1 Mathematics Practice Questions