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Data Handling and Representation

Data Handling and Representation — Free MYP3 Mathematics Practice Questions

1QuestionUsing Tally Charts for CountingConcept Practice

2 marks~3 minCriterion A

A tally chart shows the number of coloured pencils in a box.

Color	Red	Blue	Green
Tally	$IIII$	$IIII\ II$	$IIII\ I$

(a) Interpret the tally marks for blue pencils and calculate the total number of blue pencils in the box. [2]

Solutions

2QuestionConverting Frequency into Angles for Pie ChartsConcept Practice

2 marks~3 minCriterion A

A pie chart shows four sectors. Three sectors measure

90°

120°

, and

60°

. The fourth sector is unlabelled.

State the total number of degrees in a full circle. [1]

Calculate the angle of the missing sector. [1]

Solutions

3QuestionComparing Data Sets Using Dot PlotsConcept Practice

3 marks~5 minCriterion A

The dot plots below show the test scores (out of 20) for two classes.

Class A scores: 15, 16, 16, 17, 17, 17, 18, 18, 19, 20

Class B scores: 10, 11, 12, 14, 15, 16, 17, 18, 19, 20

Calculate the range of scores for Class A. [1]

Calculate the range of scores for Class B. [1]

Explain which class has more consistent scores. Use your results from parts (a) and (b) to support your answer. [1]

Solutions

4QuestionMatching Data Types to Appropriate ChartsConcept Practice

2 marks~3 minCriterion A

A class of students was asked to name their favourite ice cream flavour. The results are shown in the bar chart below.

Flavour	Vanilla	Chocolate	Strawberry
Number of students	8	12	5

Identify the type of data shown in the chart. [1]

Explain which flavour is the mode and why. [1]

Solutions

5QuestionChoosing Appropriate Data Collection MethodsConcept Practice

2 marks~3 minCriterion A

A student measures the height of a plant using a ruler marked in centimetres.

Identify whether the height of the plant is discrete data or continuous data. [1]

Describe one suitable method for collecting this type of data. [1]

Solutions

6QuestionChoosing Sample Size and Target GroupConcept Practice

2 marks~3 minCriterion B

A survey estimates the percentage of students who walk to school. The table below shows sample size and the corresponding margin of error.

Sample size ( $n$ )	10	20	50	100	200
Margin of error (\%)	32	22	14	10	7

Describe the relationship between sample size and margin of error. [1]

Estimate the margin of error for a sample size of 400 students. Justify your answer using the data in the table. [1]

Solutions

7QuestionChoosing Sample Size and Target GroupConcept Practice

2 marks~3 minCriterion A

A school survey is being planned. The number of students in each class is shown below.

Grade 6A: 25 students
Grade 6B: 28 students
Grade 7A: 30 students
Grade 7B: 27 students

The target group for the survey is all Grade 6 students.

Calculate the total number of students in the target group. [2]

Solutions

8QuestionUsing Tally Charts for CountingAssessment Practice

8 marks~12 minCriterion B

A tally chart records counts using groups of 5 marks (four vertical lines crossed by one diagonal). The table below shows data from one chart.

Total tally marks: 5, 10, 15, 20, 25

Complete groups	1	2	3	4	5
Leftover marks	0	0	0	0	0

Describe the relationship between the total number of tally marks and the number of complete groups shown in the table. [1]

A tally chart shows 4 complete groups and 3 leftover marks. Calculate the total number of tally marks and explain why your method works. [3]

A student claims: "If two tally charts both show a total of 37 tally marks, they must have the same number of complete groups and the same number of leftover marks." Analyse this claim and justify your answer using the rule

T = 5G + L

, where

0 \leq L < 5

. [4]

Solutions

9QuestionReading and Interpreting Frequency DataAssessment Practice

6 marks~9 minCriterion D

A student council surveys students about weekly homework hours. Classmates collect responses during lunch. The results are shown below.

Hours per week	0–2	3–5	6–8	9–11	12+
Frequency	15	40	25	10	5

Calculate the total number of students surveyed and the percentage of students in the 3–5 hour category. [2]

Explain why collecting data only during lunch may affect how well the results represent the whole school. [2]

Analyse whether the data supports the conclusion that most students spend 3–5 hours on homework per week. [2]

Solutions

10QuestionReading and Interpreting Frequency DataAssessment Practice

4 marks~6 minCriterion C

A school records the number of books read by each student in one month in the grouped frequency table below.

Number of books	0–2	3–5	6–8	9–11
Frequency	10	15	8	2

The school estimates the mean using the midpoint of each group: 1, 4, 7, 10.

Calculate the estimated mean number of books read per student. Show all working. [2]

Explain why grouping the data means the estimated mean may not reflect students' actual reading habits. [2]

Solutions

11QuestionPlotting and Analyzing Line GraphsAssessment Practice

10 marks~15 minCriterion B

A cyclist records the distance travelled each hour during a 5-hour ride.

Hour ( $h$ )	0	1	2	3	4	5
Distance ( $d$ , km)	0	8	18	30	44	60

Plot a line graph of distance against hour on a suitable grid. Label both axes clearly. [2]

Calculate the difference in distance between each pair of consecutive hours. Describe the pattern you see and use it to predict the distance at hour 6. [4]

Analyse the differences to explain why the relationship between

d

and

h

is quadratic, and write a formula for

d

in terms of

h

. Verify your formula for

h = 2

and

h = 4

. [4]

Solutions

12QuestionChoosing the Right Graph for the DataAssessment Practice

4 marks~6 minCriterion C

A school recorded the total money raised each month in a fundraiser from January to June.

Month	January	February	March	April	May	June
Amount raised (dollars)	1200	1500	1100	1800	1600	2000

Two students disagree about how to display this data for parents.
Student A says a line graph is best because it shows change over time.
Student B says a bar chart is better because the data is not continuous.

Explain why using a line graph could be misleading for this data. [2]

Explain one limitation of using a bar chart to display this data. [2]

Solutions

13QuestionConverting Frequency into Angles for Pie ChartsAssessment Practice

4 marks~6 minCriterion D

A student surveys 30 classmates about their favourite fruit. The bar chart shows the results.

Calculate the pie chart angle for each fruit. [2]

The student discovers that 5 classmates were each asked twice, so their responses were recorded twice. Explain how this double-counting affects the pie chart angles calculated in part (a). [2]

Solutions

14QuestionPlotting Dot Plots from Small Data SetsAssessment Practice

6 marks~9 minCriterion D

A school surveys 5 students about their daily screen time (in hours): 1, 1, 2, 4, 7.

A dot plot is created from this data. The school principal claims: "The average daily screen time for all students in the school is about 3 hours."

Calculate the mean screen time for the 5 students. [1]

Explain why this dot plot and data set may not be suitable for supporting the principal's claim about the whole school. [3]

Analyse how the value of 7 hours affects the mean, and explain what a different average could be used to better represent the data. [2]

Solutions

15QuestionCreating and Interpreting Stem-and-Leaf DiagramsAssessment Practice

6 marks~9 minCriterion B

The stem-and-leaf diagram shows test scores from a class.

Stem	Leaf
5	0 5
6	0 5
7	0 5 0 5 0
8	0 5 0 5

Key: 5 | 0 means 50

List all the scores shown in the diagram in order from smallest to largest. [1]

Describe the pattern you notice in the scores. [2]

Predict the next three scores that continue the pattern. Construct an updated stem-and-leaf diagram that includes your predicted scores and explain why the pattern is still consistent. [3]

Solutions

16QuestionComparing Data Sets Using Dot PlotsAssessment Practice

6 marks~9 minCriterion C

Two classes, Class X and Class Y, took the same mathematics test scored out of 10. The dot plots below show their results.

A student claims: "Class X performed better than Class Y because it has a higher median."

Calculate the median and range for each class. [2]

Compare the spread and clustering of scores in the two classes. Use your values from part (a) to support your comparison. [2]

Analyse whether the student's claim is correct. Use evidence from both the median and the range in your answer. [2]

Solutions

17QuestionAvoiding Misleading GraphsAssessment Practice

6 marks~9 minCriterion D

A news website publishes a bar chart titled "Teenage Social Media Use Surges!" showing the percentage of 13–17-year-olds who report using social media daily:

Year	2019	2020	2021	2022	2023
Percentage	52%	54%	53%	55%	57%

The y-axis starts at 50% instead of 0%.

Calculate the actual increase in percentage from 2019 to 2023. Describe how the truncated y-axis changes the appearance of this change. [2]

Explain how a policymaker who misreads this chart could make a poorly justified decision about school phone use. [2]

Analyse the bar chart to identify one way a reader could detect the misleading axis, and suggest one reason why the designer may have chosen to start the y-axis at 50%. [2]

Solutions

18QuestionAvoiding Misleading GraphsAssessment Practice

6 marks~9 minCriterion B

A company's January sales figures are:
Product A: 100 thousand dollars
Product B: 90 thousand dollars

A bar chart displays these values with the y-axis starting at 80.

Calculate the visual height ratio of Product A to Product B when the y-axis starts at 80. [1]

Calculate the actual value ratio of Product A to Product B. Explain why the two ratios differ and what this means for someone reading the chart. [3]

A second chart shows the same data with the y-axis starting at 50. Using the formula

E = \frac{v_1 - b}{v_2 - b} \cdot \frac{v_2}{v_1}

where

b

is the baseline,

v_1 = 100

and

v_2 = 90

, calculate the exaggeration factor

E

and compare it with the exaggeration factor when

b = 80

. Analyse what this tells you about how the choice of baseline affects the perceived difference between the two products. [2]

Solutions

19QuestionAvoiding Misleading GraphsAssessment Practice

5 marks~8 minCriterion C

A bar chart shows a company's monthly sales. The y-axis starts at 100 instead of 0. January sales = 100 units; February sales = 110 units. A manager claims: "Sales doubled from January to February."

Describe what "doubled" means in terms of percentage increase. [1]

Calculate the actual percentage increase in sales from January to February using:

\text{Percentage Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100

[2]

Analyse whether the manager's claim is valid. In your answer, refer to both your calculation and the effect of the y-axis starting at 100. [2]

Solutions

20QuestionChoosing Appropriate Data Collection MethodsAssessment Practice

8 marks~12 minCriterion B

A school surveys students from four age groups about their preferred data collection method. The response rates are shown below.

Age group	11–12	13–14	15–16	17–18
Online survey	45\%	55\%	70\%	80\%
In-person interview	60\%	65\%	55\%	45\%
Phone interview	30\%	40\%	50\%	60\%
Mail	20\%	25\%	30\%	35\%

Describe the trend in response rate for each of the four methods as age group increases. [2]

Explain which data collection method would be most effective for younger students (ages 11–12) and which would be most effective for older students (ages 17–18), using evidence from the data. [3]

A new survey targets 9–10 year old students. Analyse the data to decide which collection method is most likely to achieve the highest response rate for this age group, and justify your choice. [3]

Solutions

21QuestionComparing Discrete and Continuous GraphsAssessment Practice

2 marks~3 minCriterion C

A student records the number of text messages sent each day for one week and measures the outdoor temperature every hour throughout one day.

State the correct graph type for each dataset and explain why each choice is appropriate. [1]

Explain one consequence of displaying the temperature data as a bar chart instead of a line graph. [1]

Solutions

22QuestionChoosing Appropriate Data Collection MethodsAssessment Practice

6 marks~9 minCriterion D

A school wants to find the most popular lunch option among its 800 students. The student council surveys only the 150 students eating in the cafeteria at 12:30 PM.

Describe the type of bias introduced by this survey method. [1]

Explain how this bias could lead to a poor school decision about lunch provision. [2]

Analyse how surveying at a different time or location might change the results, and suggest one improvement to make the survey more representative of all 800 students. [3]

Solutions

23QuestionCreating Effective Survey QuestionsAssessment Practice

5 marks~8 minCriterion C

A student surveyed two separate groups of 50 students about homework.

Group A: "How many hours per week do you spend on homework?"

Response options	0–2 hours	3–5 hours	6–8 hours	9+ hours
Results	10	20	12	8 students

Group B: "Do you agree that homework is essential for learning?"

Response options	Strongly agree	Agree	Disagree	Strongly disagree
Results	25	15	7	3 students

The bar charts below display these results.

Describe one feature of Question B's wording that could influence how students respond. [1]

Explain how the response options in Question B could contribute to response bias. [2]

Justify which survey question is biased by comparing specific values from both bar charts. [2]

Solutions

24QuestionAvoiding Bias in Data CollectionAssessment Practice

2 marks~3 minCriterion D

A school surveys student opinions on cafeteria food by interviewing only students present in the cafeteria at lunchtime.

Explain how surveying only lunchtime cafeteria visitors creates selection bias. [1]

Propose one alternative sampling method and explain how it would produce a more representative sample of the whole student population. [1]

Solutions