Finding Missing Data with Given Averages

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Finding Missing Data with Given Averages — Free MYP2 Mathematics Practice Questions

1QuestionSolving 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.

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

Calculate the value of

x

. [1]

Solutions

2QuestionCreating 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.

Calculate one possible pair of whole-number values for

x

and

y

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

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

3QuestionCreating 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.

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

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

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

Solutions

4QuestionCreating 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 $= 7$

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

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]

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

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