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Edexcel IGCSE Math A Higher 6.2 Statistical Measures Questions

Use this statistical-measures page to calculate averages, estimate grouped means and read median or IQR values from cumulative frequency graphs.

Syllabus
First assessment 2018
Course
Math A 4MA1
Level
Higher

Exam points

  • Calculate mean, median, mode and range from lists, tables or contextual totals.
  • Estimate grouped means and identify modal classes from frequency tables.
  • Use cumulative frequency diagrams to estimate medians and interquartile ranges.

Covered syllabus points

6.2.A The concept of average6.2.B The mean, median, mode and range for a discrete data6.2.C Estimating the mean from grouped data6.2.D The modal class for grouped data6.2.HA The median from a cumulative frequency diagram6.2.HB Measures of spread6.2.HC Interquartile range from discrete data6.2.HD The interquartile range from a cumulative frequency

Question 1

[Maximum number: 4]

Here are the numbers of aces that Rutger served in each of 11 tennis matches.

1, 1, 2, 4, 6, 8, 8, 9, 11, 12, 15

Question (a)

(a)

Find the interquartile range of the numbers of aces.

Show your working clearly.

[ 2 ]

Question (b)

(b)

Kim also plays in 11 tennis matches.
For Kim, the median number of aces is 11 and the interquartile range of the numbers of aces is 5.

State, giving a reason, whether Rutger or Kim

[ 2 ]

Question (i)

(i)

served more aces on average,

[ 1 ]

Question (ii)

(ii)

was more consistent with the number of aces served.

[ 1 ]

Question 2

[Maximum number: 5]

The table shows information about the weights, in kilograms, of 40 babies.

Table for Question 2 — Edexcel IGCSE Math A Higher

Question (a)

(a)

Write down the modal class.

[ 1 ]

Question (b)

(b)

Work out an estimate for the mean weight of the 40 babies. kg

One of the 40 babies is going to be chosen at random.

[ 4 ]

Question 3

[Maximum number: 4]

A group of 60 students each sat an algebra test and a geometry test.
Each test was marked out of 110
The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.

Cumulative frequency

Figure for Question 3 — Edexcel IGCSE Math A Higher

Question (a)

(a)

Use the graph to find an estimate for the median mark in the algebra test.

[ 1 ]

Question (b)

(b)

Use the graph to find an estimate for the interquartile range of the marks gained in the algebra test.

[ 2 ]

Question (c)

(c)

The interquartile range of the marks gained in the geometry test is 9
Luis says
"The students' marks are more spread out in the algebra test than in the geometry test."
(d) Is Luis correct?

Give a reason for your answer.

[ 1 ]

Question 4

[Maximum number: 1]

Here are the numbers of aces that Rutger served in each of 11 tennis matches.

1, 1, 2, 4, 6, 8, 8, 9, 11, 12, 15

Kim also plays in 11 tennis matches.
For Kim, the median number of aces is 11 and the interquartile range of the numbers of aces is 5.

State, giving a reason, whether Rutger or Kim

served more aces on average,

Question 5

[Maximum number: 4]

The table shows information about the weights, in kilograms, of 40 babies.

Table for Question 5 — Edexcel IGCSE Math A Higher

Work out an estimate for the mean weight of the 40 babies. kg

One of the 40 babies is going to be chosen at random.

Question 6

[Maximum number: 1]

The table shows information about the weights, in kilograms, of 40 babies.

Table for Question 6 — Edexcel IGCSE Math A Higher

Write down the modal class.

Question 7

[Maximum number: 1]

A group of 60 students each sat an algebra test and a geometry test.
Each test was marked out of 110
The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.

Cumulative frequency

Figure for Question 7 — Edexcel IGCSE Math A Higher

Use the graph to find an estimate for the median mark in the algebra test.

Question 8

[Maximum number: 1]

A group of 60 students each sat an algebra test and a geometry test.
Each test was marked out of 110
The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.

Cumulative frequency

Figure for Question 8 — Edexcel IGCSE Math A Higher

The interquartile range of the marks gained in the geometry test is 9
Luis says
"The students' marks are more spread out in the algebra test than in the geometry test."
(d) Is Luis correct?

Give a reason for your answer.

Question 9

[Maximum number: 2]

Here are the numbers of aces that Rutger served in each of 11 tennis matches.

1, 1, 2, 4, 6, 8, 8, 9, 11, 12, 15

Find the interquartile range of the numbers of aces.

Show your working clearly.

Question 10

[Maximum number: 2]

A group of 60 students each sat an algebra test and a geometry test.
Each test was marked out of 110
The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.

Cumulative frequency

Figure for Question 10 — Edexcel IGCSE Math A Higher

Use the graph to find an estimate for the interquartile range of the marks gained in the algebra test.

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