1Vikram Recorded the Number of Absences for Each Student in Form 9M During Last Year

Cambridge Essentials MathematicsExtension 9S2.1Homework

/ S2.1 Homework

1Vikram recorded the number of absences for each student in Form 9M during last year.

The table shows his results.

Number of absences / Frequency
0–4
5–9
10–14
15–19
20–24
25–29 / 14
7
5
2
3
1

aHow many students were in Form 9M?

bCalculate an estimate of the mean numbers of absences.

cWhich class interval does the median lie in?

dWhat is the modal class interval?

2Members of a youth club walked a sponsored mile.

The results in the table shows the time taken by each member.

Time t inminutes / Frequency
12 ≤ t < 16
16 ≤ t < 20
20 ≤ t < 24
24 ≤ t < 28
28 ≤ t < 32 / 2
9
42
23
4

aWhat is the modal class for the time taken?

bCalculate an estimate of the mean time taken.

cFind the class interval in which the median lies.

dWhat percentage of the walkers completed the mile in less than 20 minutes?

3The table shows the results of a survey on the lengths of leaves.

Draw a frequency polygon to show this information.

Length of leaf (mm) / Frequency
15 ≤ y< 25
25 ≤ y < 35
35 ≤ y < 45
45 ≤ y < 55
55 ≤ y < 65 / 8
15
13
9
2

4A group of people took a fitness test.

They exercised hard.

Then they were timed to see how long their pulses took to return to normal.

This time is called the ‘recovery time’.

The recovery times for the group are shown in the table.

Recovery time t secs / Frequency / Cumulative Frequency
0 ≤ t < 20 / 2
20 ≤ t < 40 / 8
40 ≤ t < 60 / 10
60 ≤ t < 80 / 18
80 ≤ t < 100 / 16
100 ≤ t < 120 / 12
120 ≤ t < 140 / 8
140 ≤ t < 160 / 6

aComplete the cumulative frequency table.

bDraw a cumulative frequency diagram for your table.

cUse your graph to find how many people took more than minutes torecover.

dUse your diagram to find estimates for the following.

ithe median recovery time

iithe interquartile range.

5Nadia recorded the scores of some people taking part in a competition.

She drew this box plot from the data.

aComplete this table.

Minimum score
Lower quartile
Median
Upper quartile
Maximum score

bUse the information in your table to find

ithe range

iithe interquartile range