Cambridge International Mathematics

Continuous data (Chapter 17) 359

Sometimes it is useful to know the number of scores that lie above or below a particular value. In

such situations it is convenient to construct acumulative frequency distribution tableand acumulative

frequency graphto represent the data.

The cumulative frequency gives arunning totalof the scores up to a particular value.

It is the total frequency up to a particular value.

From a frequency table we can construct a cumulative frequency column and then graph this data on a

cumulative frequency curve. The cumulative frequencies are plotted on the vertical axis.

From the cumulative frequency graph we can find:

² the median Q 2

² the quartiles Q 1 and Q 3

² percentiles

¾

These divide the ordered data into quarters.

ThemedianQ 2 splits the data into two halves, so it is50%of the way through the data.

Thefirst quartileQ 1 is the score value25%of the way through the data.

Thethird quartileQ 3 is the score value75%of the way through the data.

Thenth percentile Pn is the score valuen%of the way through the data.

So, P 25 =Q 1 ,P 50 =Q 2 and P 75 =Q 3.

Example 4 Self Tutor

Weight (w kg) Frequency

656 w< 70 1

706 w< 75 2

756 w< 80 8

806 w< 85 16

856 w< 90 21

906 w< 95 19

956 w< 100 8

1006 w< 105 3

1056 w< 110 1

1106 w< 115 1

The data shown gives the weights of 80 male basketball players.

a Construct a cumulative frequency distribution table.

b Represent the data on a cumulative frequency graph.

c Use your graph to estimate the:

i median weight

ii number of men weighing less than 83 kg

iii number of men weighing more than 92 kg

iv 85 th percentile.

a Weight (w kg) frequency cumulative frequency

656 w< 70 1 1

706 w< 75 2 3

756 w< 80 8 11

806 w< 85 16 27

856 w< 90 21 48

906 w< 95 19 67

956 w< 100 8 75

1006 w< 105 3 78

1056 w< 110 1 79

1106 w< 115 1 80

this is 1+2

this is 1+2+8

C CUMULATIVE FREQUENCY [11.7]

this 48 means that there are 48

players who weigh less than 90 kg,

so ( 90 , 48 ) is a point on the

cumulative frequency graph.

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Y:\HAESE\IGCSE01\IG01_17\359IGCSE01_17.CDR Tuesday, 18 November 2008 11:50:37 AM PETER