information : cumulative frequency
 

introduction

 

 

 

Introduction

Frequency is used to describe the number of times results occur. On the other hand, cumulative frequency is a 'running total'. It is the sum of frequencies moving through the data.

Example - A survey was done to look at how many TV's there were in a household.

 

no. of TV's

frequency

 

cumulative frequency

0

4

4

4

1

15

4+15

19

2

18

4+15+18

37

3

7

4+15+18+7

44

4

2

4+15+18+7+2

46

 

The definition of the median is that particular value half way through the data.

If the cumulative total of frequencies is 46, then the median is the 23 rd. value.

 

info - cumulative frequency

 

So the median is 1(nearest whole number).

Where there are lots of values, say more than 10, the data is best presented as 'grouped data'.

 

back to top

 

Quartiles

The upper quartile is the particular value 3/4 through the cumulative frequency.

The lower quartile is the particular value 1/4 through the cumulative frequency.

In the example given above:

upper quartile = 0.75 x 46 = 34.5 (rounded to 36) - this gives a value close to 2

lower quartile =0.25 x 46 = 11.5 (rounded to 12) - this gives a value close to zero

note: values are the readings along the bottom of a cumulative frequency graph

 

back to top

 

Ranges

The interquartile range is the difference between the lower and upper quartiles.

interquartile range = 34.5 - 11.5 = 23

The interquartile range is a measure of how spread out data is. With reference to products( eg the shelf-life of foods) a small value for the interquartile range means a more accurate result.

 

back to top

 

Box & Whisker Plot (Box Plot)

The plot is derived from a cumulative frequency graph and shows the range of data , the interquartile range, and where the quartiles are in relation to the median.

 

box & whisker plot

 

back to top

 

Contact GCSE Maths Tutor here - info@gcsemathstutor.com

Google

A FREE resource

    mechanics

    matter

    nuclear phys.

    quantum mechs.

    electricity

    thermal phys.

    waves

    optics

    fields