A Level Maths Notes: S1 – Quartiles and Median From Frequency Tables By Interpolation
We start with the table below which summarises the daily sales in a newspaper shop over a year for the 360 days the shop was open.
|
Sales |
Number of Days |
|
1 -200 |
166 |
|
201- 400 |
100 |
|
401 - 700 |
59 |
|
701 - 1000 |
30 |
|
1001 -1500 |
3 |
To find the lower quartile we use
where
are
the lower and upper bounds of the frequency class in which the lower
quartile lies,1-200,
is
the total number of data points,
is
the sum of the frequencies of the classes BELOW that class in which
the lower quartile is found and
is
the frequency of the interval in which the lower quartile is found.
To find the median we use
whereare
the lower and upper bounds of the frequency class in which the median
lies, 201-300,is
the total number of data points,
is
the sum of the frequencies of the classes ABOVE that class in which
the median is found (in the table above) andis
the frequency of the interval in which the median is found.
To find the upper quartile we use
whereare
the lower and upper bounds of the frequency class in which the upper
quartile lies, 401-700,is
the total number of data points,
is
the sum of the frequencies of the classes BELOW that class in which
the upper quartile is found andis
the frequency of the interval in which the upper quartile is found.