Question

A shop has an event where 80 items are on sale. Each item is discounted by up to

£60.
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a) Find the upper and lower quartiles of the discounts.
b) Find the interquartile range of the discounts.

Answer 1

a)The upper quartile of the discounts is £40

The lower quartile of the discounts is £25

b)The interquartile range is £15

Explanation:

a) Upper and lower quartiles,

The upper quartile contains 75% or 3/4 of the total number of values,

In our case, since there are 80 items ,so 3/4 of 80 is, (3/4)(80) = 60

Hence for the upper quartile, the cumulative frequency should be 60, which gives a discount value of £40. (60 items have a discount less than or equal to £40)

So, The upper quartile of the discounts is £40

The lower quartile contains 25% or 1/4 of the values,

So, In our case, 1/4 of 80 is, (1/4)(80) = 20

Hence for the lower quartile, the cumulative frequency should be 20,

which gives a discount value of £25

So, the lower quartile of the discounts is £25

b) The interquartile range,

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

so,

interquartile range = upper quartile - lower quartile

interquartile range = 40 - 25

interquartile range = £15

Hence, the interquartile range is £15