Question

A shop has an event where 80 items are on sale.

Each item is discounted by up to £60.
a) Find the upper and lower quartiles of the
discounts.
b) Find the interquartile range of the discounts.

Answer 1

We can actually see here that:

a) Lower Quartile (Q1) = £15

Upper Quartile (Q3) = £45

b) Interquartile Range (IQR) = £30

a) Upper and lower quartiles:

• Lower Quartile (Q1): This is the value below which 25% of the discounts fall.

• Upper Quartile (Q3): This is the value below which 75% of the discounts fall.

We'll first find the position of Q1 and Q3 in the ordered list of discounts.

Thus,

Position of Q1 = 1/4 × 80 = 20

Position of Q3 = 3/4 × 80 = 60

Thus,

Q1 corresponds to the 20th discount and

Q3 corresponds to the 60th discount.

b) Interquartile range (IQR): The IQR is the range between Q3 and Q1.

To find the values of Q1 and Q3:

• Lower Quartile (Q1) = Value of the 20th discount in ascending order

• Upper Quartile (Q3) = Value of the 60th discount in ascending order

Since each item can be discounted by up to £60 and the discounts are evenly distributed within that range:

Q1 = 20/80 × 60 = £15

Q2 = 60/80 × 60 = £45

c) Interquartile range (IQR):

IQR = Q3 - Q1

IQR = £45 - £15 = £30

Therefore, we see here that:

a) Lower Quartile (Q1) = £15

Upper Quartile (Q3) = £45

b) Interquartile Range (IQR) = £30