To find the upper and lower quartiles of the discounts, we need to consider the range of possible discounts.
Given that each item is discounted by up to £60, the possible discounts range from £0 (no discount) to £60 (maximum discount).
a) Upper Quartile (Q3): The upper quartile divides the data into the upper 25% and lower 75%. Since there are 80 items, the upper quartile, Q3, would be the value that separates the highest 25% of discounts from the lower 75%.
To find Q3, we can calculate 75% of 80:
Q3 = 0.75 * 80 = 60
Therefore, the upper quartile (Q3) is £60.
Lower Quartile (Q1): The lower quartile divides the data into the lower 25% and upper 75%. It would be the value that separates the lowest 25% of discounts from the upper 75%.
To find Q1, we can calculate 25% of 80:
Q1 = 0.25 * 80 = 20
Therefore, the lower quartile (Q1) is £20.
b) Interquartile Range: The interquartile range (IQR) is the range between the upper and lower quartiles. It provides a measure of the spread or variability of the data.
IQR = Q3 - Q1
IQR = £60 - £20 = £40
Therefore, the interquartile range of the discounts is £40.