Question

See image for question. Please show workings.

Sorry for the wobbly writing.

*freq= frequency.​

Answer 1

• See below and attached

Explanation:

• Refer to the graph attached

1. The mean is calculated using below table

Marks Frequencies Midpoint Product

10 to 14 18 12 216

15 to 19 9 17 153

20 to 24 11 22 242

25 to 29 25 27 675

30 to 34 14 32 448

35 to 39 3 37 111

Sum 80 1845

The mean is:

• 1845/80 ≈ 23

2. The mode is the midpoint of the tallest bar.

The mode is

• (25 + 29)/2 = 27

3. The median is the middle of the data set. The number of frequencies is 80, the middle frequency is number 40, which is within the 25 to 29 bar.

Formula to calculate median:

• L + ( (n/2 – F) / f ) * w

where

• L: The lower limit of the median group = 25
• n: The total number of observations = 80
• F: The cumulative frequency up to the median group = 18 + 9 + 11 = 38
• f: The frequency of the median group = 25
• w: The width of the median group = 29 - 25 = 4

Substitute values and calculate:

• 25 + ((80/2 - 38)/25) *4 = 25.32