Question

See image for question. Please show workings.

Answer 1

Answer:

• See below and attached

Step-by-step 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