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Assoli18 [71]
2 years ago
8

See image for question. Please show workings.

Mathematics
1 answer:
zalisa [80]2 years ago
6 0

Answer:

  • See below and attached

Step-by-step explanation:

  • <em>Refer to the graph attached</em>

1. The mean is calculated using below table

<u>Marks          Frequencies       Midpoint       Product</u>

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

<u>35 to 39              3                         37                 111      </u>

Sum                    80                                          1845

<u>The mean is:</u>

  • 1845/80 ≈ 23

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

<u>The mode is </u>

  • (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.

<u>Formula to calculate median:</u>

  • 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

<u>Substitute values and calculate:</u>

  • 25 + ((80/2 - 38)/25) *4 = 25.32

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