The distribution below gives the weights of 30 students of a class. Find the median weight of the students:

Class 10th Mathematics Question Paper 2023 :The distribution below gives the weights of 30 students of a class. Find the median weight of the students:

By
Rohit Sharma
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Question :The distribution below gives the weights of 30 students of a class. Find the median weight of the students:

The correct answer :To find the median weight of the students, we need to arrange the weights in ascending order. However, the weights in the table are given in intervals, so we need to first calculate the midpoint of each interval.

Weight interval

Midpoint

40-45

42.5

45-50

47.5

50-55

52.5

55-60

57.5

60-65

62.5

65-70

67.5

70-75

72.5

Next, we need to calculate the cumulative frequency of the weights, which is the sum of the number of students up to that interval.

Weight interval

Midpoint

Number of Students

Cumulative Frequency

40-45

42.5

2

2

45-50

47.5

3

5

50-55

52.5

8

13

55-60

57.5

6

19

60-65

62.5

6

25

65-70

67.5

3

28

70-75

72.5

2

30

The total number of students is 30, which is an even number. Therefore, the median weight will be the average of the middle two weights. The middle two weights are the ones that have a cumulative frequency of 15 and 16, which correspond to the weight intervals 50-55 and 55-60.

To find the median weight, we need to calculate the midpoint of these two intervals:

Median weight = (midpoint of 50-55 interval + midpoint of 55-60 interval) / 2

Median weight = (52.5 + 57.5) / 2

Median weight = 55 kg

Therefore, the median weight of the students is 55 kg.

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