Question 21 of 21intermediate🔧 ApplyNumerical3 marks

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

Weight (in kg)40 - 4545 - 5050 - 5555 - 6060 - 6565 - 7070 - 75
Number of students2386632
Correct Answer

The median weight of the students is 56.67 kg.

Exercise: EXERCISE 13.3 | Q: 7 | (Page 30)
For More Understanding

Explanation

To find the median for grouped data, we first calculate cumulative frequencies and identify the median class where n/2 lies. Then we apply the formula: Median = l + [(n/2 - cf)/f] × h. The median class is 55-60 since cumulative frequency 19 is the first to exceed n/2 = 15.

Solution Steps

  1. Step 1: Calculate total number of students: n = 2 + 3 + 8 + 6 + 6 + 3 + 2 = 30

  2. Step 2: Calculate cumulative frequencies: For classes 40-45, 45-50, 50-55, 55-60, 60-65, 65-70, 70-75, the cumulative frequencies are 2, 5, 13, 19, 25, 28, 30 respectively.

  3. Step 3: Find n/2 = 30/2 = 15. The median class is where cumulative frequency first exceeds 15, which is 55-60 (cf = 19).

  4. Step 4: Apply the formula: Median = l + [(n/2 - cf)/f] × h

  5. Step 5: Substitute values: l = 55, n/2 = 15, cf = 13, f = 6, h = 5

  6. Step 6: Median = 55 + [(15 - 13)/6] × 5 = 55 + (2/6) × 5 = 55 + 5/3 = 55 + 1.67 = 56.67 kg

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