The median of the distribution given below is 14.4. If the total frequency is…
2024
The median of the distribution given below is 14.4. If the total frequency is 20, the values of x and y, respectively, are:
Class | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 |
|---|---|---|---|---|---|
Frequency | 4 | x | 5 | y | 1 |
Answer: B. 4, 6 — ConceptFor grouped data, the median is found from the median class using the formula Median = l + ((N/2 - C)/f) × h. Here l is the lower limit of the median…
- A.
6, 4
- B.
4, 6
- C.
5, 5
- D.
7, 3
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Correct answer: B
Concept
For grouped data, the median is found from the median class using the formula Median = l + ((N/2 - C)/f) × h.
Here l is the lower limit of the median class, N is the total frequency, C is the cumulative frequency before the median class, f is the frequency of the median class, and h is the class width.
Application
From the total frequency, 4 + x + 5 + y + 1 = 20, so x + y = 10.
Since 14.4 lies in 12-18, this is the median class. Thus l = 12, h = 6, f = 5, and C = 4 + x.
Substitute these values: 14.4 = 12 + ((10 - (4 + x))/5) × 6.
Therefore 2.4 = ((6 - x)/5) × 6 = 1.2(6 - x), so 6 - x = 2 and x = 4.
Using x + y = 10 gives y = 6.
Cross-check
With x = 4 and y = 6, the frequencies total 4 + 4 + 5 + 6 + 1 = 20. The cumulative frequency before 12-18 is 8, so the 10th observation lies in that class.
The median is 12 + ((10 - 8)/5) × 6 = 14.4, which matches the given value.
Therefore, x = 4 and y = 6.