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Question
Heights of 50 students of class X of a school are recorded and following data is obtained:
| Height (in cm) | 130 – 135 | 135 – 140 | 140 – 145 | 145 – 150 | 150 – 155 | 155 – 160 |
| Number of students | 4 | 11 | 12 | 7 | 10 | 6 |
Find the median height of the students.
Solution
Let us first construct the table of cumulative frequency as shown below:
| Height (in cm) |
Number of students (fi) |
Cucumulative Frequency (c.f.) |
| 130 – 135 | 4 | 4 |
| 135 – 140 | 11 | 15 |
| 140 – 145 | 12 | 27 |
| 145 – 150 | 7 | 34 |
| 150 – 155 | 10 | 44 |
| 155 – 160 | 6 | 50 |
| Total | `sum"f"_"i"` = 50 |
Here, `"N"/2 = 50/2` = 25, which lies in cumulative frequency of 27
∴ The median class is 140 – 145.
So, l = 140, c.f. = 15, f = 12 and h = 5
Now, as median (Me) = `"l" + ("N"/2 - "c.f.")/"f" xx "h"`
∴ Required median = `140 + (25 - 15)/12 xx 5`
= `140 + 10/12 xx 5`
= 140 + 4.17
= 144.17
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