Q. 45.0( 1 Vote )

# Find the median for the following data.

Answer :

This is a grouped frequency distribution, in which median is calculated as follows.

First, we need to convert this inclusive type of data values into exclusive type. For this, subtract 0.5 from lower limits of each class and add 0.5 to upper limits of each class interval.

We have the following table:

Here, we get total frequency, N = 50. So,

Since, N/2 = 25. Mark a cumulative frequency which is just greater than 25.

Here, it is 31. So, median class would be 29.5 – 39.5.

Median is given by

Where, l = lower limit of the median class = 29.5

N/2 = 25 (as calculated above)

m = cumulative frequency of the class preceding the median class = 20

f = frequency of the median class = 11

c = width of the median class = 10

Putting all these values in the formula, we get

⇒

⇒ Median = 29.5 + 4.55 = 34.05

Thus, median is 34.05.

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