Q. 44.3( 10 Votes )
We have been given class intervals and frequency.
Let us create greater than type as well as less than type of cumulative frequency distribution table.
Taking Class as x-axis and cumulative frequency as y-axis separately for greater than type as well as less than type.
Thus plotting the points on a graph, we get
The median is given by intersection point of less-than type and more-than type ogives and is represented on x-axis.
Note here, the arrow points at approximately 139.
Even if we verify by using the formula, we’d get an answer around 139.
Observe in the less than type cumulative frequency, cf = 26 is just greater than 25.
Thus, median class = 120 – 140
Median is given by
L = Lower class limit of median class = 120
N/2 = 25
cf = cumulative frequency of the class preceding median class = 12
f = frequency of the median class = 14
h = class interval of the median class = 20
Substituting these values in the formula of median, we get
⇒ Median = 120 + 18.57
⇒ Median = 138.57 ∼ 139
Thus, the median of data is 138.57 and it is verified too.
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