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Using points (38,0), (40,3), (42,5), (44,9), (46,14), (48,28), (50, 32) and (52,35), plot a graph.

To find median graphically,

We have total frequency, N = 35

⇒ N/2 = 35/2 = 17.5

Plot 17.5 on the y-axis and draw a horizontal line intersecting the ogive parallel to x-axis.

Observe, from the graph the vertical line parallel to y-axis touches y-axis at 46.5 (approx.).

Hence, median is 46.5.

Finding median by formula:

For median:

We have, total frequency, N = 35

N/2 = 35/2 = 17.5

Observe, cf = 28 is just greater than 17.5.

Thus, median class = 46-48

Median is given by

Where,

L = Lower class limit of median class = 46

N/2 = 17.5

cf = cumulative frequency of the class preceding median class = 14

f = frequency of the median class = 14

h = class interval of the median class = 2

Substituting these values in the formula of median, we get

⇒

⇒ Median = 46 + 0.5

⇒ Median = 46.5

Thus, median is 46.5.

Hence, verified.