Question

Median class of frequency distribution is 89.5 - 99.5 if number of observation is 98 and cumulative frequency of preceding if median class is 40 find the frequency of median class given that median is 92.5

Answer 1

Answer:Frequency of median class is 30.

Solution:

we know that

$median \: = l + ( \frac{ \frac{n}{2} - cf}{f} )h \\ \\ l = lower \: limit \: of \: median \: class \\ \frac{n}{2} = number \: of \: observation \: by \: 2 \\ \\ cf = cumulative \: freq \: of \: preceding \: class \\ \\ f = freq \: of \: median \: class \\ h =class \:interval$
here l=89.5

n/2 = 49

cf= 40

f=?

h=10

median = 92.5

just put all values in the formula and solve for f
$median \: = l + ( \frac{ \frac{n}{2} - cf}{f} )h \\ \\ 92.5 = 89.5 + ( \frac{49 - 40}{f} ) \times 10 \\ \\ 3 = ( \frac{49 - 40}{f} ) \times 10 \\ \\ \frac{3}{10} = \frac{9}{f} \\ \\ f = 3 \times 10 \\ \\ f = 30$
So the frequency of median class is 30.

Hope it helps you.