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

Question

Q. Find the frequency of the median class if the following information is known for a grouped data whose median is = 45:

Lower limit of median class = 25
Sum of frequencies = 100
Cumulative frequency of the class preceding the median class = 30
And, class size = 10.

Answer 1

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

Answer 2

here l =89.5
n/2 = 49
cf = 40
f = ?
h = 10
median = 92.5

Answer 3

Now substitute all values in the formula and solve for f

Answer 4

$median \: = l + ( \frac{ \frac{n}{2} - cf}{f} )h \\ \\ 92.5 = 89.5 + ( \frac{49 - 40}{f} ) \times 10 \\ \\ 3 = ( \frac{49 - 40}{f} ) \times 10 \\ \\ \frac{3}{10} = \frac{9}{f} \\ \\ f = 3 \times 10 \\ \\ f = 30$

Answer 5

So the frequency of median class is 30.

Class	30-35	35-40	40-45	45-50	50-55	55-60	60-65
Frequency	14	16	18	23	18	8	3

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

we know that here l =89.5n/2 = 49cf = 40f = ?h = 10median = 92.5Now substitute all values in the formula and solve for f So the frequency of median class is 30.