Revision: Statistics and Probability >> Statistics Maths English Medium Class 10 CBSE

In a grouped frequency distribution, the modal class is the class interval that has the highest frequency.

The cumulative frequency of a class interval is the sum of the frequencies of all the classes up to this class interval.

Direct Method:

\[\bar{x}=\frac{\sum f_ix_i}{\sum f_i}\]

where x_i​ = class mark, f_i​ = frequency

Short-cut (Assumed Mean) Method:

\[\bar{x} = A+\frac{\sum f_id_i}{\sum f_i}\]

where d_i = x_i - A
A is the assumed mean

Step-deviation Method:

\[\bar{x}=a+h\frac{\sum f_iu_i}{\sum f_i}\]

where \[u_i=\frac{x_i-a}{h}\]

h is the class width / common factor

\[\mathrm{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h\]

l = lower limit of the modal class,
h = size of the class interval (assuming all class sizes to be equal),
f₁ = frequency of the modal class,
f₀ = frequency of the class preceding the modal class,
f₂ = frequency of the class succeeding the modal class.

If n is odd:
Median =\[\left(\frac{n+1}{2}\right)\]th observation

If n is even:
Median average of  =\[\frac{n}{2}\mathrm{th}\] and \[\left(\frac{n}{2}+1\right)\mathrm{th}\]observations

\[\mathrm{Median}=l+\frac{\left(\frac{n}{2}-cf\right)}{f}\times h\]

• l = lower limit of median class

• n = total frequency

• cf = cumulative frequency of class before median class

• f = frequency of median class

Classes must be continuous before applying the median formula.