Using step-deviation method, find mean for the following

Using step-deviation method, find mean for the following frequency distribution:

ICSE Specimen Question Paper (SQP) 2026

Ans:

Step 1: From the given frequency distribution table, first we calculate class marks (x) for each class interval.

Step 2: we take 45-60 as mean class. Hence, its class marks 52.5 as our assumed mean

∴ A = 52.5

Next, we calculate deviation (d) for each class interval now by deviation, d = x – A

Step 3: We calculate step-deviation (u) for each class interval now:

Step deviation, u = $\frac{d}{h}$

Here, class width, h is 15 (difference of upper & lower limit of any class width from the given table)

Step 4: Next, we calculate value of (f x u) for each class interval, Also calculate $\Sigma {fu}$ and $\Sigma {f}$ for given data.

Step 5: Mean = A + $\frac{\Sigma{fu}}{\Sigma{f}}$ x h

from above, we have: A = 52.5, $\Sigma{fu}$ = – 12, ${\Sigma{fu}}$ = 30, h = 15

By substituting the values in the above formula, we get:

Mean = 52.5 + $\frac{-12}{30}$ x (15)

= 52.5 – $\frac{2}{5}$ x (15)

= 52.5 – 6 = 46.5

Therefore, the mean value of the given frequency distribution is 46.5.

Please press the “Heart” button if you like the solution.

Contact us