Question

Find the mean of the following distribution :

Hint:

Using the Assumed Mean Method keeps the numbers small and manageable, reducing the chance of arithmetic errors compared to the Direct Method!

Answer 1

Step 1: Switch to the step-deviation method.
With assumed mean $A = 55$ and class width $h = 10$, define $u_i = \frac{x_i - A}{h}$ instead of working with $d_i = x_i - A$ directly.
Step 2: Rescale the known deviation sum.
Since $\sum f_i d_i = 90$ and $h = 10$, we get $\sum f_i u_i = \frac{90}{10} = 9$.
Step 3: Apply the step-deviation mean formula.
\[ \bar{x} = A + \left(\frac{\sum f_iu_i}{\sum f_i}\right) \times h = 55 + \frac{9}{50} \times 10 = 55 + 1.8 \]
\[ \boxed{56.8} \]