Question

The number of years of education acquired by a sample of 100 adults in a locality is as follows.

$\begin{array}{ccccccc}\text{Years of education}& 0-4& 4-8& 8-12& 12-16& 16-20& 20-24\\ \text{No. of people}& 10& 22& 32& 24& 8& 4\end{array}$

• A. 2.85
• B. 3.75
• C. 4.95
• D. 6.05

Answer 1

The correct option is C

4.95

Let the assumed mean be 10 i.e. A = 10

$\begin{array}{ccccc}X& F& D=X-A& FD& F{D}^2\\ 2& 10& -8& -80& 640\\ 6& 22& -4& -88& 352\\ 10& 32& 0& 0& 0\\ 14& 24& 4& 96& 384\\ 18& 8& 8& 64& 512\\ 22& 4& 12& 48& 576\\ & \sum F=100& & \sum FD=40& \sum F{D}^2=2464\end{array}$

$\sigma =\sqrt{\frac{\sum F{D}^2}{\sum F}-{\left(\frac{\sum FD}{\sum F}\right)}^2}=\sqrt{\frac{2464}{100}-{\left(\frac{40}{100}\right)}^2}=\sqrt{24.64-0.16}=\sqrt{24.48}=4.95$