Question

A random survey of the number of children of various age groups playing in park was found as follows:

$\begin{array}{cc}Age\left(inyears\right)& Numberofchildren\\ 1-2& 5\\ 2-3& 3\\ 3-5& 6\\ 5-7& 12\\ 7-10& 9\\ 10-15& 10\\ 15-17& 4\end{array}$

What are the adjusted frequency values for the classes of children in the age group 2-3, 5-7 and10-15?

• A. 5,3 and 6
• B. 3,6 and 3
• C. 5,3 and 2
• D. 3,6 and 2

Answer 1

The correct option is D

3,6 and 2

Here, it can be observed that the data has class intervals of varying width. So, we calculate the adjusted frequency.

$Adjustedfrequency=\frac{frequency\times requiredsizeofinterval}{currentsizeofinterval}$

The required size of the interval = Minimum size of the interval = 2-1=1.

$\begin{array}{cccc}Age\left(inyears\right)& Frequency\left(Numberofchildren\right)& Widthofclass\left(currentinterval\right)& Adjustedfrequency\\ 1-2& 5& 1& \frac{5\times 1}{1}=5\\ 2-3& 3& 1& \frac{3\times 1}{1}=3\\ 3-5& 6& 2& \frac{6\times 1}{2}=3\\ 5-7& 12& 2& \frac{12\times 1}{2}=6\\ 7-10& 9& 3& \frac{9\times 1}{3}=3\\ 10-15& 10& 5& \frac{10\times 1}{5}=2\\ 15-17& 4& 2& \frac{4\times 1}{2}=2\end{array}$

Thus, the adjusted frequency value for the class of children in the age group 2-3 is 3, the adjusted frequency value for the class of children in the age group 5-7 is 6 and the adjusted frequency value for the class of children in the age group 10-15 is 2.