Question

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

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

Draw a histogram to represent the data above. [4 MARKS]

Answer 1

Tabular form: 1 Mark
Graph: 3 Marks

Here, it can be observed that the data has class intervals of varying width. The proportion of children per 1 year interval can be calculated as follows.

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

Taking the age of children on x-axis and proportion of children per 1 year interval on y-axis, the histogram can be drawn as follows.