# Ex.14.3 Q8 Statistics Solution - NCERT Maths Class 9

## Question

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

Age (in years) |
Number of children |

\(1 - 2\) | \(5\) |

\(2 – 3\) | \(3\) |

\(3 – 5\) | \(6\) |

\(5 – 7\) | \(12\) |

\(7 – 10\) | \(9\) |

\(10 – 15\) | \(10\) |

\(15 - 17\) | \(4\) |

Draw a histogram to represent the data above.

## Text Solution

**What is known?**

A random survey of the number of children of various age groups playing in a park.

**What is Unknown?**

A Histogram to represent the data.

**Reasoning:**

(i) From the given data, we can observe that the class intervals have varying width. This will make the rectangular bars to have varying widths and will give us a misleading picture of the data.

(ii) The areas of the rectangles should be proportional to the frequencies in a histogram.

(iii) So we need to make certain modification in the lengths so that area’s again proportional to the frequencies. For that,

(a) Select a class interval in the minimum. Class size.

(b)The lengths of the rectangles are then modified to be proportionate to the class size \(1.\)

(c) For instance, when the class size is \(5,\) the length of the rectangle is \(10.\) So when the class size is \(1,\) the length of the rectangle will be \(\begin{align}\frac{10}{5} \times 1=2\end{align}\).

**Steps:**

We need to proceed in similar manner, to get the following table:

Age (in years) |
Number of children |
Width of the Class |
Length of the rectangle |

\(1 - 2\) | \(5\) | \(1\) | \(\begin{align}\frac{5 \times 1}{1}=5\end{align}\) |

\(2 – 3\) | \(3\) | \(1\) | \(\begin{align}\frac{3 \times 1}{1}=3\end{align}\) |

\(3 – 5\) | \(6\) | \(2\) | \(\begin{align}\frac{6 \times 1}{1}=6\end{align}\) |

\(5 – 7\) | \(12\) | \(2\) | \(\begin{align}\frac{12 \times 1}{1}=6\end{align}\) |

\(7 – 10\) | \(9\) | \(3\) | \(\begin{align}\frac{12 \times 1}{1}=6\end{align}\) |

\(10 – 15\) | \(10\) | \(5\) | \(\begin{align}\frac{10 \times 1}{1}=2\end{align}\) |

\(15 - 17\) | \(4\) | \(2\) | \(\begin{align}\frac{4 \times 1}{1}=2\end{align}\) |

Will take the age of children on \(x\)-axis and proportion of children per \(1\) year interval per year on \(y\)-axis, the histogram can be