# Ex.14.2 Q4 Statistics Solution - NCERT Maths Class 9

## Question

The heights of \(50\) students, measured to the nearest centimeters, have been found to be as follows:

\(161\,\,\,\, 150\,\,\,\, 154\,\,\,\, 165\,\,\,\, 168\,\,\,\, 161\,\,\,\, 154\,\,\,\, 162\,\,\,\, 150\,\,\,\, 151\\ 162\,\,\,\, 164\,\,\,\, 171\,\,\,\, 165\,\,\,\, 158\,\,\,\, 154\,\,\,\, 156\,\,\,\, 172\,\,\,\, 160\,\,\,\, 170\\ 153\,\,\,\, 159\,\,\,\, 161\,\,\,\, 170\,\,\,\, 162\,\,\,\, 165\,\,\,\, 166\,\,\,\, 168\,\,\,\, 165\\ 164\,\,\,\, 154\,\,\,\, 152\,\,\,\, 153\,\,\,\, 156\,\,\,\, 158\,\,\,\, 162\,\,\,\, 160\,\,\,\, 161\,\,\,\, 173\\ 166 \,\,\,\,161\,\,\,\, 159\,\,\,\, 162\,\,\,\, 167\,\,\,\, 168\,\,\,\, 159\,\,\,\, 158\,\,\,\, 153\,\,\,\, 154\,\,\,\, 159\)

- Represent the data given above by a grouped frequency distribution table,Taking the class intervals as \((160 – 165), (165 – 170),\) etc.
- What can you conclude about their heights from the table?

## Text Solution

**What is known?**

- The heights of \(50\) students in \(\rm cm.\)
- Class size is \(5\) [from the given instruction of class intervals to be taken as \(160- 165, 165-170, 170-175\) …. and so on].

**What is unknown?**

- Constructing a grouped frequency distribution table.
- Making inferences and drawing conclusions from the data of “heights of students”.

**Reasoning:**

According to class interval we can check how many numbers lie in between , like this we can draw frequency distribution table and can be conclude about height from table.

**Steps:**

A grouped frequency distribution table with a class size of \(5,\) for the heights of \(50\) students can be constructed as follows:

Height (in cm) |
Number of Students (frequency) |

\(150-155\) | \(12\) |

\(155-160\) | \(9\) |

\(160-165\) | \(14\) |

\(165-170\) | \(10\) |

\(170-175\) | \(5\) |

Total |
\(50\) |

Since ‘\(150\)’ is the lowest value, we started the \(1\rm st\) class interval at \(150.\)

The following features / conclusions can be drawn from the table:

- A majority of \(70\%\) of the students (\(35\) students) are below \(165\rm cm\) height.
- Only a \(10\%\) of the students (\(5\) students) are at a height of \(170\rm cm\) or above.