#### Question

The following is the distribution of height of students of a certain class in a certain city:

Height (in cm): | 160 - 162 | 163 - 165 | 166 - 168 | 169 - 171 | 172 - 174 |

No. of students: | 15 | 118 | 142 | 127 | 18 |

Find the median height.

#### Solution

First we prepare the following cummulative table to compute the median.

Height (in cm) | Frequency (f1) | Cumulative Frequency (c.f) |

160 - 162 | 15 | 15 |

163 - 165 | 118 | 133 |

166 - 168 | 142 | 275 |

169 - 171 | 127 | 402 |

172 - 174 | 18 | 420 |

N = 420 |

Now, N = 420

`thereforeN/2=420/2=210`

Thus, the cumulative frequency just greater than 210 is 275 and the corresponding class is 166 - 168.

Therefore, 166 - 168 is the median class.

l = 166, f = 142, F = 133 and h = 2

We know that,

Median `=l+{(N/2-F)/f}xxh`

`=166+{(210-133)/142}xx2`

`=166+(77xx2)/142`

`=166+154/142`

= 166 + 1.08

= 167.08

Hence, the median height is approximately 167.1 cm.

Is there an error in this question or solution?

#### APPEARS IN

Solution The Following is the Distribution of Height of Students of a Certain Class in a Certain City: Concept: Median of Grouped Data.