# draw a less than ogive from the following data and hence find out the value of median: age 0-10 10-2020-30 30-40 40-5050-60 60-70 70-80 number 10 15 22 16 14 12 6 5

To construct a less than ogive, we first need to convert the series into a less than cumulative frequency distribution.

Age | Number(f) | Cumulative frequency(c.f) |

Less than 10 | 10 | 10 |

Less than 20 | 15 | 25 |

Less than 30 | 22 | 47 |

Less than 40 | 16 | 63 |

Less than 50 | 14 | 77 |

Less than 60 | 12 | 89 |

Less than 70 | 6 | 95 |

Less than 80 | 5 | 100 |

Median class is given by the size of the ${\left(\frac{N}{2}\right)}^{th}$ item, i.e. the ${\left(\frac{100}{2}\right)}^{th}$item, which is the 50th item.

This corresponds to the class interval 30−40, so this is the median class.

$\mathrm{Median}\left(M\right)={l}_{1}+\frac{{\displaystyle \frac{N}{2}}-cf}{f}\times i\phantom{\rule{0ex}{0ex}}=30+\frac{{\displaystyle \frac{100}{2}}-47}{16}\times 10\phantom{\rule{0ex}{0ex}}=30+\frac{30}{16}\phantom{\rule{0ex}{0ex}}M=31.88\phantom{\rule{0ex}{0ex}}$

**
**