# Calculate the mean deviation about median age for the age distribution of 100 persons given below:

Age(in years) 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55

Number 5 6 12 14 26 12 16 9

[Hint: Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval]

**Solution:**

The given data is not continuous.

Therefore,

it has to be converted into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval.

The table is formed as follows

Age (in years) | Number of person fi | c. f | Mid-point xi | x_{i} - M |
f_{i} x_{i} - M |

15.5 - 20.5 | 5 | 5 | 18 | 20 | 100 |

20.5 - 25.5 | 6 | 11 | 23 | 15 | 90 |

25.5 - 30.5 | 12 | 23 | 28 | 10 | 120 |

30.5 - 35.5 | 14 | 37 | 33 | 5 | 70 |

35.5 - 40.5 | 26 | 63 | 38 | 0 | 0 |

40.5 - 45.5 | 12 | 75 | 43 | 5 | 60 |

45.5 - 50.5 | 16 | 91 | 48 | 10 | 160 |

50.5 - 55.5 | 9 | 100 | 53 | 15 | 135 |

100 | 735 |

The class interval containing the (N/2)^{th} or 50)^{t}^{h} item is 35.5 - 40.5

Therefore,

35.5 - 40.5 is the median class.

It is known that,

Median = (l + (N/2 - C))f' × h

Here, l = 35.5, C = 37, f = 26, h = 5, N = 100

M = 35.5 + (50 - 37)/26 × 5

= 35.5 + (13 × 5)/26

= 35.5 + 2.5

= 38

Thus, the mean deviation about the median is given by:

M.D. (M) = 1/N ^{8}∑_{i = 1} f_{i}|x_{i} - M|

= 1/100 × 735

= 7.35

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 12

## Calculate the mean deviation about median age for the age distribution of 100 persons given below: Age(in years) 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 Number 5 6 12 14 26 12 16 9 [Hint: Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval]

**Summary:**

The mean deviation about the median for the given data is 7.35