#### Question

If the median of the distribution is given below is 28.5, find the values of x and y

Class interval | Frequency |

0 - 10 | 5 |

10 - 20 | x |

20 - 30 | 20 |

30 - 40 | 15 |

40 - 50 | y |

50 - 60 | 5 |

Total | 60 |

#### Solution

The cumulative frequency for the given data is calculated as follows

Class interval | Frequency | Cumulative frequency |

0 - 10 | 5 | 5 |

10 - 20 | x | 5+ x |

20 - 30 | 20 | 25 + x |

30 - 40 | 15 | 40 + x |

40 - 50 | y | 40+ x + y |

50 - 60 | 5 | 45 + x + y |

Total (n) | 60 |

From the table, it can be observed that n = 60

45 + x + y = 60

x + y = 15 (1)

Median of the data is given as 28.5 which lies in interval 20 - 30.

Therefore, median class = 20 - 30

Lower limit (l) of median class = 20

Cumulative frequency (cf) of class preceding the median class = 5 + x

Frequency (f) of median class = 20

Class size (h) = 10

`"Median" = l + (((n/2)-cf)/f)xxh`

28.5 = 20 + [(60/2-(5+x))/20]xx10

8.5 = ((25-x)/2)

17 = 25 - x

8 + y = 15

y = 7

Hence, the values of x and y are 8 and 7 respectively.

#### Related QuestionsVIEW ALL [20]

Following is the distribution of I.Q. of loo students. Find the median I.Q.

I.Q.: | 55 - 64 | 65 - 74 | 75 - 84 | 85 - 94 | 95 - 104 | 105 - 114 | 115 - 124 | 125 - 134 | 135 - 144 |

No of Students: | 1 | 2 | 9 | 22 | 33 | 22 | 8 | 2 | 1 |

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg) |
40 − 45 | 45 − 50 | 50 − 55 | 55 − 60 | 60 − 65 | 65 − 70 | 70 − 75 |

Number of students |
2 | 3 | 8 | 6 | 6 | 3 | 2 |

Compute the median for the following data:

Marks | No. of students |

Less than 10 | 0 |

Less than 30 | 10 |

Less than 50 | 25 |

Less than 70 | 43 |

Less than 90 | 65 |

Less than 110 | 87 |

Less than 130 | 96 |

Less than 150 | 100 |

The table below shows the salaries of 280 persons :

Salary (In thousand Rs) |
No. of Persons |

5 – 10 | 49 |

10 – 15 | 133 |

15 – 20 | 63 |

20 – 25 | 15 |

25 – 30 | 6 |

30 – 35 | 7 |

35 – 40 | 4 |

40 – 45 | 2 |

45 – 50 | 1 |

Calculate the median salary of the data.

Compute the median for the following data:

Marks | No. of students |

More than 150 | 0 |

More than 140 | 12 |

More than 130 | 27 |

More than 120 | 60 |

More than 110 | 105 |

More than 100 | 124 |

More than 90 | 141 |

More than 80 | 150 |