#### description

- Computation of Measures of Central Tendency - Median of Grouped Data
- cumulative frequency column

#### notes

Example : A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data was obtained:

Height (in cm) |
Number of girls |

Less than 140 | 4 |

Less than 145 | 11 |

Less than 150 | 29 |

Less than 155 | 40 |

Less than 160 | 46 |

Less than 165 | 51 |

Find the median height.

Solution : To calculate the median height, we need to find the class intervals and their corresponding frequencies.

The given distribution being of the less than type, 140, 145, 150, . . ., 165 give the upper limits of the corresponding class intervals. So, the classes should be below 140, 140 - 145, 145 - 150, . . ., 160 - 165. Observe that from the given distribution, we find that there are 4 girls with height less than 140, i.e., the frequency of class interval below 140 is 4. Now, there are 11 girls with heights less than 145 and 4 girls with height less than 140. Therefore, the number of girls with height in the interval 140 - 145 is 11 – 4 = 7. Similarly, the frequency of 145 - 150 is 29 – 11 = 18, for 150 - 155, it is 40 – 29 = 11, and so on. So, our frequency distribution table with the given cumulative frequencies becomes:

Class intervals | Frequency | Cumulative frequency |

Below 140 | 4 | 4 |

140 - 145 | 7 | 11 |

145 - 150 | 18 | 29 |

150 - 155 | 11 | 40 |

155 - 160 | 6 | 46 |

160 - 165 | 5 | 51 |

Now n = 51. So, n/2=51/2 =25.5. This observation lies in the class 145 - 150. Then,

l (the lower limit) = 145,

cf (the cumulative frequency of the class preceding 145 - 150) = 11,

f (the frequency of the median class 145 - 150) = 18,

h (the class size) = 5.

Using the formula, Median `= l +((n/2-cf)/f)xxh` we have

Median `= 145 +((25.5-11)/18)xx5`

`=145+72.5/18=149.03`

So, the median height of the girls is 149.03 cm.

This means that the height of about 50% of the girls is less than this height, and 50% are taller than this height.

#### Related QuestionsVIEW ALL [51]

In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.

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0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 - 75 |

No. of patients | 5 | 20 | 40 | 50 | 25 |

Compute mean from the following data:

Marks | 0 – 7 | 7 – 14 | 14 – 21 | 21 – 28 | 28 – 35 | 35 – 42 | 42 – 49 |

Number of Students | 3 | 4 | 7 | 11 | 0 | 16 | 9 |

The following table shows the daily wages of workers in a factory:

Daily wages in (Rs) | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 |

Number of workers | 40 | 32 | 48 | 22 | 8 |

Find the median daily wage income of the workers.

Calculate the median from the following frequency distribution table:

Class | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 | 40 – 45 |

Frequency | 5 | 6 | 15 | 10 | 5 | 4 | 2 | 2 |

Given below is the number of units of electricity consumed in a week in a certain locality:

Class | 65 – 85 | 85 – 105 | 105 – 125 | 125 – 145 | 145 – 165 | 165 – 185 | 185 – 200 |

Frequency | 4 | 5 | 13 | 20 | 14 | 7 | 4 |

Calculate the median.