# Median Under Less Than Cumulative Frequency Distribution

Median is the mid-value of any given series. To find median under less than cumulative frequency distribution, when continuous series is given to us. We need to correct the class intervals and find the frequencies related to that class interval.

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## How to find median in case of less than cumulative frequency distribution?

The following steps are to be applied to find the median:

- Re-write the given table by creating Class intervals.
- Given the number of students is cumulative frequency. Find frequency by doing subtraction, but keeping the first frequency and cumulative frequency as same.
- For frequency calculation; Present CF – Previous CF
- Find the median class using N/2, where N is the sum of frequency. Locate the number obtained in the cumulative frequency and select the next number available in CF. Bold this, it is median class.
- Apply the median formula.

## Calculate median of the following series:

Marks | Number of Students |
---|---|

Less than 10 | 12 |

Less than 20 | 26 |

Less than 30 | 40 |

Less than 40 | 58 |

Less than 50 | 80 |

Less than 60 | 110 |

Less than 70 | 138 |

Less than 80 | 150 |

Step 1: Re-write the given table by creating Class intervals.

Marks | Number of Students |
---|---|

0 – 10 | 12 |

10 – 20 | 26 |

20 – 30 | 40 |

30 – 40 | 58 |

40 – 50 | 80 |

50 – 60 | 110 |

60 – 70 | 138 |

70 – 80 | 150 |

Step 2: Given the number of students is cumulative frequency. Find frequency by doing subtraction, but keeping the first frequency and cumulative frequency as same.

Marks | Cumulative Frequency | Frequency |
---|---|---|

0 – 10 | 12 | 12 |

10 – 20 | 26 | 26-12 = 14 |

20 – 30 | 40 | 40-26 = 14 |

30 – 40 | 58 | 58-40 = 18 |

40 – 50 | 80 | 80-58 = 22 |

50 – 60 | 110 | 110-80 = 30 |

60 – 70 | 138 | 138-110 = 28 |

70 – 80 | 150 | 150-138 = 12 |

Sum of Frequency = 150 |

Step 3: Find the median class using N/2

Where N is the sum of frequency. Median Class = 150/2 = 75.

Locate 75 (N/2) in cumulative frequency and pick the next number available in cf after 75.

Marks | Cumulative Frequency | Frequency |
---|---|---|

0 – 10 | 12 | 12 |

10 – 20 | 26 | 14 |

20 – 30 | 40 | 14 |

30 – 40 | 58* | 18 |

40 – 50* | 80 | 22* |

50 – 60 | 110 | 30 |

60 – 70 | 138 | 28 |

70 – 80 | 150 | 12 |

Sum of Frequency = 150 |

Median = Lower limit of the median class + {(N/2) – Previous CF} * Class Interval/ Existing frequency

Median = 40 + {(75 – 58) * 10}/ 22

Median = 40 + 170/22

Median = 40 + 7.727

Median = 47.727 or 47.73 (Approx)

I hope it was helpful, you can refer to more posts related to the statistics.

- Individual Series Arithmetic Mean
- Discrete Series Arithmetic Mean
- Continuous Series Arithmetic Mean
- Inclusive and Exclusive Series – Arithmetic mean
- Introduction to the statistics.
- Functions and importance of statistics.
- Calculating Correct Arithmetic mean

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