## Finding the Mode, Median and Mean From Frequency Tables

Suppose we start from a frequency table of lengths versus frequencies.

Length |
Frequency |

0-10 |
2 |

10-20 |
16 |

20-30 |
46 |

30-40 |
35 |

40-50 |
7 |

**Finding the Mode**

The mode is just the most common length interval, with the highest frequency: 20-30.

To find the median interval we insert an extra column, a cumulative frequency column.

To find the numbers in the cumulative frequency column we find the totals of the frequency column as we go down.

Length |
Frequency |
Cumulative Frequency |

0-10 |
2 |
2 |

10-20 |
16 |
2+16=18 |

20-30 |
46 |
2+16+46=64 |

30-40 |
35 |
2+16+46+35=99 |

40-50 |
7 |
2+16+46+35+7=106=99 |

**Finding the Median**

The median will lie in the length interval in which the cumulative frequency just passes the halfway point:

The total frequency is 106 so the halfway point is 53.

The cumulative frequency just passes this point in the row where the cumulative frequency is 64, so the median class interval is 20-30

Note: It does not matter how the they label the length intervals:

The calculations are the same as long as the distribution is continuous – if the table involves lengths heights etc.

**Finding the Mean**

We insert two extra columns – the midpoint and midpoint*frequency columns.

Length |
Frequency |
Midpoint |
Midpoint*Frequency |

0-10 |
2 |
5 |
10 |

10-20 |
16 |
15 |
240 |

20-30 |
46 |
25 |
1150 |

30-40 |
35 |
35 |
1225 |

40-50 |
7 |
45 |
245 |

Total |
106 |
2870 |

The Mean is now the

Note: It does not matter how the they label the length intervals:

The calculations are the same as long as the distribution is continuous – if the table involves lengths heights etc.