Find the mean, median and mode of the following data:

Classes: | 0-20 | 20-40 | 40-60 | 40-60 | 80-100 | 100-120 | 120-140 |

Frequency: | 6 | 8 | 10 | 12 | 6 | 5 | 3 |

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#### Solution

Consider the following data.

Class |
Frequency (f_{i}) |
x_{i} |
f_{i} x_{i} |
C.f. |

0−20 | 6 | 10 | 60 | 6 |

20−40 | 8 | 30 | 240 | 14 |

40−60 | 10 | 50 | 500 | 24 |

60−80 | 12 | 70 | 840 | 36 |

80−100 | 6 | 90 | 540 | 42 |

100−120 | 5 | 110 | 550 | 47 |

120−140 | 3 | 130 | 390 | 50 |

`N=sumf=50` | `sumf_1x_1=3120` |

Here, the maximum frequency is 12 so the modal class is 60−80.

Therefore,

l = 60

h = 20

f = 12

f1 = 10

f2 = 6

F = 24

Median `=l+(N/2-F)/fxxh`

`=60+(25-24)/12xx20`

`=60+1/12xx20`

`=60+20/12`

= 60 + 1.67

= 61.67

Thus, the median of the data is 61.66.

Mean `=(sumf_1x_1)/sumf`

`=3120/50=32.4`

Thus, the mean of the data is 62.4.

Mode `=l+(f-f1)/(2f-f1-f2)xxh`

`=60+(12-10)/(24-10-6)xx20`

`=60+2/8xx20`

`=60+40/8`

= 60 + 5

= 65

Thus, the mode of the data is 65.

Concept: Mode of Grouped Data

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