#### Question

Find the mean, variance and standard deviation using short-cut method

Height in cms |
No. of children |

70-75 |
3 |

75-80 |
4 |

80-85 |
7 |

85-90 |
7 |

90-95 |
15 |

95-100 |
9 |

100-105 |
6 |

105-110 |
6 |

110-115 |
3 |

#### Solution

Class Interval |
Frequency f_{i} |
Mid-point x_{i} |
`y_i = (X_i - 92.5)/5` | y_{i}^{2} |
f_{i}y_{i} |
f_{i}y_{i}^{2} |

70-75 |
3 |
72.5 |
–4 |
16 |
–12 |
48 |

75-80 |
4 |
77.5 |
–3 |
9 |
–12 |
36 |

80-85 |
7 |
82.5 |
–2 |
4 |
–14 |
28 |

85-90 |
7 |
87.5 |
–1 |
1 |
–7 |
7 |

90-95 |
15 |
92.5 |
0 |
0 |
0 |
0 |

95-100 |
9 |
97.5 |
1 |
1 |
9 |
9 |

100-105 |
6 |
102.5 |
2 |
4 |
12 |
24 |

105-110 |
6 |
107.5 |
3 |
9 |
18 |
54 |

110-115 |
3 |
112.5 |
4 |
16 |
12 |
48 |

60 |
6 |
254 |

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Solution Find the Mean, Variance and Standard Deviation Using Short-cut Method Height in Cms and No. of Children Concept: Variance and Standard Deviation - Shortcut Method to Find Variance and Standard Deviation.