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# Find the mean and variance for the first 10 multiples of 3

**Solution:**

The first ten multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Here, the number of observations, n = 10

Mean of the data

x = (∑^{10}_{i = 1}x_{i})/10

= 165/10

= 16.5

The following table is obtained for the first 10 multiples of 3

x_{i} |
(x_{i} - x) |
(x_{i} - x)² |

3 | - 13.5 | 182.25 |

6 | - 10.5 | 110.25 |

9 | - 7.5 | 56.25 |

12 | - 4.5 | 20.25 |

15 | - 1.5 | 2.25 |

18 | 1.5 | 2.25 |

21 | 4.5 | 20.25 |

24 | 7.5 | 56.25 |

27 | 10.5 | 110.25 |

30 | 13.5 | 182.25 |

742.5 |

The variance of the data

**(σ²) = 1/n ∑ ^{10}_{i = 1}(x_{i} - x)^{2}**

= 1/10 × 742.5

= 74.25

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.2 Question 3

## Find the mean and variance for the first 10 multiples of 3

**Summary:**

The mean and variance for the first 10 multiples of 3 are 16.5 and 74.25

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