# NCERT Class 11-Math՚S: Exemplar Chapter – 15 Statistics Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 18**:

Determine the mean and standard deviation for the following distribution:

Marks | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

Frequency | 1 | 6 | 6 | 8 | 8 | 2 | 2 | 3 | 0 | 2 | 1 | 0 | 0 | 0 | 1 |

**Answer**:

Given: the frequency distribution

To find: the mean and standard deviation

Let us make a table of the given data and append other columns after calculations

Marks | Frequency | |

2 | 1 | |

3 | 6 | |

4 | 6 | |

5 | 6 | |

6 | 8 | |

7 | 2 | |

8 | 2 | |

9 | 3 | |

10 | 0 | |

11 | 2 | |

12 | 1 | |

13 | 0 | |

14 | 0 | |

15 | 0 | |

16 | 1 | |

Total |

Here mean,

So the above table with more columns is as shown below,

Marks | Frequency | ||||

2 | 1 | ||||

3 | 6 | ||||

4 | 6 | ||||

5 | 6 | ||||

6 | 8 | ||||

7 | 2 | ||||

8 | 2 | ||||

9 | 3 | ||||

10 | 0 | ||||

11 | 2 | ||||

12 | 1 | ||||

13 | 0 | ||||

14 | 0 | ||||

15 | 0 | ||||

16 | 1 | ||||

Total |

And we know standard deviation is

Substituting values from above table, we get

Hence the mean and standard deviation of the marks are and respectively.