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Answer the given question with proper steps.

**Q. ** The mean of the following distribution is 18. Find the frequency f of the class 19 — 21.

To solve this question, we first need to find the midpoints of each class and the product of midpoint and frequency.

Class | Frequency | Midpoint | Midpoint x Frequency |

11-13 | 3 | 12 | 36 |

13-15 | 6 | 14 | 84 |

15-17 | 9 | 16 | 144 |

17-19 | 13 | 18 | 234 |

19-21 | f | 20 | 20f |

21-23 | 5 | 22 | 110 |

23-25 | 4 | 24 | 96 |

Now, the formula for calculating the mean is:

$Mean=\frac{Sumof(Frequency\times Midpoint)}{Totalfrequency}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Itisgiventhatmean=18\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}So,\phantom{\rule{0ex}{0ex}}18=\frac{36+84+144+234+20f+110+96}{3+6+9+13+f+5+4}\phantom{\rule{0ex}{0ex}}18=\frac{704+20f}{40+f}\phantom{\rule{0ex}{0ex}}720+18f=704+20f\phantom{\rule{0ex}{0ex}}20f-18f=720-704\phantom{\rule{0ex}{0ex}}2f=16\phantom{\rule{0ex}{0ex}}f=8\phantom{\rule{0ex}{0ex}}$

Thus, the frequency of the class 19-21 is 8.

Hope it helps.

Regards

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