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If the mean of the following data is 20.2, then find the value of p.

x_{i} |
10 | 15 | 20 | 25 | 30 |

f_{i} |
6 | 8 | p | 10 | 6 |

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#### Solution

We have,

`bb(x_i)` | `bb(f_i)` | `bb(x_i f_i)` |

10 | 6 | 60 |

15 | 8 | 120 |

20 | p | 20p |

25 | 10 | 250 |

30 | 6 | 180 |

Total N = (30 + p) |
Total sum = (610 + 20 p) |

since, mean = 20.2

⇒ `(610 + 20"p")/(30 + "p")` = 20.2

⇒ 610 + 20p = 20.2 (30 + p)

⇒ 610 + 20p = 606 + 20.2p

⇒ 20.2p - 20p = 610 - 606

⇒ 0.2p = 4

⇒ p = `4/0.2`

⇒ p = 20

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