#### Question

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 |

#### Solution

We have,

`x_i` | `f_i` | `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 + 20p) / ( 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

Is there an error in this question or solution?

Solution If the Mean of the Following Data is 20.2, Then Find the Value of P. Concept: Measures of Central Tendency.