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# Find the missing frequency $(p)$ for the following distribution whose mean is 7.68.

$x$ | 3 | 5 | 7 | 9 | 11 | 13 |

$f$ | 6 | 8 | 15 | $p$ | 8 | 4 |

Given:

The mean of the given data is 7.68.

To do:

We have to find the value of $p$.

Solution:

$x$ | $f$ | $f \times\ x$ |

3 | 6 | 18 |

5 | 8 | 40 |

7 | 15 | 105 |

9 | $p$ | $9p$ |

11 | 8 | 88 |

13 | 4 | 52 |

Total | $41+p$ | $303+9p$ |

We know that,

Mean$=\frac{\sum fx}{\sum f}$

Therefore,

Mean $7.68=\frac{303+9p}{41+p}$

$7.68(41+p)=303+9p$

$314.88+7.68p=303+9p$

$9p-7.68p=314.88-303$

$p=\frac{11.88}{1.32}$

$p=\frac{1188}{132}$

$p=9$

The value of $p$ is $9$.

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