Class 10 Math All topics Statistics

If the mean of the following distribution $54$, find the value of $p$:

Class: | $0−20$ | $20−40$ | $40−60$ | $60−80$ | $80−100$ |

Frequency: | $7$ | $p$ | $10$ | $9$ | $13$ |

Solution: Computation Arithematic Mean

We have,

A= 50, N= 39 +p, h= 20, $∑f_{i}u_{i}=21−p$ and $X=54$

Class | Mid-values ($x_{i}$) | requency ($f_{i}$) | $d_{i}=x_{i}−50$ | $u_{i}=20x_{i}−50 $ | $f_{i}u_{i}$ |

0-20 | 10 | 7 | -40 | -2 | -14 |

20-40 | 30 | pF | -20 | -1 | -p |

40-60 | 50 | 10 | 0 | 0 | 0 |

60-80 | 70 | 9 | 20 | 1 | 9 |

80-100 | 90 | 13 | 40 | 2 | 26 |

$∑f_{i}=39+p$ | $∑f_{i}u_{i}=21−p$ |

A= 50, N= 39 +p, h= 20, $∑f_{i}u_{i}=21−p$ and $X=54$

$∴Mean=A+h(N1 ∑f_{i}u_{i})$

$⇒54=50+20×(39+p21−p )$

$⇒4=20×(39+p21−p )$

$⇒1=5(39+p21−p )⇒39+p=105−5p⇒6p=66⇒p=11$

$⇒1=5(39+p21−p )⇒39+p=105−5p⇒6p=66⇒p=11$

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