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Number of mangoes |
50-52 |
53-55 |
56-58 |
59-61 |
62-64 |

Number of boxes |
15 |
110 |
135 |
115 |
25 |

Answer :

Since, the given data is not continuous so we add 0.5 to the upper limit and subtract 0.5 from the lower limit as the gap between two intervals are 1

Here, assumed mean (A) = 57, Class size (h)

= 3

Here, the step deviation is used because the frequency values are big.

Class Interval | Number of boxes \( (f_i) \) | Mid-point \( (x_i) \) | \( d_i \ = \ x_i \ - \ A \) | \( f_i d_i \) |

49.5-52.5 | 15 | 51 | -6 | 90 |

52.5-55.5 | 110 | 54 | -3 | -330 |

55.5-58.5 | 135 | 57 | 0 | 0 |

58.5-61.5 | 115 | 60 | 3 | 345 |

61.5-64.5 | 25 | 63 | 6 | 150 |

\( \sum f_i \ = \ 400 \) | \( \sum f_i d_i \ = \ 75 \) |

The formula to find out the Mean is:

\( \overline{x} \ = \ A \ + h \frac{ \sum \ f_i d_i}{ \sum f_i} \ = \ 57 \ + \ 3 × \frac{75}{400} \)

\(= \ 57 \ + \ 0.1875 \ = \ 57.19 \)

\(\therefore \) The mean number of mangoes kept in a packing box is 57.19

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