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Daily expenditure(in Rs) |
100-150 |
150-200 |
200-250 |
250-300 |
300-350 |

Number of households |
4 |
5 |
12 |
2 |
2 |

Answer :

Let us assume the mean (A) = 225, Class size (h) = 50

Class Interval | Number of households \( ( f_i ) \) | Mid-point \( ( x_i ) \) | \( d_i \ = \ x_i \ - \ A \) | \( u_i \ = \ \frac{d_i}{50} \) | \( f_i u_i \) |

100-150 | 4 | 125 | -100 | -2 | -8 |

150-200 | 5 | 175 | -50 | -1 | -5 |

200-250 | 12 | 225 | 0 | 0 | 0 |

250-300 | 2 | 275 | 50 | 1 | 2 |

300-350 | 2 | 325 | 100 | 2 | 4 |

\( \sum f_i \ = \ 25 \) | \( \sum f_i u_i \ = \ -7 \) |

\( \overline{x} \ = \ A \ + h \frac{ \sum \ f_i u_i}{ \sum f_i} \)

\( = \ 225 \ + \ 50 × \frac{-7}{25} \)

\(= \ 225 \ - \ 14 \ = \ 211 \)

\(\therefore \) The mean daily expenditure on food is 211

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