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The following table gives the distribution of manual workers in a city, find the mean expenditure (In Rupees) per household by using an appropriate method expenditure =100-150,150-200,200-250,250-300,300-350,350-400,400-450,450-500 frequency=24,40,33,28,30,22,16,7

    • Posted by Umang Thakre 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    <th scope="col">Expenditure
    100-150 24 125 -200 -4 -96
    150-200 40 175 -150 -3 -120
    200-250 33 225 -100 -2 -66
    250-300 28 275 -50 -1 -28
    300-350 30 325 0 0 0
    350-400 22 375 50 1 22
    400-450 16 425 100 2 32
    450-500 7 475 150 3 21
      {tex} N = \sum f _ { i } = 200{/tex}       {tex} \sum f _ { i } u _ { i } = - 235{/tex}

    Let the assumed mean be A=325.
    N = 200, A =325, h=50, and {tex} \Sigma f _ { i } u _ { i }{/tex}=-235
    {tex} mean=\overline { x} = A + h \frac { 1 } { N } \Sigma f _ { i } u _ { i }{/tex}
    {tex} \Rightarrow \quad \overline { x } = 325 + 50 \times \left\{ \frac { - 235 } { 200 } \right\}{/tex}
    {tex} \Rightarrow \quad \overline { x } = 325 - \frac { 235 } { 4 } = 325 - 58.75 = 266.25{/tex}

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