Class 10

Math

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Statistics

During the medical check-up of $35$ students of a class, their weights were recorded as follows:

Weight (in kg) | Number of students |

Less than $38$ Less than $40$ Less than $42$ Less than $44$ Less than $46$ Less than $48$ Less than $50$ Less than $52$ | $0$ $3$ $5$ $9$ $14$ $28$ $32$ $35$ |

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Now,

Weight (in kg) | Number of students (Frequency) |

$0−38$ | $0$ |

$38−40$ | $3−0=3$ |

$40−42$ | $5−3=2$ |

$42−44$ | $9−5=4$ |

$44−46$ | $14−9=5$ |

$46−48$ | $28−14=14$ |

$48−50$ | $32−28=4$ |

$50−52$ | $35−32=3$ |

Mode: The class which have highest frequency.

In this case, class interval $46−48$ is the modal class.

Now,

Lower limit of modal class, $l=46,h=2,f_{1},=14,f_{0}=5,f_{2}=4$

We know that,

Mode $=l+(2f_{1}−f_{0}−f_{2}f_{1}−f_{0} )×h$$=46+(2(14)−5−414−5 )×2$

$=46+199 ×2$

$=46+0.95$

Mode $=46.95$, verified.