Class 10

Math

All topics

Statistics

Compute the median from the following data:

Marks | $0−7$ | $7−14$ | $14−21$ | $21−28$ | $28−35$ | $35−42$ | $42−49$ |

Number of students | $3$ | $4$ | $7$ | $11$ | $0$ | $16$ | $9$ |

Marks | No of students $fi$ | $cf$ |

$0−7$ | $3$ | $3$ |

$7−14$ | $4$ | $7$ |

$14−21$ | $7$ | $14$ |

$21−28$ | $11$ | $25$ |

$28−35$ | $0$ | $25$ |

$35−42$ | $16$ | $41$ |

$42−49$ | $9$ | $50$ |

Sum $=50$ |

Median $=L+⎩⎨⎧ h×f(2N −cf) ⎭⎬⎫ $

Here:

$N=50$

$N/2=25$

Here cumulative frequency is $25$

Median class $=21−28$

So, $L=21,h=7,f=11$ and

$cf=cf$ of preceding class i.e $14$

Substitute all the value in the above formula, we get

Median $=21+{7×(25−14)/11}$

$=28$