The following frequency distribution shows the profit (in ₹) of shops in a particular area of city:

Profit per shop (in ‘000) |
No. of shops |

0 – 10 | 12 |

10 – 20 | 18 |

20 – 30 | 27 |

30 – 40 | 20 |

40 – 50 | 17 |

50 – 60 | 6 |

Find graphically The limits of middle 40% shops.

#### Solution

The less than cumulative frequency table is

Profit per shop (in ‘000) |
No. of shops (f) |
CumulativeFrequency (less than type) |

0 – 10 | 12 | 12 |

10 – 20 | 18 | 30 |

20 – 30 | 27 | 57 |

30 – 40 | 20 | 77 |

40 – 50 | 17 | 94 |

50 – 60 | 6 | 100 |

Total |
100 |

Points to be plotted are (10, 12), (20, 30), (30, 57), (40, 77), (50, 94), (60, 100).

The middle 40% shops will lie between the limits given by P_{30} and P_{70.}

N = 100

For P_{30} `(30"N")/(100)=(30(100))/(100)` = 30

For P_{70} `(70"N")/(100)=(70(100))/(100)` = 70

∴ We take the points having Y co-ordinates 30 and 70 on Y-axis. From these points, we draw lines parallel to X-axis. From the points where these lines intersect the curve, we draw perpendiculars on X-axis.

X-Co-ordinates of these points gives the values of P_{30} and P_{70}.

∴ P_{30} ≈ 20, P_{70} ≈ 36