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Weight in kg |
Number of students |

Less than 38 |
0 |

Less than 40 |
3 |

Less than 42 |
5 |

Less than 44 |
9 |

Less than 46 |
14 |

Less than 48 |
28 |

Less than 50 |
32 |

Less than 52 |
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

Answer :

From the given data, to represent the table in the form of graph, choose the upper limits of the class intervals are in x-axis and frequencies on y-axis by choosing the convenient scale.

Now plot the points corresponding to the ordered pairs given by (38, 0), (40, 3), (42, 5), (44, 9),(46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper an join them to get a smooth curve. The curve obtained is known as less than type ogive.

Locate the point 17.5 on the y-axis and draw a line parallel to the x-axis cutting the curve at a point. From the point, draw a perpendicular line to the x-axis.
The intersection point perpendicular to x-axis is the median of the given data.
Now, to find the mode by making a table.

Class interval | Number of students(Frequency) | Cumulative Frequency |

Less than 38 | 0 | 0 |

Less than 40 | 3-0=3 | 3 |

Less than 42 | 5-3=2 | 8 |

Less than 44 | 9-5=4 | 9 |

Less than 46 | 14-9=5 | 14 |

Less than 48 | 28-14=14 | 28 |

Less than 50 | 32-28=4 | 32 |

Less than 52 | 35-22=3 | 35 |

The class 46-48 has the maximum frequency, therefore, this is modal class

Here, l = 46, h = 2, f

Now, Mode \( = \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)

\(= \ 46 \ + \ \frac{14 \ - \ 5}{28 \ - \ 5 \ - \ 4} \ × \ 2 \ \)

\( = \ 46 \ + \ \frac{9}{19} \ × \ 2 \)

\(= \ 46 \ + \ 0.95 \ = \ 46.95 \)

Thus, mode is verified.

- The following distribution gives the daily income of 50 workers of a factory. Daily income in Rupees 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.
- The following tables gives production yield per hectare of wheat of 100 farms of a village. Production Yield 50-55 55-60 60-65 65-70 70-75 75-80 Number of farms 2 8 12 24 38 16 Change the distribution to a more than type distribution and draw its ogive.

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