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

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

**Solution:**

The graphical representation of cumulative frequency distribution is known as a cumulative frequency curve or an ogive.

The given cumulative frequency distributions of less than type are:

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 |

Taking upper-class limits on the x-axis and their respective cumulative frequencies on the y-axis, its ogive can be drawn as follows:

Here, n = 35 ⇒ n/2 = 17.5

Mark the point ‘A’ whose ordinate is 17.5 and its x-coordinate is 46.5.

Therefore, the median of this data is 46.5.

It can be observed that the difference between two consecutive upper-class limits is 2.

The class marks with their respective frequencies are obtained as below:

Weight (in Kg) | Frequency | Cumulative Frequency |

Less than 38 | 0 | 0 |

38-40 | 3 - 0 = 3 | 3 |

40-42 | 5 - 3 = 2 | 5 |

42-44 | 9 - 5 = 4 | 9 |

44-46 | 14 - 9 = 5 | 14 |

46-48 | 28 - 14 = 14 | 28 |

48-50 | 32 - 28 = 4 | 32 |

50-52 | 35 - 32 = 3 | 35 |

Total | n = 35 |

Cumulative frequency (cf) just greater than 17.5 is 28, belonging to class 46 - 48.

Therefore, median class = 46 - 48

- Class size, h = 2
- Lower limit of median class, l = 46
- Frequency of median class, f = 14
- Cumulative frequency of class preceding median class, cf = 14

Median = l + [(n/2 - cf)/f] × h

= 46 + [(17.5 - 14)/14] × 2

= 46 + 3.5/7

= 46 + 0.5

= 46.5

Therefore, the median of this data is 46.5. Hence, the value of the median is verified.

**ā Check: **NCERT Solutions for Class 10 Maths Chapter 14

**Video Solution:**

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

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.2 Question 2

**Summary:**

During the medical check-up of 35 students of a class, their weights were recorded. A less than type ogive for the given data is drawn. The median weight of the class of 35 students is 46.5 kg and the result is verified by using the formula.

**ā Related Questions:**

- 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
- The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
- The following distribution gives the daily income of 50 workers of a factory. Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.
- The following table gives production yield per hectare of wheat of 100 farms of a village. Change the distribution to a more than type distribution, and draw its ogive.

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