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# The percentage of marks obtained by 100 students in an examination are given below

Marks 30-35 35-40 40-45 45-50 50-55 55-60 60-65

Frequency 14 16 18 23 18 8 3

Determine the median percentage of marks

**Solution:**

Given, the table represents the marks and frequency of 100 students in an examination.

We have to determine the median percentage of marks.

Marks | Frequency | Cumulative frequency |

30 - 35 | 14 | 14 |

35 - 40 | 16 | 30 |

40 - 45 | 18 | 48 |

45 - 50 | 23 | 71 |

50 - 55 | 18 | 89 |

55 - 60 | 8 | 97 |

60 - 65 | 3 | 100 |

Median = l + [(n/2 - cf)/f]h

Where, l is lower limit of the median class

n is the number of observations

h is the class size

cf is the cumulative frequency of the class preceding the median class

f is the frequency of the median class

From the table,

n/2 = 100/2 = 50

The observation lies in the class 45 - 50

Lower limit of the class, l = 45

Class size, h = 5

Cumulative frequency of the class preceding the median class, cf = 48

Frequency of the median class, f = 23

Now, median = 45 + [(50 - 48)/23](5)

= 45 + (2/23)5

= 45 + (10/23)

= 45.4

Therefore, the median percentage of marks is 45.4

**✦ Try This: **The percentage of marks obtained by 100 students in an examination are given below:

Marks | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 | 55-60 |

Frequency | 12 | 14 | 16 | 22 | 19 | 9 |

Determine the median percentage of marks.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 14

**NCERT Exemplar Class 10 Maths Exercise 13.3 Sample Problem 3**

## The percentage of marks obtained by 100 students in an examination are given below: Marks 30-35 35-40 40-45 45-50 50-55 55-60 60-65 Frequency 14 16 18 23 18 8 3. Determine the median percentage of marks

**Summary:**

From the above data, the median percentage of marks obtained by 100 students in an examination is 45.4

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