**Example:**Suppose we have the following data set:

Class Interval |
Frequency |

10 – 20 |
2 |

20 – 30 |
4 |

30 – 40 |
2 |

40 – 50 |
4 |

Find the lower and the upper quartiles of the above continuous data?

**Solution:**First we determine the class marks and cumulative frequencies as follows:

Class Interval |
Class marks |
Frequency |
Cumulative Frequency |

10 – 20 |
15 |
2 |
2 |

20 – 30 |
25 |
4 |
6 |

30 – 40 |
35 |
2 |
8 |

40 – 50 |
45 |
4 |
12 |

We then find the Median as: sum of frequencies /2 = 12 /2 = 6,

So, our median class is: 30 – 40. The value of median will be evaluated as:

M = 30 + (6 – 6)/4 * 10 = 30,

Next we determine smallest and largest values in the data set:

Smallest Value: 15 and,

Largest value: 45,

To find the lower quartile: (15 + 30) /2 = 45 /2 = 22.5,

To find the upper quartile: (45 + 30) /2 = 75 /2 = 37.5,

Thus we get the values for upper and lower quartiles as 37.5 and 22.5 respectively.