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**Quartiles**

**Quartiles**are the values that divide the data arranged in ascending or descending order into four equal parts. A distribution is divided into four equal parts by three

**quartiles**.

**-**The first or lower quatile (Q

_{1}) is the point below which 25% of the items lie and above which 75% of the items lie.

**-**The second quartile (Q

_{2}) is the point below which 50 percent of the items lie and above which 50 % of the items lie. Of course, the second quartile is the median.

**-**The third (upper) quartile ( Q

_{3 }) is the point below which 75 % of the items lie and above which 25 % of the items lie.

If N be the number of items in ascending
or descending order of a distribution then in the case of individual and
discrete data,

In case of the grouped data,

*Where, L= lower limit of the quartile class*

*f = frequency of the quartile class*

*cf = cumulative frequency of preceding class*

*i = height of class-interval*

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*Workout Examples*

*Workout Examples*

*Example 1: Calculate the quartiles from the data: 4, 6, 5, 9, 8, 10, 3*

*Solution:*

*Here,*

*Data in ascending order: 3, 4, 5, 6, 8, 9, 10*

*No. of data (N) = 7*

*Example 2: Calculate the quartiles from the data: 5, 8, 10, 11, 12, 14, 16, 18, 20, 4*

*Solution:*

*Here,*

*Data in ascending order: 4, 5, 8, 10, 11, 12, 14, 16, 18, 20*

*No. of data (N) = 10*

*Example 3: Compute Q*_{1}and Q_{3}from the following data.

x |
5 |
20 |
24 |
29 |
35 |

f |
2 |
3 |
4 |
3 |
5 |

*Solution:*

*Here, frequency table,*

x |
f |
cf |

520242935 |
23435 |
2591217 |

N = 17 |

*Total number of data (N) = 17*

*Example 4: Compute Q*_{1}and Q_{3}from the following data.

Marks in maths |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |

No. of students |
5 |
20 |
10 |
15 |
7 |

*Solution:*

*Here, frequency table,*

Marks (x) |
f |
cf |

0-1010-2020-3030-4040-50 |
52010157 |
525355057 |

N = 57 |

*Here, N = 57*

*You can comment your questions or problems regarding the*

**quartiles**here.
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