A system of dividing the given random distribution of the data or values in a series into ten groups of similar frequency is known as deciles.

Li = Lower limit of the decile class
N = Sum of the absolute frequency
F_{i-1} = Absolute frequency lies below the decile class
a_{i} = Width of the class containing the decile class

Find the deciles for the following data. 3, 15, 24, 28, 33, 35, 38, 42, 43, 38, 36, 34, 29, 25, 17, 7, 34, 36, 39, 44, 31, 26, 20, 11, 13, 22, 27, 47, 39, 37, 34, 32, 35, 28, 38, 41, 48, 15, 32, 60, 56, 13.

Data = 3, 15, 24, 28, 33, 35, 38, 42, 43, 38, 36, 34, 29, 25, 17, 7, 34, 36, 39, 44, 31, 26, 20, 11, 13, 22, 27, 47, 39, 37, 34, 32, 35, 28, 38, 41, 48, 15, 32, 60, 56, 13. N = 42

Deciles Statistics

Let us calculate the Cumulative Frequency value for the given data,
Cumulative Frequency is calculated using the formula,
**F _{i} = F_{i-1} + f_{i}**

Class | Frequency f_{i} | Cumulative Frequency F_{i} |
---|---|---|

3 - 10 | 2 | 2 |

10 - 17 | 5 | 7 |

17 - 24 | 3 | 10 |

24 - 31 | 7 | 17 |

31 - 38 | 12 | 29 |

38 - 45 | 9 | 38 |

45 - 52 | 2 | 40 |

52 - 59 | 1 | 41 |

59 - 66 | 1 | 42 |

In the above table, class denotes the range of values Frequency (fi) denotes the number of values between the class range from the given data. For Ex: Class range 3-10 represents that there are two values i.e. 3 and 7 in the given data

Now let us calculate the deciles for each class.
**Calculation of First Decile:**
First, consider k = 1
Since the value is 4.2, it is present inside the class range [3, 10)]
Now, substitute the values in the formula,
D1 = 3 + (4.2-0) / 2 * 7
D1 = 3+2.1*7
D1 = 17.7

**Calculation of Second Decile:**
Consider, k = 2
K.N / 10 = 2*42 / 10 = 8.4
The value is 8.4. So, it is present inside the class range [10, 17)]
Substitute the values in the formula,
D2 = 10 + (8.4-2) / 5 * 7
D2 = 3+1.28*7
D2 = 18.96
Similarly, calculate the deciles for rest of the seven classes.