**Decile for Grouped Data**

Decile for grouped data can be calculated from the following formulae;

Where,

*ℓ*= lower boundary of the class containing the

*D*

_{2}or

*D*

_{9}, i.e. the class corresponding to the cumulative frequency in which 2

*N*/10 or 9

*N*/10 lies

*w*= class interval size of the class containing

*D*

_{2}or

*D*

_{9}

*f*= frequency of the class containing

*D*

_{2}or

*D*

_{9}

*N*= number of values, or the total frequency

‹

*C*= cumulative frequency of the class preceding the class containing

*D*

_{2}or

*D*

_{9}

For Example:

We will calculate fourth, seventh and ninth deciles from the frequency distribution of weights of 120 students, as provided in this table.

=182.83 pounds

Conclusion:

From

*D*

_{4},

*D*

_{7}and

*D*

_{9}we conclude that 40% students weigh 148.79 pounds or less, 70% students weigh 164.5 pounds or less and 90% students weigh 182.83 pounds or less.

Another example:

Find the deciles *D*_{1}, *D*_{5}, and *D*_{9} of the following data.

Columns Load | Freqency (f)_{i} |
---|---|

50-69 | 3 |

70-89 | 7 |

90-109 | 4 |

110-129 | 4 |

130-149 | 9 |

Solution:

1) Find each cumulative frequency and each real interval.

2) Remember the decile common formula of continuous or discrete distribution (Grouped Data).

*ℓ*= the lower boundary of relevant decile class

*N*= total frequency =Σ

*f*

‹

*C*= the cumulative frequency of the previous interval of relevant decile class

*f*= the frequency of relevant decile class

*w*= the length of the real interval

3) Find first decile.

4) Find fifth decile.

5) Find ninth decile.

Let’s read post Calculation of Percentiles for Grouped Data.

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