**Percentiles for Grouped Data**:

Percentiles can also be calculated for grouped data which is done with the help of following formulae;

Where,

*ℓ*= lower boundary of the class containing the

*P*

_{35}or

*P*

_{99}, i.e. the class corresponding to the cumulative frequency in which 35

*N*/100 or 99

*N*/100 lies

*w*= class interval size of the class containing

*P*

_{35}or

*P*

_{99}.

*f*= frequency of the class containing

*P*

_{35}or

*P*

_{99}.

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

‹

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

*P*

_{35}or

*P*

_{99}.

For Example:

We will calculate thirty-seventh, forty-fifth and ninetieth percentile from the frequency distribution of weights of 120 students, by using the this table.

=182.83 pounds

Conclusion

From

*P*

_{37},

*P*

_{45}and

*P*

_{90}we have concluded or interpreted that 37% student weigh 147.5 pounds or less. Similarly, 45% students weigh 151.1 pounds or less and 90% students weigh 182.83 pounds or less.

Big Example:

Find the percentiles *P*_{8}, *P*_{50}, and *P*_{85} of the following data.

Columns Load | Frequency |
---|---|

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 percentile common formula of continuous or discrete distribution (Grouped Data).

*ℓ*= the lower boundary of relevant percentile class

‹

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

*f*= the frequency of relevant percentile class

*w*= the length of the real interval

4) find eighth percentile.

5) find fiftieth percentile.

6) find eighty-fifth percentile.

7)

**Find the percentile number of the estimated datum**of 115 in the above data.

*ℓ*= the lower boundary of related percentile class=109.5

‹

*C*= the cumulative frequency of the previous interval of related percentile class=14

*f*= the frequency of related percentile class=4

*w*= the length of the real interval =20

then

*X*=15.1, then the percentile number

Let’s read post Calculation of Quartiles, Deciles & Percentiles for Grouped Data.

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