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Home > Statistical Methods calculators > Quartile, Decile, Percentile, Octile, Quintile for grouped data example
Quartile Example for grouped data ( Enter your problem )
( Enter your problem )
  1. Formula & Example
  2. Quartile Example
  3. Decile Example
  4. Percentile Example
  5. Octile Example
  6. Quintile Example
 		Other related methods
  1. Mean, Median and Mode
  2. Quartile, Decile, Percentile, Octile, Quintile
  3. Population Variance, Standard deviation and coefficient of variation
  4. Sample Variance, Standard deviation and coefficient of variation
  5. Population Skewness, Kurtosis
  6. Sample Skewness, Kurtosis
  7. Geometric mean, Harmonic mean
  8. Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
  9. Five number summary
  10. Box and Whisker Plots
  11. Mode using Grouping Method
  12. Less than type Cumulative frequency table
  13. More than type Cumulative frequency table
  14. Class and their frequency table
1. Formula & Example
(Previous example)		3. Decile Example
(Next example)

2. Quartile Example


1. Calculate Quartile-3 from the following grouped data
XFrequency
01
15
210
36
43


Solution:
`x`Frequency
`f`		`cf`
011
156
21016
3622
4325
---------
n = 25--


Here, `n = 25`

`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*26)/4)^(th)` value of the observation

`=(19.5)^(th)` value of the observation

`=3`

2. Calculate Quartile-1 from the following grouped data
XFrequency
103
1112
1218
1312
143


Solution:
`x`Frequency
`f`		`cf`
1033
111215
121833
131245
14348
---------
n = 48--


Here, `n = 48`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(49/4)^(th)` value of the observation

`=(12.25)^(th)` value of the observation

`=11`

3. Calculate Quartile-3 from the following grouped data
ClassFrequency
2 - 43
4 - 64
6 - 82
8 - 101


Solution:
ClassFrequency
`f`		`cf`
2 - 433
4 - 647
6 - 829
8 - 10110
---------
n = 10--


Here, `n = 10`


`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*10)/4)^(th)` value of the observation in `cf` column

`=(7.5)^(th)` value of the observation in `cf` column

and it lies in the class `6 - 8`.

`:. Q_3` class : `6 - 8`

The lower boundary point of `6 - 8` is `6`.

`:. L = 6`

`Q_3 = L + ((3 n)/4 - cf)/f * c`

`=6 + (7.5 - 7)/2 * 2`

`=6 + (0.5)/2 * 2`

`=6 + 0.5`

`=6.5`

4. Calculate Quartile-1 from the following grouped data
ClassFrequency
0 - 25
2 - 416
4 - 613
6 - 87
8 - 105
10 - 124


Solution:
ClassFrequency
`f`		`cf`
0 - 255
2 - 41621
4 - 61334
6 - 8741
8 - 10546
10 - 12450
---------
n = 50--


Here, `n = 50`


`Q_1` class :

Class with `(n/4)^(th)` value of the observation in `cf` column

`=(50/4)^(th)` value of the observation in `cf` column

`=(12.5)^(th)` value of the observation in `cf` column

and it lies in the class `2 - 4`.

`:. Q_1` class : `2 - 4`

The lower boundary point of `2 - 4` is `2`.

`:. L = 2`

`Q_1 = L + (( n)/4 - cf)/f * c`

`=2 + (12.5 - 5)/16 * 2`

`=2 + (7.5)/16 * 2`

`=2 + 0.9375`

`=2.9375`

5. Calculate Quartile-3 from the following grouped data
ClassFrequency
10 - 2015
20 - 3025
30 - 4020
40 - 5012
50 - 608
60 - 705
70 - 803


Solution:
ClassFrequency
`f`		`cf`
10 - 201515
20 - 302540
30 - 402060
40 - 501272
50 - 60880
60 - 70585
70 - 80388
---------
n = 88--


Here, `n = 88`


`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*88)/4)^(th)` value of the observation in `cf` column

`=(66)^(th)` value of the observation in `cf` column

and it lies in the class `40 - 50`.

`:. Q_3` class : `40 - 50`

The lower boundary point of `40 - 50` is `40`.

`:. L = 40`

`Q_3 = L + ((3 n)/4 - cf)/f * c`

`=40 + (66 - 60)/12 * 10`

`=40 + (6)/12 * 10`

`=40 + 5`

`=45`

6. Calculate Quartile-1 from the following grouped data
ClassFrequency
20 - 25110
25 - 30170
30 - 3580
35 - 4045
40 - 4540
45 - 5035


Solution:
ClassFrequency
`f`		`cf`
20 - 25110110
25 - 30170280
30 - 3580360
35 - 4045405
40 - 4540445
45 - 5035480
---------
n = 480--


Here, `n = 480`


`Q_1` class :

Class with `(n/4)^(th)` value of the observation in `cf` column

`=(480/4)^(th)` value of the observation in `cf` column

`=(120)^(th)` value of the observation in `cf` column

and it lies in the class `25 - 30`.

`:. Q_1` class : `25 - 30`

The lower boundary point of `25 - 30` is `25`.

`:. L = 25`

`Q_1 = L + (( n)/4 - cf)/f * c`

`=25 + (120 - 110)/170 * 5`

`=25 + (10)/170 * 5`

`=25 + 0.2941`

`=25.2941`

This material is intended as a summary. Use your textbook for detail explanation.
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