Quartile

Quartile

A quartile is the variate value which divides the value of given frequency into four equal parts. There are three quartiles, they are: -

  1. Lower Quartile (Q1)
  2. Middle Quartile (Q2)
  3. Upper Quartile (Q3)

.

Quartiles can be calculated as following ways: -


Individual series
After arranging the data in ascending order, the quartiles are calculated by applying the following formula:
Lower quartile (Q1) = value of (\(\frac{N+1}{4}\))thitem.

Upper Quartile (Q3) =value of 3(\(\frac{N+1}{4}\))th item.

Where, N = Total sum of frequency.

Discrete Series
When the data are arranged in ascending order, the quartile is calculated by the following formula:
Lower quartile (Q1) = value of (\(\frac{N+1}{4}\))thitem

Upper quartile (Q3) = value of 3(\(\frac{N+1}{4}\))th item

Where N = Total sum of frequency

Continuous Series
For continuous series, the following formulae area used.
Lower quartile class = value of 3(\(\frac{N}{4}\))th item

Exact Lower Quartile (Q1) = L + \(\frac{\frac{N}{4} - C.F}{f}\)× i
where,
L = Lower limit of corresponding class
f = frequency
c.f = cumulative frequency
i = class size
N = Total sum of frequency

Upper quartile class = value of 3(\(\frac{N}{4}\))th item

Exact upper quartile (Q3) = L + \(\frac{\frac{3N}{4} - C.F}{f}\)× i

  • Quartile is the variate value which divides the value of given frequency into four equal parts.
  • There are three quartiles, they are: lower quartile, middle quartile and upper quartile

 

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  • In the data set below, what is the lower quartile?

    1, 2, 4, 4, 5, 6, 6, 6, 7, 7, 8

    4
    2
    6
    7
  • In the data set below, what is the upper quartile?

    1, 2. 4, 4, 5, 6, 6, 6 , 7, 7, 8

    6
    5
    8
    7
  • In the data set below, what is the lower quartile?

    29, 34, 38, 41, 51, 57, 65, 65, 81, 83

    41
    29
    38
    34
  • In the data set below, what is the upper quartile?

    17, 23, 32, 36, 52, 54, 67, 83, 98, 99

    67
    99
    83
    98
  • In the data set below, what is the lower quartile?
    2, 2, 2, 2, 3 , 5, 5, 5, 7, 8, 9, 9

    5
    3
    2
    7
  • In the data set below, what is the upper quartile?
    2, 2, 2, 2, 3 , 5, 5, 5, 7, 8, 9, 9

    7
    9
    8
    5
  • In the data set below, what is the upper quartile?

    20, 38, 52, 54, 60, 87, 93

    54
    93
    87
    60
  • In the data set below, what is the lower quartile?

    10, 27, 27, 29, 44, 6727

    44
    27
    10
    29
  • In the data set below, what is the lower quartile?

    19,   37,   41,   43,   83,  85,   94

     

     

     

     

    43
     85
    37
    19
  • In the data set below, what is the upper quartile?

    19,   37,   41,   43,   83,  85,   94

     

     

     

     

     

    43
    94
    85
    83
  • In the data set below, what is the lower quartile?

    23, 26, 26, 30, 34, 42, 49, 60, 96, 96, 96

    32
    34
    26
    30
  • In the data set below, what is the upper quartile?
    59, 86, 86, 88, 96, 96

    86
    59
    88
    96
  • In the data set below, what is the lower quartile?

    2, 4, 5, 6, 6, 7, 8, 8, 8, 9

    6
    5
    4
    2
  • In the data set below, what is the upper quartile?

    2, 4, 5, 6, 6, 7, 8, 8, 8, 9

    7
    8
    9
    6
  • In the data set below, what is the upper quartile?

    1, 1, 1, 2, 2, 4, 4, 5, 5, 6

    4
    5
    6
    1
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