# Given this data, determine the standard deviation.(Range/Frequency) [12-15/7;16-19/4; 20-23/6; 24-27/2;28-31/1)

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thilina-g | Certified Educator

Range       frequency(f)    midpoint(x)      x*f

12-15        7                      13.5              94.5

16-19        4                       17.5             70

20-23        6                      21.5              129

24-27        2                      25.5              51

28-31        1                      29.5               29.5

The total number of elements, `sumf = 20`

`sumxf = 374`

`barx = (sumxf)/(sumf) = 374/20 = 18.7` = mean

freq(f)   midpoint(x)     x*f           `x-barx`        `(x-barx)^2`      `(x-barx)^2f`

7            13.5          94.5            -5.2            27.04         189.28

4            17.5           70              -1.2            1.44           5.76

6            21.5          129             2.8              7.84           47.04

2            25.5          51               6.8             46.24          92.48

1            29.5          29.5             10.8           116.64        116.64

`sum(x-barx)f = 451.2`

Variance = `s^2 = (sum(x-barx)^2)/(sumf -1) = 451.2 /(20-1) = 23.747`

the standard deviation  = sqrt(s^2) = sqrt(23.747) = 4.873

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