Measure of Dispersion Part (2)

Standard Deviation

Deviation: the difference between an individual value in a set of data and the mean for the data.

Standard Deviation is the square root of the variance. 

        

Key for formula:

FORMULA 

Standard Deviation for Grouped Data

Extra Key:

f_i = the frequency for a given interval

m_i = the midpoint of the interval

FORMULA

Example 1 (Ungrouped - Population):

The table below shows the height of 5 friends:

NAME	HEIGHT (m)
Barry	1.60
Michael	1.70
David	1.90
Steven	1.65
Ronaldo	1.85

Find out the Mean, the Variance, and the Standard Deviation.

Find the mean

Find the variance:

1^st step: find the difference of each height and the average (mean):

Barry = 1.60 – 1.74

            = -0.14m

Michael = 1.70 – 1.74

               = -0.04m

David = 1.90 – 1.74

            = -0.16m

Steven = 1.65 – 1.74

              = -0.09m

Ronaldo = 1.85 – 1.74

                = -0.11m

2^nd step: Take each difference, square it, and then average the result:

Standard Deviation (Square root of Variance)

Measure of Dispersion part (1)

The measures of dispersion are used examine the spread of the data. These are the methods used:

• Range
• Quartiles
• Variance
• Standard Deviation

RANGE

Range is the simplest method for measuring dispersion. It is the difference between the largest value and the smallest value in the data set. 

R = X_max – X_min

Example:
3, 5, 7, 9, 16, 18, 25

Range, R = 25 – 3

   = 22

QUARTILE

Quartiles divide a set of ordered data into four groups with equal numbers of values.

The interquartile range (IQR) is Q₃ – Q_1.

Example:

Calculate the median and interquartile of Brunei Darussalam’s temperature during the day in the following dates.