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When to Use Mean, Median and Mode
Central tendency as we now know is used to summarise the data. Let us now understand when can we use the mean,
median and mode.
u The mean is the most widely used measure of central tendency and is generally considered the best measure.
u When there are some missing or uncertain values in the data, the median is the preferred measure of central tendency.
u Mode is the preferred metric when measuring data on nominal (and sometimes even ordinal) scales.

Variance and Standard Deviation
Measures of central tendency (mean, median, and mode) provide the central value of the data set. Variance and
standard deviation are measures of dispersion (quartile, percentile, range). They provide information about the
distribution of data around the centre.
In this section, we will look at two other measures of dispersion: variance and standard deviation.

Variance
Variance measures the distance of each number in the data set from the mean and also from every other number in
2
the set. Variance is often depicted by the symbol: σ .
Calculating the variance
10 + 8 + 10 + 8 + 8 + 4
1 2 3 4 5 6 = 48
10, 8, 10, 8, 8, 4
48 ÷ n = 48 ÷ 6
n = 6
MEAN = 8
u The variance represents how far the data in your sample are grouped
around the mean.
u Data sets with low variance have data grouped closely about the mean.
u Data sets with high variance have data grouped far from the mean.

Step 1 Subtract the mean from each of your numbers in your sample. MEAN

Step 2 Square all the differences.

Step 3 Add all the squared numbers together. This number is called the sum of squares.

Mathematics for AI 139