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Descriptive statistics

Placeholder topic. Summarising data with the mean, median and standard deviation.

Placeholder content. This sample topic exists to demonstrate the platform. Preview reference: FREE-NOTES-EN-2c91.

Why describe data?

Before testing anything, we summarise a sample with a few numbers. The mean (average) tells us where the data is centred, and the standard deviation tells us how spread out it is.

The mean

For a sample of $n$ observations $x_1, \dots, x_n$ , the sample mean is

\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i

The standard deviation

The sample standard deviation measures the typical distance from the mean:

s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}

Worked example: Weekly sales

A shop sells 4, 6 and 8 units in three weeks. The mean is $\bar{x} = (4+6+8)/3 = 6$ . The deviations are $-2, 0, 2$ , so $s = \sqrt{(4+0+4)/2} = 2$ .

Mean or median?

Measure	Sensitive to outliers?	Use when
Mean	Yes	Data is roughly symmetric
Median	No	Data is skewed (e.g. incomes)

Test yourself

Topic 1 of 2· 15 minFree preview

Descriptive statistics

Placeholder topic. Summarising data with the mean, median and standard deviation.

Placeholder content. This sample topic exists to demonstrate the platform. Preview reference: FREE-NOTES-EN-2c91.

Why describe data?

Before testing anything, we summarise a sample with a few numbers. The mean (average) tells us where the data is centred, and the standard deviation tells us how spread out it is.

The mean

For a sample of $n$ observations $x_1, \dots, x_n$ , the sample mean is

\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i

The standard deviation

The sample standard deviation measures the typical distance from the mean:

s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}

Worked example: Weekly sales

A shop sells 4, 6 and 8 units in three weeks. The mean is $\bar{x} = (4+6+8)/3 = 6$ . The deviations are $-2, 0, 2$ , so $s = \sqrt{(4+0+4)/2} = 2$ .

Mean or median?

Measure	Sensitive to outliers?	Use when
Mean	Yes	Data is roughly symmetric
Median	No	Data is skewed (e.g. incomes)

Test yourself