TR

Descriptive statistics

Enter your data and every measure of centre, spread and shape is calculated. Click a measure to see how it was worked out. What these measures are for is explained in Chapter 3.

Sample data:

100 numbers read.

Centre Which value does the data cluster around?

  • The most widely used measure of centre. It uses every value, so it is affected by extreme values.

    1. Add up all values and divide by the number of values.

      xˉ=∑xin\bar{x} = \dfrac{\sum x_i}{n}
    2. xˉ=2+28+93+64+⋯+18+23100\bar{x} = \dfrac{2 + 28 + 93 + 64 + \cdots + 18 + 23}{100}
    3. xˉ=4995100=49.95\bar{x} = \dfrac{4995}{100} = 49.95

Spread How different are the values from each other?

Shape Is the distribution symmetric or piled to one side?

What do these numbers say?

  • Values range from 1 to 99 points; the mean is 49.95 points.
  • There is a small gap between the mean (49.95) and the median (55.5): the distribution is slightly left-skewed.
  • The standard deviation is 29.76 points. Roughly speaking, most values lie between 20.19 and 79.71 points.
  • The coefficient of variation is 59.6%, so variability is high: the values differ quite a lot (heterogeneous). Because the CV has no unit, it lets you compare different measurements (e.g. height and weight).