How To Describe The Center And Spread Of Data

Centre and spread

Mean and median

The median and mean are both measures of the centre of a set up of information. They are sometimes called measures of central trend. They provide a summary measure out that attempts to depict a whole set of information with a unmarried value that represents the middle or the centre of its distribution.

The median is the center value when the data is in society.

The hateful ( $\bar{x}$ ) (or boilerplate) is the sum of all the values in the set divided by the number of values in the information set.

$\bar{x} = \frac{\sum x_i}{n}$

e.g.Information set: 6, 4, 6, v, 7, 0, 3
To find the median we demand to arrange the values in order: 0, iii, 4, v, 6, half dozen, 7
The median (middle score) is the five
The mean of this data

$\bar{x} = \frac{0+3+4+5+6+6+7}{7} = \frac{31}{7} =$ $4.4$ (one dp)

Since the mean includes every value in the distribution information technology is influenced by outliers and skewed distributions. The median is less affected by outliers and skewed information than the hateful and information technology is normally the preferred measure of key tendency when the information is not symmetrical.

The following video from Crash Course explains more almost measures of central tendencies and some examples in context.

Spread

Measures of spread describe how similar or varied the ready of observed values are. Measures of spread include range, interquartile range, variance and standard difference.

Range is the difference between the largest and smallest value in the data set.

The interquartile range (IQR) is the deviation between the Upper Quartile and Lower Quartile. This describes the eye fifty% of the values when they are ordered from lowest to highest. The IQR is frequently seen as a meliorate measure of spread than range as it is not afflicted past outliers.

The variance and standard difference are measures of the spread of the information nearly the mean. They summarise how close the data values are to the mean value. The smaller the variance and standard deviation, the more the mean value is indicative of the whole data set.

The variance $\sigma^2$ can be viewed equally an 'boilerplate' distance each individual value is abroad from the average (hateful).