Symmetry & skewness

Symmetry & skewness

Symmetrical distribution

• it is symmetrical if it can be divided into two equal sizes of the same shape

Skewed distribution

• contrast of what symmetrical distribution is, thus refers to asymmetry

• The distributions can be skewed to the left or skewed to the right

• we read skewness based on the direction of which the datapoints cluster

Distribution skewed to the left

• long tail that trails towards the left

Distribution skewed to the right

• long tail that trails towards the right side

The skew in a box-plot

• the side of the box that is larger determines the skew

The skew in a box which is equal in size

• we will have to look at the whiskers to determine the skew

• the longer whisker will determine the skew

Finding the skew, if the boxes are equal and the same whisker length

• the distribution is set to be symmetrical

symmetrical distribution & median

• The plane of symmetry will always be at the median, because the median is the middle point of the data

symmetrical distribution & mean

• the mean is the balance point of a distribution

• the mean is equal to the value of the median in symmetrical distribution

Skewed distribution & median

• if it is skewed to the left, the mean is less than the median (the mean will be closer to the left side of distribution, and the median will be closer to the right side of distribution)

• if it is skewed to the right, the mean is greater than the median (the mean is closer to the right side of distribution, & the median will be closer to the left side of distribution)