in this video we will be looking at symmetry and skewness when we talk about symmetry and skewness we are actually talking about the shape of a distribution we had previously talked about how we can use histograms stem plots and box plots to display a distribution we will be using these tools to help us talk about symmetry and skewness a distribution is set to be symmetrical if it can be divided into two equal sizes of the same shape in contrast this would be a histogram that is not symmetrical this is classified as a skewed distribution skewness refers to asymmetry we can have distributions that are skewed to the left and we can have distributions that are skewed to the right we read skewness based on the direction in which the data points cluster a distribution is set to be skewed to the left if it has a long tail that trails towards the left in contrast a distribution is set to be skewed to the right if it has a long tail that trails towards the right side the same thing can be applied to a stem plot this stem plot would be skewed to the right a good way to determine the skew of a stem plot is by flipping it onto its side when you view the stem plot this way you must make sure that the position of the stems are positioned like a regular number line where the lower number starts from the left and increases towards the right we can see that there is a long tail that rolls towards the right so we can say that this distribution is skewed to the right when determining skewness for boxplots the presence of outliers may affect how we interpret the skewness for example for this data set we can construct this regular box plot we might think that this distribution is skewed to the left but when we convert it to the modified box plot we can see that this data set is actually skewed to the right and so when we are trying to determine the direction of skew for box plots we can implement a strategy if we have unequal boxes the side of the box that is larger determines the skew in this case the left side of the box is larger than the right side so therefore this is skewed to the left if the boxes are equal in size then you would have to look at the whiskers to determine the skew the longer whisker will determine the skew so this would be skewed to the right if the boxes are equal in size with the same whisker length then the distribution is set to be symmetrical with symmetry and skewness in mind let's see how they affect the median and the mean when we have a symmetrical distribution you should notice that the plane of symmetry will always be at the median because it is the middle data point and because the mean is the balance point of a distribution you should also find that the mean is equal to the value of the median in this case both the median and the mean would be equal to 12 now if the distribution was skewed the median would not be at 12 anymore remember that the bars of a histogram always correspond to the frequency and so we see that to the right of 12 we have more data values than there are to the left of 12 by doing some calculations you should find that the value of the median is contained within the interval between 16 and 18 and because the mean is the balance point of a distribution skewness will affect it so it will be closer to the tail so we say that if a distribution is skewed to the left the mean is less than the median in other words the mean will be closer to the left side of the distribution and the median will be closer to the right side of the distribution in contrast if we have a distribution that is skewed to the right the mean is greater than the median in other words the mean will be closer to the right side of the distribution and the median will be closer to the left side of the distribution