Left-Skewed Histogram

A left-skewed histogram is a histogram in which, in a given continuous data, most of the observations fall to the left side of the graph’s peak. It is thus also known as the negatively skewed histogram. Such graphs have long tails on the left side and a peak towards the right.

In the data of such histograms, the bulk of the observations is medium or large, with few being much smaller than others. A real-life example of such histograms can be obtained if we plot a graph with data that gives a count of the age of people who have dementia. Most such cases happen at older ages, with fewer cases happening at younger ages.

Example

Let us draw and interpret a left-skewed histogram involving the height of trees in a region measured in feet. The variables are:

59, 58, 59, 57, 55, 59, 57, 58, 59, 56, 57, 59, 58, 58, 59, 56  

When we sketched the histogram with the above data, we found it skewed to the left. The above figure is an example of a left-skewed histogram.

Mean, Median, and Mode of Left-Skewed Histogram

Let us calculate the mean, median, and mode of the above-given data concerning the height of plants (in feet) in an area:

59, 58, 59, 57, 55, 59, 57, 58, 59, 56, 57, 59, 58, 58, 59, 56  

To find the mean, median, and mode of the above data, we will arrange the above data:

55, 56, 56, 57, 57, 57, 58, 58, 58, 58, 59, 59, 59, 59, 59

Calculating the median, median, and mode, we get

• Mean = 57.66 feet
• Median = 58 feet
• Mode = 59 feet

Thus, the relation between its mean, median, and mode is given by mean < median < mode. It can be more easily understood when we show the mean, median, and mode position in the above-prepared graph.