The graph clearly shows that the data is positively skewed because it peaks towards the left of the data. The range of the sample is 40 with minimum being 0 and maximum being 40. The average of the minimum and maximum turns out to be 20. Since, the peak of the data is at less than 20, it is safe to conclude that the sample is positively skewed. However, to confirm this, the skewness of the data can be obtained which according to Table 1 is 1.96. Positively skewed data also have the property that their mean is more than their median which in turn is more than the mode. Here, mean is 6.63, median is 2.5 and mode is 0. Clearly,
So, the data is positively skewed.
The standard deviation of the data is quite high which is 9.07. This means that data shows high variability. It implies that data changes a lot between responses. A similar measure of dispersion is the interquartile range which is the difference between the first and the third quartile. If the difference between the first and the third quartile is high, it implies that the dispersion or the spread of the data is quite high. In the given sample, it turns out to be 9 which is quite close to the standard deviation.
There are three measures of central tendency viz. mean, median and mode. Mean is affected by the extreme values and can be deviating sometimes. Median on the other hand gives the exact point which divides the data into two equal halves. It is not affected by extreme values. Mode though not affected by extreme values, is the frequency of highest occurring data. In the given case, since the standard deviation is high, the spread of the data is very high. So, mean may not be a very good measure of central tendency. Mode is not appropriate here either. The best measure of central tendency thus is the median which gives an approximate data that divides the sample into two equal halves.