The median is the better representation of the average becau

The median is the better representation of the average because the distribution is skewed to the left. The median is the better representation of the average because the distribution is skewed to the right The standard devotion indicates that nether the mean not the median are acceptable for measuring the average of the data The mean is the better representation of the average because it is the numerical average of al points.

Solution

Ans: The given histogram is right skewed histogram ( whose tail is to the right). In case of a symmetric histogram all the measures of average like Mean, Median and Mode are equal. But for an assymetric histogram Median is a better measure of average. Because Mean gets affected by the extreme values i.e. very high or low values in the observations or outliers. Since we have a right skewed histogram the Mean in this case will be affected by the higher values. So, in this case Median would be a better measure of average.

From the information given by the histogram the median can be calculated. First we have to find the cumulative frequency and from that we get that the sum of all the frequencies = 50 . So n = N/2 = 50/2 = 25. Hence, the Median is the 25th observation. But since we have a class interval series, the interval where the 25th observation lies, contains the Median. In this case, it is 65 - 75. The cumulative frequency (F_m-1) of the bar preceding the Median bar is 24. ( sum of 1, 2, 7, 5 and 9). Frequency of the median class (f_m) is 8. Class interval (c) is 10 (75-65 = 10). Lower limit (L_m) of the Median bar is 65. The formula for findind Median is given as follows:

Median = L_m + (((N/2) - (F_m-1 )) / f_m )* c = 65 + ((25 -24)/8) * 10 = 65 + 1.25 = 66.25

So, the answer is the second option that is the Median is the better representation of the average becuase the distribution is skewed to the right.