A) Mean: to find the mean, you must add up all the values multiplied to their number of frequency and divide it by the total number of frequency as shown below
(20 x 3) + (30 x 5) + (40 x 7) + (50 x 4) + (60 x 2) = 810
now dividing 810 by the sum of frequency: 810/21 = 38.6
Therefore, mean = 38.6
B) Range: it is the difference between the largest and the smallest value in the given data set, to find range simply subtract the smallest number of age from the biggest one
60 – 20 = 40
C) Mode: mode is the number that has the largest frequency so in this data set it will be 40
D) Median: it is the middle value of the given data set. To find median, the values must be in an in an increasing numerical order, here our values are already in order. We have 5 values so middle value will be (5+1= 6, 6/2 = 3rd value)
Here, 3rd value is 40 so it is the median.
E) Variance: to find variance, subtract the mean (38.6) from each value of age and square it, then add all these values and divide them by n-1 where n is the number of data points.
(20 – 38.6)^2 = 345.96
(30 – 38.6)^2 = 73.96
(40 – 38.6)^2 = 1.96
(50 – 38.6)^2 = 129.96
(60 – 38.6)^2 = 457.96
Adding the above values, we get 1009.8
Divide this value by n-1 (i.e. 5-1 = 4)
10009.8/4 = 252.45
F) Standard deviation: Just apply square root to the value of variance to find standard deviation
√252.45 = 15.889
