Answer :
Final answer:
To calculate the standard deviation of the given distribution, use the midpoint of each age interval to find the mean, calculate each midpoint's deviation from the mean, find the mean of the squared deviations (variance), and then take the square root of the variance to get the standard deviation.
Explanation:
To calculate the standard deviation of the given distribution, we first need to find the mean (average) of the distribution. Since the ages are given in intervals, we'll use the midpoint of each interval for calculations. After calculating the average age, we compute each age's deviation from the mean, square these deviations, and find the mean of these squared deviations (variance). Finally, the standard deviation is the square root of the variance. Let's start by finding the midpoints for each age group and then use them to calculate the mean.
For example, the midpoint of the first group (20-25) is 22.5, and there are 170 persons in this group. We do the same for all groups:
20-25: Midpoint = 22.5, Frequency = 170
25-30: Midpoint = 27.5, Frequency = 110
30-35: Midpoint = 32.5, Frequency = 80
35-40: Midpoint = 37.5, Frequency = 45
40-45: Midpoint = 42.5, Frequency = 40
45-50: Midpoint = 47.5, Frequency = 35
After finding the products of midpoints and frequencies, we add all these products and divide by the total number of persons to get the mean. Next, we calculate the variance by finding the squared difference between each group's midpoint and the mean, multiply these by the groups' frequencies, sum them up, and divide by the total number of persons. The standard deviation is then the square root of the variance.
Note that this is a simplified method applicable when dealing with grouped data and assumes a normal distribution for the sake of this example.
