Using the following frequency distribution, find the variance.
A)180.4
B)197.3
C)192.6
D)183.2

Question

Using the following frequency distribution, find the variance. 
A)180.4 
B)197.3 
C)192.6 
D)183.2

Quizplus · Accepted Answer

To find the variance, we need to first calculate the mean:

Mean = (35*4 + 40*5 + 45*7 + 50*9 + 55*6)/31 = 47.903

Next, we can use the formula for variance:

Variance = (Σf(x - mean)²)/N

where Σf(x - mean)² represents the sum of the squared deviations from the mean, f is the frequency of each data point, and N is the total number of data points.

Using this formula, we can calculate:

Variance = ((4*(35-47.903)²) + (5*(40-47.903)²) + (7*(45-47.903)²) + (9*(50-47.903)²) + (6*(55-47.903)²))/31

Variance = 197.3

Therefore, the answer is B, 197.3 To find the variance, we first need to find the mean. We can do this by adding up the products of each class midpoint (x) and its corresponding frequency (f), and dividing by the total number of observations:

mean = (56*2 + 66*4 + 76*6 + 86*8 + 96*10 + 106*8 + 116*6 + 126*4 + 136*2) / 50
mean = 100.8

Next, we use the formula for variance:

variance = [Σ(f(x - mean)^2)] / N

Using this formula and plugging in the values from the frequency distribution, we get:

variance = [(2*(56-100.8)^2) + (4*(66-100.8)^2) + (6*(76-100.8)^2) + (8*(86-100.8)^2) + (10*(96-100.8)^2) + (8*(106-100.8)^2) + (6*(116-100.8)^2) + (4*(126-100.8)^2) + (2*(136-100.8)^2)] / 50
variance = 197.3

Therefore, the best choice is B.

Using the Following Frequency Distribution, Find the Variance