Question

Height (in inches)

Class Frequency, f
50-52
5
53-55
8
56-58
12
59-61
13
62-64
11
What is the Sum of the Xm'f Coulumn

Answer 1

To find the sum of the Xm'f column, we first need to calculate the midpoint (Xm) for each class interval and then multiply it by the frequency (f) for that interval. The midpoint of each class interval can be calculated as the average of the lower and upper bounds of the interval.

For the first class interval 50-52:

Xm = (50 + 52) / 2 = 51

Xm'f = Xm * f = 51 * 5 = 255

For the second class interval 53-55:

Xm = (53 + 55) / 2 = 54

Xm'f = Xm * f = 54 * 8 = 432

For the third class interval 56-58:

Xm = (56 + 58) / 2 = 57

Xm'f = Xm * f = 57 * 12 = 684

For the fourth class interval 59-61:

Xm = (59 + 61) / 2 = 60

Xm'f = Xm * f = 60 * 13 = 780

For the fifth class interval 62-64:

Xm = (62 + 64) / 2 = 63

Xm'f = Xm * f = 63 * 11 = 693

Finally, we can add up the Xm'f values for each interval to get the sum of the Xm'f column:

Sum of Xm'f = 255 + 432 + 684 + 780 + 693 = 2954

So the sum of the Xm'f column is 2954.