Question

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 57.4 degrees. Low Temperature (°F) Frequency 40-44 1 45-49 5 50-54 9 55-59 5 60-64 1

Answer 1

Class interval	Mid-point: Xi	Frequency: fi	Xifi
40-44	42	1	42
45-49	47	5	235
50-54	52	9	468
55-59	57	5	285
60-64	62	1	62
		=21	=1,092

Mean, = =1092/21 =52

So, the computed mean of 52 degrees < actual mean of 57.4 degrees.

(It's because each mid-point is not the actual center (average) of values in that class interval and so is the difference between computed and actual mean values).