Question

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.6 degrees.

Low Temperature ​(circle​F) 40minus44 45minus49 50minus54 55minus59 60minus64 Frequency 3 5 12 4 2

Answer 1

Given that, the actual mean is 51.6 degrees.

We want to find computed mean from given frequency distribution.

Low Temperature	Midpoint (X)	Frequency (f)	f * X
40 - 44	42	3	126
45 - 49	47	5	235
50 - 54	52	12	624
55 - 59	57	4	228
60 - 64	62	2	124
		$\sum f = 26$	$\sum f * X= 1337$

Expected value of X ( Mean of X ) is,

$E(X) = \frac { \sum f * X}{\sum f} = \frac {1337}{26} = 51.42$

Computed mean = 51.42 degrees

The computed mean is close to the actual mean because the difference between the means is less than​ 5%.