Question

Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following​ data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of 744 households. Determine the class​ midpoint, if​ necessary, for each class and approximate the mean and standard deviation temperature

Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following​ data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of 744 households. Determine the class​ midpoint, if​ necessary, for each class and approximate the mean and standard deviation temperature

Temp Frequency Class Midpoint

61-64 34   63

65-67 68 66.5

68-69 196 69

70 191 70.5

71-72 122 72

73-76 81 75

77-80 52 79

The sample standard deviation is _____degrees°F.

Answer 1

ΣTm Σ1 Mean

	Frequency(f)	Midpoint(x)	fx
	34	63	2142
	68	66.5	4522
	196	69	13524
	191	70.5	13465.5
	122	72	8784
	81	75	6075
	52	79	4108
Total	744	495	52620.5

52620.5 ΣΤm 70.73 Mean-μ 744

Σία- μ2 Σf σ -

	Frequency(f)	Midpoint(x)	fx	(x-mu)	(x-mu)^2	f*(x-mu)^2
	34	63	2142	-7.73	59.69847	2029.748
	68	66.5	4522	-4.23	17.86312	1214.692
	196	69	13524	-1.73	2.980728	584.2227
	191	70.5	13465.5	-0.23	0.051293	9.796869
	122	72	8784	1.27	1.621857	197.8666
	81	75	6075	4.27	18.26299	1479.302
	52	79	4108	8.27	68.45116	3559.46
Total	744	495	52620.5			9075.088

Ef(-u)29075.088 Σf V12.1977 3.49 744

The sample standard deviation is 3.49 degrees°F.