Question

# Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would...

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.

 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

 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

The sample standard deviation is 3.49 degrees°F.