Data on a customer satisfaction rating (called the APEAL rating) are given for each brand of car sold in the United States in a certain year. The APEAL rating is a score between 0 and 1,000, with higher values indicating greater satisfaction.
749 760 766 767 777 781 784 786 786 788 788 790 791 791 791 793 795 797 802 813 818 821 823 836 840 841 848 858 862 880
Calculate the mean and standard deviation for this data set. (Round your answers to four decimal places.)
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The given data set is:
749, 760, 766, 767, 777, 781, 784, 786, 786, 788, 788, 790, 791, 791, 791, 793, 795, 797, 802, 813, 818, 821, 823, 836, 840, 841, 848, 858, 862, 880
To calculate the mean, we sum up all the values in the data set and divide by the total number of values:
Mean = (749 + 760 + 766 + 767 + 777 + 781 + 784 + 786 + 786 + 788 + 788 + 790 + 791 + 791 + 791 + 793 + 795 + 797 + 802 + 813 + 818 + 821 + 823 + 836 + 840 + 841 + 848 + 858 + 862 + 880) / 30
Mean = 24102 / 30
Mean = 803.4
The mean of the data set is 803.4.
To calculate the standard deviation, we first need to find the deviation of each value from the mean. Then, we square each deviation, sum them up, divide by the total number of values, and take the square root of the result:
Deviation = (749 - 803.4)^2 + (760 - 803.4)^2 + (766 - 803.4)^2 + (767 - 803.4)^2 + (777 - 803.4)^2 + (781 - 803.4)^2 + (784 - 803.4)^2 + (786 - 803.4)^2 + (786 - 803.4)^2 + (788 - 803.4)^2 + (788 - 803.4)^2 + (790 - 803.4)^2 + (791 - 803.4)^2 + (791 - 803.4)^2 + (791 - 803.4)^2 + (793 - 803.4)^2 + (795 - 803.4)^2 + (797 - 803.4)^2 + (802 - 803.4)^2 + (813 - 803.4)^2 + (818 - 803.4)^2 + (821 - 803.4)^2 + (823 - 803.4)^2 + (836 - 803.4)^2 + (840 - 803.4)^2 + (841 - 803.4)^2 + (848 - 803.4)^2 + (858 - 803.4)^2 + (862 - 803.4)^2 + (880 - 803.4)^2
Deviation = 3528.84 + 1600.84 + 1296.04 + 1225.84 + 829.24 + 226.44 + 46.24 + 41.64 + 41.64 + 27.04 + 27.04 + 6.84 + 0.36 + 0.36 + 0.36 + 2.44 + 9.64 + 5.44 + 0.16 + 10.24 + 42.24 + 54.44 + 66.04 + 1060.44 + 1266.24 + 1277.64 + 1739.24 + 2510.24 + 2840.84 + 5493.64
Deviation = 29992.92
Standard Deviation = √(Deviation / (Total Number of Values - 1))
Standard Deviation = √(29992.92 / (30 - 1))
Standard Deviation = √(29992.92 / 29)
Standard Deviation = √1034.5862069
Standard Deviation = 32.1686
The standard deviation of the data set is 32.1686.
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