John listens to a variety of music including easy listening

John listens to a variety of music, including easy listening, classical, and pop/rock. These are the lengths of some of his favorite albums for each of these categories:

Easy Listening

Classical

Pop/Rock

39

67

47

60

76

47

40

51

66

56

51

50

41

36

78

55

61

41

What is the standard deviation of the \"easy listening\" data set? (Round your answer to one place past the decimal.)

Solution

The standard deviation for a set of data is the square root of mean of the sum of the squares of differences of all the numbers from the mean.

Here, the mean of the easy listening data set is = (39+ 60 + 40 + 56 + 41 + 55 + 41)/7 = 332/7 = 47.43

Then, ( 39 –47.43)² = 71.065,( 60 - 47.43)² =158.005,( 40 -47.43)² = 55.205 ,( 56 - 47.43)² = 73.445, ( 41 – 47.43)² = 41.345, (55- 47.43)² = 57.305, and ( 41 – 47.43)² = 41.345. Also, (71.065 + 158.005 + 55.205+73.445+41.345+57.305+41.345)/7 = 497.715/7 = 71.102. Therefore, the standard deviation of the easy listening data set = = 71.102 = 8.432 = 8.4( on rounding off to one decimal place)