Question

Size of u.s. states the total surface area (in square miles) for each of six selected eastern states is listed here. 28,995 pa 37,534 fl 31,361 ny 27,087 va 20,966 me 37,741 ga the total surface area for each of six selected western states is listed (in square miles). 72,964 az 70,763 nv 101,510 ca 62,161 or 66,625 co 54,339 ut find the standard deviation for each data set. which set is more variable?answer

Answer 1

Standard deviation of first data set = 5879.1 Standard deviation of second data set = 14768.78 The second data set is more variable. The basic definition of standard deviation is the square root of the mean of the squares of the difference from the mean. It's a bit of a mouthful, but easy enough to do. For the first data set, first calculate the mean. (28995 + 37534 + 31361 + 27087 + 20966 + 37741) / 6 = 30614 Now calculate the square of the differences from the mean (28995 - 30614)^2 = 2621161 (37534 - 30614)^2 = 47886400 (31361 - 30614)^2 = 558009 (27087 - 30614)^2 = 12439729 (20966 - 30614)^2 = 93083904 (37741 - 30614)^2 = 50794129 And now the average of the squares (2621161 + 47886400 + 558009 + 12439729 + 93083904 +50794129) / 6 = 34563888.67 And finally, take the square root to get the standard deviation. sqrt(34563888.67) = 5879.1 Now for the second data set of western states. First, the mean (72964 + 70763 + 101510 + 62161 + 66625 + 54339) / 6 = 71393.67 Now the squares of the differences (72964 - 71393.67)^2 = 2465946.778 (70763 - 71393.67)^2 = 397740.4444 (101510 - 71393.67)^2 = 906993533.4 (62161 - 71393.67)^2 = 85242133.78 (66625 - 71393.67)^2 = 22740181.78 (54339 - 71393.67)^2 = 290861655.1 And the average of the squares is 218116865.2 Finally, the square root of the average is 14768.78 So the standard deviation of the 2nd data set is 14768.78 And since the standard deviation of the 2nd data set is larger than the standard deviation of the 1st data set, that means that the 2nd data set is more variable.