Find the standard deviation for the group of data items
1. 13, 13,13,16,19,19,19
2. 11,12,13,14,15
Please explain how you do these
1. 13, 13,13,16,19,19,19
2. 11,12,13,14,15
Please explain how you do these
-
1) find the mean (average) of the set
(13+13+13+16+19+19+19)/7 = 16
compute the difference of each data point from the mean, and square the result of each:
(13 - 16)² = (-3)² = 9
(13 - 16)² = (-3)² = 9
(13 - 16)² = (-3)² = 9
(16 - 16)² = (0)² = 0
(19 - 16)² = (3)² = 9
(19 - 16)² = (3)² = 9
(19 - 16)² = (3)² = 9
compute the average of these values, and take the square root
√[(9+9+9+0+9+9+9)/7]
= √(54/7)
= 2.777...
2) find the mean of the set
(11+12+13+14+15)/5 = 13
compute the difference of each data point from the mean, and square the result of each:
(11 - 13)² = (-2)² = 4
(12 - 13)² = (-1)² = 1
(13 - 13)² = (0)² = 0
(14 - 13)² = (1)² = 1
(15 - 13)² = (2)² = 4
compute the average of these values, and take the square root
√[(4+1+0+1+4)/5]
= √(10/5) = √2
= 1.414...
(13+13+13+16+19+19+19)/7 = 16
compute the difference of each data point from the mean, and square the result of each:
(13 - 16)² = (-3)² = 9
(13 - 16)² = (-3)² = 9
(13 - 16)² = (-3)² = 9
(16 - 16)² = (0)² = 0
(19 - 16)² = (3)² = 9
(19 - 16)² = (3)² = 9
(19 - 16)² = (3)² = 9
compute the average of these values, and take the square root
√[(9+9+9+0+9+9+9)/7]
= √(54/7)
= 2.777...
2) find the mean of the set
(11+12+13+14+15)/5 = 13
compute the difference of each data point from the mean, and square the result of each:
(11 - 13)² = (-2)² = 4
(12 - 13)² = (-1)² = 1
(13 - 13)² = (0)² = 0
(14 - 13)² = (1)² = 1
(15 - 13)² = (2)² = 4
compute the average of these values, and take the square root
√[(4+1+0+1+4)/5]
= √(10/5) = √2
= 1.414...