Answer:
1) c. 5
2) 1.29
Explanation:
1. To calculate the standard deviation, we first need to find the variance. The variance is the average of the squared differences from the mean.
Step 1: Find the differences from the mean:
15 - 21 = -6
21 - 21 = 0
17 - 21 = -4
16 - 21 = -5
26 - 21 = 5
18 - 21 = -3
29 - 21 = 8
Step 2: Square the differences:
(-6)^2 = 36
0^2 = 0
(-4)^2 = 16
(-5)^2 = 25
5^2 = 25
(-3)^2 = 9
8^2 = 64
Step 3: Find the average of the squared differences:
(36 + 0 + 16 + 25 + 25 + 9 + 64) / 7 = 175 / 7 = 25
Step 4: Take the square root of the variance to find the standard deviation:
√25 = 5
Therefore, the standard deviation is 5.
2. To calculate the standard deviation for the set of numbers 2, 3, 4, 4, 5, 6:
Step 1: Find the mean:
(2 + 3 + 4 + 4 + 5 + 6) / 6 = 24 / 6 = 4
Step 2: Find the differences from the mean:
2 - 4 = -2
3 - 4 = -1
4 - 4 = 0
4 - 4 = 0
5 - 4 = 1
6 - 4 = 2
Step 3: Square the differences:
(-2)^2 = 4
(-1)^2 = 1
0^2 = 0
0^2 = 0
1^2 = 1
2^2 = 4
Step 4: Find the average of the squared differences:
(4 + 1 + 0 + 0 + 1 + 4) / 6 = 10 / 6 ≈ 1.67
Step 5: Take the square root of the variance to find the standard deviation:
√1.67 ≈ 1.29
Therefore, the standard deviation is approximately 1.29