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1. Given that the mean of the scores 15, 21, 17, 16, 26, 18 and 29 is 21. Calculate the standard deviation. A.√10 b. 4 c. 5 d. √30 2.

2. Calculate the standard deviation of the following set of numbers 2, 3, 4, 4, 5,6.​

1 Answer

2 votes

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

User Samuel Negru
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