Question
Find the standard deviation for the group of data items. \[ 9,10,11,12,13 \]
Ask by Pierce Clark. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The standard deviation is approximately 1.414.
Solution
To find the standard deviation for the data set 9, 10, 11, 12, 13, follow these steps:
1. Calculate the mean (average):
Mean = (9 + 10 + 11 + 12 + 13) / 5 = 55 / 5 = 11
2. Subtract the mean from each number to find the deviation:
9 - 11 = -2
10 - 11 = -1
11 - 11 = 0
12 - 11 = 1
13 - 11 = 2
3. Square each deviation:
(-2)² = 4
(-1)² = 1
0² = 0
1² = 1
2² = 4
4. Find the variance by averaging these squared differences:
Variance = (4 + 1 + 0 + 1 + 4) / 5 = 10 / 5 = 2
5. Take the square root of the variance to get the standard deviation:
Standard Deviation = √2 ≈ 1.414
Thus, the standard deviation for the group of data items is approximately 1.414.
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Simplify this solution Beyond the Answer
To find the standard deviation, first calculate the mean (average): Mean = (9 + 10 + 11 + 12 + 13) / 5 = 11. Next, find the squared differences from the mean: - (9 - 11)² = 4 - (10 - 11)² = 1 - (11 - 11)² = 0 - (12 - 11)² = 1 - (13 - 11)² = 4 Now, add those squared differences: 4 + 1 + 0 + 1 + 4 = 10. To find the variance, divide by the number of data points: Variance = 10 / 5 = 2. Finally, take the square root of the variance to find the standard deviation: Standard Deviation = √2 ≈ 1.41.
