Answer:
the standard deviation for the given data set is approximately 1.41.
Explanation:
To find the standard deviation for the group of data items 14, 15, 16, 17, 18, you can follow these steps:
1. Find the mean (average) of the data set. Add up all the values and divide the sum by the total number of values:
- (14 + 15 + 16 + 17 + 18) / 5 = 80 / 5 = 16
2. Calculate the deviation of each data item from the mean. Subtract the mean from each data item:
- 14 - 16 = -2
- 15 - 16 = -1
- 16 - 16 = 0
- 17 - 16 = 1
- 18 - 16 = 2
3. Square each deviation to eliminate negative values:
- (-2)^2 = 4
- (-1)^2 = 1
- 0^2 = 0
- 1^2 = 1
- 2^2 = 4
4. Find the sum of all the squared deviations:
- 4 + 1 + 0 + 1 + 4 = 10
5. Divide the sum of squared deviations by the total number of data items:
- 10 / 5 = 2
6. Take the square root of the result to find the standard deviation:
- √2 ≈ 1.41
Therefore, the standard deviation for the given data set is approximately 1.41.