Answer:
Approximately 7.29
Explanation:
To find the standard deviation for the set of data {25, 4, 15, 19, 20, 18, 7, 21, 24}, we need to follow these steps:
1. Find the mean (average) of the data set.
- Sum all the numbers in the data set: 25 + 4 + 15 + 19 + 20 + 18 + 7 + 21 + 24 = 143.
- Divide the sum by the number of data points (9 in this case): 143 / 9 = 15.89 (rounded to two decimal places).
- The mean of the data set is 15.89.
2. Calculate the deviation for each data point by subtracting the mean from each number in the data set.
- Deviations: 25 - 15.89 = 9.11, 4 - 15.89 = -11.89, 15 - 15.89 = -0.89, 19 - 15.89 = 3.11, 20 - 15.89 = 4.11, 18 - 15.89 = 2.11, 7 - 15.89 = -8.89, 21 - 15.89 = 5.11, 24 - 15.89 = 8.11.
3. Square each deviation to eliminate negative values and emphasize differences.
- Squared deviations: 9.11^2 = 83.12, (-11.89)^2 = 141.97, (-0.89)^2 = 0.79, 3.11^2 = 9.67, 4.11^2 = 16.93, 2.11^2 = 4.45, (-8.89)^2 = 79.12, 5.11^2 = 26.12, 8.11^2 = 65.84.
4. Find the variance by summing up all the squared deviations and dividing by the number of data points minus one.
- Variance: (83.12 + 141.97 + 0.79 + 9.67 + 16.93 + 4.45 + 79.12 + 26.12 + 65.84) / (9 - 1) = 426.01 / 8 = 53.25.
5. Finally, calculate the standard deviation by taking the square root of the variance.
- Standard deviation: √53.25 ≈ 7.29 (rounded to two decimal places).
Therefore, the standard deviation for the given data set is approximately 7.29.