The variance and standard deviation of the data set {9, 4, 7, 8, 5, 8, 24, 5} are approximately 41.19 and 6.42, respectively. No outliers are identified using a 2-standard deviation criterion.
Problem 1:
Calculate the Mean:
Mean = (9 + 4 + 7 + 8 + 5 + 8 + 24 + 5) / 8 = 70 / 8 = 8.75
Calculate the Squared Differences from the Mean:
(9-8.75)^2 + (4-8.75)^2 + ... + (5-8.75)^2 = 329.5
Calculate the Variance:
Variance = 329.5 / 8 = 41.1875
Calculate the Standard Deviation:
Standard Deviation = sqrt(41.1875) ≈ 6.42
Now, the corrected variance is approximately 41.1875, and the standard deviation is approximately 6.42.
Problem 2:
Given the small size of the dataset, let's use a common rule: Identify any data points more than 2 standard deviations away from the mean as potential outliers.
Z = (9 - 8.75) / 6.42, ..., Z = (5 - 8.75) / 6.42
None of the calculated z-scores exceed 2, indicating that there are no outliers according to this criterion.