Question

Use this data set for Problems 1 and 2: {9,

4, 7, 8, 5, 8, 24, 5}
1. Find the variance and the standard deviation of
the data set.
2. Use the standard deviation to identify any
outliers in the data set.

Answer 1

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.