Question

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

4, 7, 8, 5, 8, 24, 5}

Find the variance and the standard deviation of
the data set.

Answer 1

The variance of the dataset {9, 4, 7, 8, 5, 8, 24, 5} is 35.9 and the standard deviation is approximately 5.99.

Step-by-step explanation:

To find the variance and standard deviation of the dataset {9, 4, 7, 8, 5, 8, 24, 5}, follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result (to get the squared differences).
3. Calculate the average of these squared differences. This is the variance.
4. Take the square root of the variance to find the standard deviation.

Here's how the calculations work for this dataset:

1. The mean is (9+4+7+8+5+8+24+5)/8 = 8.75.
2. The squared differences are: (0.25^2 + 4.75^2 + 1.75^2 + 0.75^2 + 3.75^2 + 0.75^2 + 15.25^2 + 3.75^2).
3. The variance is the average of these squared differences: (0.0625 + 22.5625 + 3.0625 + 0.5625 + 14.0625 + 0.5625 + 232.5625 + 14.0625) / 8 = 35.9.
4. The standard deviation is the square root of the variance: √35.9 ≈ 5.99.

So, the variance is 35.9 and the standard deviation is approximately 5.99.