Question

Calculate the standard deviation of each of these

dummy samples:
(a) 8, 6,9, 48.
(b) 4, 7,5, 4.
(c) 9, 2, 6, 7, 6.

Answer 1

To calculate the standard deviation of a set of numbers, find the mean, subtract the mean from each number and square the result, find the mean of the squared differences, and take the square root to find the standard deviation.

Step-by-step explanation:

To calculate the standard deviation of a set of numbers, follow these steps:

1. Find the mean of the set of numbers.
2. Subtract the mean from each number in the set and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean of the squared differences to find the standard deviation.

For example, for sample (a):

• Mean: (8 + 6 + 9 + 48) / 4 = 17.75
• Squared differences: (8 - 17.75)^2 = 97.5625, (6 - 17.75)^2 = 135.0625, (9 - 17.75)^2 = 76.5625, (48 - 17.75)^2 = 924.5625
• Mean of squared differences: (97.5625 + 135.0625 + 76.5625 + 924.5625) / 4 = 308.9375
• Standard deviation: sqrt(308.9375) ≈ 17.57

Repeat this process for samples (b) and (c) to find their standard deviations.