What is the standard deviation of the set {5, 7, 3, 4, 8}?

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Multiple Choice

What is the standard deviation of the set {5, 7, 3, 4, 8}?

Explanation:
To find the standard deviation of the set {5, 7, 3, 4, 8}, we start by calculating the mean (average) of the numbers. First, we sum the values in the set: 5 + 7 + 3 + 4 + 8 = 27. Next, we divide this sum by the number of values, which is 5: Mean = 27 / 5 = 5.4. Now, we calculate the variance by finding the squared differences between each number and the mean, and then averaging those squared differences: 1. (5 - 5.4)² = (-0.4)² = 0.16 2. (7 - 5.4)² = (1.6)² = 2.56 3. (3 - 5.4)² = (-2.4)² = 5.76 4. (4 - 5.4)² = (-1.4)² = 1.96 5. (8 - 5.4)² = (2.6)² = 6.76 Next, we sum these squared differences: 0.16

To find the standard deviation of the set {5, 7, 3, 4, 8}, we start by calculating the mean (average) of the numbers.

First, we sum the values in the set:

5 + 7 + 3 + 4 + 8 = 27.

Next, we divide this sum by the number of values, which is 5:

Mean = 27 / 5 = 5.4.

Now, we calculate the variance by finding the squared differences between each number and the mean, and then averaging those squared differences:

  1. (5 - 5.4)² = (-0.4)² = 0.16

  2. (7 - 5.4)² = (1.6)² = 2.56

  3. (3 - 5.4)² = (-2.4)² = 5.76

  4. (4 - 5.4)² = (-1.4)² = 1.96

  5. (8 - 5.4)² = (2.6)² = 6.76

Next, we sum these squared differences:

0.16

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