Question

Find the standard deviation for the given data: 3, 5, 6, 6, 9, 1.

A) 2.3

B) 2.4

C) 2.6

D) 2.8

Answer 1

To find the standard deviation, calculate the mean, subtract the mean from each data point and square the result, find the average of these squared differences, and then take the square root. The standard deviation for the data set (3, 5, 6, 6, 9, 1) is approximately 2.5, with the nearest answer choice being 2.6 (Option C).

Step-by-step explanation:

To find the standard deviation for the given data: 3, 5, 6, 6, 9, 1, you would follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result (this is the squared difference).
3. Find the average of these squared differences.
4. Take the square root of the average squared difference; this is the standard deviation.

To calculate the mean, add up all the data points and then divide by the number of points:

(3 + 5 + 6 + 6 + 9 + 1) / 6 = 30 / 6 = 5

Next, calculate each data point's squared difference from the mean:

• (3 - 5)^2 = 4
• (5 - 5)^2 = 0
• (6 - 5)^2 = 1
• (6 - 5)^2 = 1
• (9 - 5)^2 = 16
• (1 - 5)^2 = 16

Now, find the average of these squared differences:

(4 + 0 + 1 + 1 + 16 + 16) / 6 = 38 / 6 = 6.33

Finally, take the square root of the average squared difference:

√6.33 = 2.517, rounded to one decimal place is 2.5.

The nearest answer choice is 2.6 (Option C).