Answer: the mean of the data set is 4.8, and the standard deviation is about 1.94. The answer is C.
Explanation:
To find the mean and the standard deviation of the data set {2, 3, 6, 7, 6}, we can use the following formulas:
Mean = (sum of all data values) / (number of data values)
Standard deviation = sqrt[(sum of squared differences from the mean) / (number of data values)]
First, we need to find the mean:
Mean = (2 + 3 + 6 + 7 + 6) / 5
Mean = 4.8
Next, we can find the standard deviation:
Calculate the differences between each data value and the mean:
2 - 4.8 = -2.8
3 - 4.8 = -1.8
6 - 4.8 = 1.2
7 - 4.8 = 2.2
6 - 4.8 = 1.2
Square each difference:
(-2.8)^2 = 7.84
(-1.8)^2 = 3.24
(1.2)^2 = 1.44
(2.2)^2 = 4.84
(1.2)^2 = 1.44
Find the sum of the squared differences:
7.84 + 3.24 + 1.44 + 4.84 + 1.44 = 18.80
Divide the sum by the number of data values:
18.80 / 5 = 3.76
Take the square root:
sqrt(3.76) = 1.94 (rounded to two decimal places)
Therefore, the mean of the data set is 4.8, and the standard deviation is about 1.94. The answer is C.