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Math  /  Data & Statistics

QuestionUse the following distribution to complete parts (a) through (d) below. 3,6,7,10,9□3,6,7,10,9 \square a) Compute the mean and standard deviation of the distribution.
The mean is 7 . The standard deviation is □\square (Round to the nearest hundredth as needed.)

Studdy Solution

STEP 1

1. The data set is 3,6,7,10,9 3, 6, 7, 10, 9 .
2. The mean of the data set is given as 7.
3. The standard deviation needs to be calculated and rounded to the nearest hundredth.

STEP 2

1. Verify the mean calculation.
2. Calculate the variance.
3. Calculate the standard deviation.

STEP 3

Verify the mean calculation:
The mean is calculated as:
Mean=3+6+7+10+95=355=7\text{Mean} = \frac{3 + 6 + 7 + 10 + 9}{5} = \frac{35}{5} = 7
The given mean is correct.

STEP 4

Calculate the variance:
First, find the deviations from the mean:
3−7=−4,6−7=−1,7−7=0,10−7=3,9−7=23 - 7 = -4, \quad 6 - 7 = -1, \quad 7 - 7 = 0, \quad 10 - 7 = 3, \quad 9 - 7 = 2
Square each deviation:
(−4)2=16,(−1)2=1,02=0,32=9,22=4(-4)^2 = 16, \quad (-1)^2 = 1, \quad 0^2 = 0, \quad 3^2 = 9, \quad 2^2 = 4
Calculate the average of these squared deviations (variance):
Variance=16+1+0+9+45=305=6\text{Variance} = \frac{16 + 1 + 0 + 9 + 4}{5} = \frac{30}{5} = 6

STEP 5

Calculate the standard deviation:
The standard deviation is the square root of the variance:
Standard Deviation=6≈2.45\text{Standard Deviation} = \sqrt{6} \approx 2.45
Round to the nearest hundredth: 2.45 2.45
The standard deviation is:
2.45 \boxed{2.45}

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