2. Find the variance and standard deviation of the following sample.

0 -5 -3 6 4 -4 1 -5 0 3

Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

I'll let you do the calculations.

To find the variance and standard deviation of the given sample, follow these steps:

Step 1: Calculate the mean (average) of the sample:
To find the mean, sum up all the values in the sample and divide by the total number of values.

Mean = (0 + (-5) + (-3) + 6 + 4 + (-4) + 1 + (-5) + 0 + 3) / 10
= (-3)/10
= -0.3

Step 2: Calculate the deviation of each value from the mean:
Subtract the mean from each value in the sample to get the deviation.

Deviation = [0 - (-0.3), -5 - (-0.3), -3 - (-0.3), 6 - (-0.3), 4 - (-0.3), -4 - (-0.3), 1 - (-0.3), -5 - (-0.3), 0 - (-0.3), 3 - (-0.3)]
= [0.3, -4.7, -2.7, 6.3, 4.3, -3.7, 1.3, -4.7, 0.3, 3.3]

Step 3: Square each deviation value:
Multiply each deviation value by itself.

Squared Deviation = [0.3^2, -4.7^2, -2.7^2, 6.3^2, 4.3^2, -3.7^2, 1.3^2, -4.7^2, 0.3^2, 3.3^2]
= [0.09, 22.09, 7.29, 39.69, 18.49, 13.69, 1.69, 22.09, 0.09, 10.89]

Step 4: Find the sum of squared deviations:
Add up all the squared deviation values.

Sum of Squared Deviations = 0.09 + 22.09 + 7.29 + 39.69 + 18.49 + 13.69 + 1.69 + 22.09 + 0.09 + 10.89
= 135.1

Step 5: Calculate the variance:
Divide the sum of squared deviations by the total number of values minus 1.

Variance = Sum of Squared Deviations / (Total number of values - 1)
= 135.1 / (10 - 1)
= 135.1 / 9
≈ 15.0111

Step 6: Calculate the standard deviation:
Take the square root of the variance.

Standard Deviation = Square root of Variance
= Square root of 15.0111
≈ 3.872

Therefore, the variance of the given sample is approximately 15.0111 and the standard deviation is approximately 3.872.

To find the variance and standard deviation of a sample, you can follow these steps:

1. Calculate the mean (average) of the sample.
- Add up all the values in the sample: 0 + (-5) + (-3) + 6 + 4 + (-4) + 1 + (-5) + 0 + 3 = -3.
- Divide the sum by the number of values in the sample: -3 ÷ 10 = -0.3.
- The mean of the sample is -0.3.

2. Calculate the differences between each value and the mean.
- Subtract the mean from each value in the sample:
0 - (-0.3) = 0.3
-5 - (-0.3) = -4.7
-3 - (-0.3) = -2.7
6 - (-0.3) = 6.3
4 - (-0.3) = 4.3
-4 - (-0.3) = -3.7
1 - (-0.3) = 1.3
-5 - (-0.3) = -4.7
0 - (-0.3) = 0.3
3 - (-0.3) = 3.3

3. Square the differences obtained in step 2.
- Square each difference:
(0.3)^2 = 0.09
(-4.7)^2 = 22.09
(-2.7)^2 = 7.29
(6.3)^2 = 39.69
(4.3)^2 = 18.49
(-3.7)^2 = 13.69
(1.3)^2 = 1.69
(-4.7)^2 = 22.09
(0.3)^2 = 0.09
(3.3)^2 = 10.89

4. Calculate the mean of the squared differences obtained in step 3.
- Add up all the squared differences: 0.09 + 22.09 + 7.29 + 39.69 + 18.49 + 13.69 + 1.69 + 22.09 + 0.09 + 10.89 = 136.89.
- Divide the sum by the number of values in the sample (which is the same as the number of squared differences): 136.89 ÷ 10 = 13.689.
- The mean of the squared differences is 13.689.

5. Calculate the variance.
- The variance is the mean of the squared differences: 13.689.

6. Calculate the standard deviation.
- The standard deviation is the square root of the variance: √13.689 ≈ 4.23.

Therefore, the variance of the sample is 13.689 and the standard deviation is approximately 4.23.