Find the sum of squared deviations, the variance, and the standard deviation of:2,2,0,5,1,4,1,3,0,0,1,4,4,0,1,4,3,4,2,1,0

To find the sum of squared deviations, variance, and standard deviation, follow these steps:

Step 1: Find the mean (average) of the data set.
Step 2: Subtract the mean from each data point and square the result.
Step 3: Sum up all the squared deviations.
Step 4: Divide the sum of squared deviations by the total number of data points minus 1 to find the variance.
Step 5: Take the square root of the variance to find the standard deviation.

Let's calculate:

Step 1: Calculate the mean:
(2+2+0+5+1+4+1+3+0+0+1+4+4+0+1+4+3+4+2+1+0) / 21 = 2.238095

Step 2: Subtract the mean from each data point and square the result:

(2-2.238095)^2 = 0.054870
(2-2.238095)^2 = 0.054870
(0-2.238095)^2 = 5.006803
(5-2.238095)^2 = 7.626111
(1-2.238095)^2 = 1.537541
(4-2.238095)^2 = 3.951986
(1-2.238095)^2 = 1.537541
(3-2.238095)^2 = 0.577982
(0-2.238095)^2 = 5.006803
(0-2.238095)^2 = 5.006803
(1-2.238095)^2 = 1.537541
(4-2.238095)^2 = 3.951986
(4-2.238095)^2 = 3.951986
(0-2.238095)^2 = 5.006803
(1-2.238095)^2 = 1.537541
(4-2.238095)^2 = 3.951986
(3-2.238095)^2 = 0.577982
(4-2.238095)^2 = 3.951986
(2-2.238095)^2 = 0.054870
(1-2.238095)^2 = 1.537541
(0-2.238095)^2 = 5.006803

Step 3: Sum up all the squared deviations:
0.054870 + 0.054870 + 5.006803 + 7.626111 + 1.537541 + 3.951986 + 1.537541 + 0.577982 + 5.006803 + 5.006803 + 1.537541 + 3.951986 + 3.951986 + 5.006803 + 1.537541 + 3.951986 + 0.577982 + 3.951986 + 0.054870 + 1.537541 + 5.006803 = 59.857757

Step 4: Calculate the variance:
Variance = Sum of squared deviations / (total number of data points - 1)
Variance = 59.857757 / (21 - 1)
Variance = 59.857757 / 20
Variance = 2.992893

Step 5: Calculate the standard deviation:
Standard Deviation = Square root of variance
Standard Deviation = Square root of 2.992893
Standard Deviation = 1.731693

Therefore, the sum of squared deviations is 59.857757, the variance is 2.992893, and the standard deviation is 1.731693.

To find the sum of squared deviations, variance, and standard deviation of a given set of numbers, follow these steps:

1. Find the mean of the numbers:
To do this, sum all the numbers in the set and divide by the total count.
(2 + 2 + 0 + 5 + 1 + 4 + 1 + 3 + 0 + 0 + 1 + 4 + 4 + 0 + 1 + 4 + 3 + 4 + 2 + 1 + 0) / 21 = 2.095

2. Find the deviation of each number from the mean:
Subtract the mean calculated in step 1 from each number in the set.

Deviation of each number:
2 - 2.095 = -0.095
2 - 2.095 = -0.095
0 - 2.095 = -2.095
5 - 2.095 = 2.905
1 - 2.095 = -1.095
4 - 2.095 = 1.905
1 - 2.095 = -1.095
3 - 2.095 = 0.905
0 - 2.095 = -2.095
0 - 2.095 = -2.095
1 - 2.095 = -1.095
4 - 2.095 = 1.905
4 - 2.095 = 1.905
0 - 2.095 = -2.095
1 - 2.095 = -1.095
4 - 2.095 = 1.905
3 - 2.095 = 0.905
4 - 2.095 = 1.905
2 - 2.095 = -0.095
1 - 2.095 = -1.095
0 - 2.095 = -2.095

3. Square each deviation:
Square each deviation calculated in step 2.

Squared deviations:
(-0.095)^2 = 0.009025
(-0.095)^2 = 0.009025
(-2.095)^2 = 4.383025
(2.905)^2 = 8.423025
(-1.095)^2 = 1.198025
(1.905)^2 = 3.629025
(-1.095)^2 = 1.198025
(0.905)^2 = 0.820025
(-2.095)^2 = 4.383025
(-2.095)^2 = 4.383025
(-1.095)^2 = 1.198025
(1.905)^2 = 3.629025
(1.905)^2 = 3.629025
(-2.095)^2 = 4.383025
(-1.095)^2 = 1.198025
(1.905)^2 = 3.629025
(0.905)^2 = 0.820025
(1.905)^2 = 3.629025
(-0.095)^2 = 0.009025
(-1.095)^2 = 1.198025
(-2.095)^2 = 4.383025

4. Find the sum of squared deviations:
Sum all the squared deviations calculated in step 3.

Sum of squared deviations:
0.009025 + 0.009025 + 4.383025 + 8.423025 + 1.198025 + 3.629025 + 1.198025 + 0.820025 + 4.383025 + 4.383025 + 1.198025 + 3.629025 + 3.629025 + 4.383025 + 1.198025 + 3.629025 + 0.820025 + 3.629025 + 0.009025 + 1.198025 + 4.383025 = 65.671

5. Calculate the variance:
Divide the sum of squared deviations calculated in step 4 by the total count of numbers, in this case, 21.

Variance = 65.671 / 21 = 3.125

6. Calculate the standard deviation:
Take the square root of the variance calculated in step 5.

Standard Deviation = √(3.125) = 1.768

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.