Find the variance for the set of data: 24, 31, 16, 22,22.

is it 22

X = {24,31,16,22,22}

µ(X) = 23
X-µ = {1,8,-7,-1,-1}

n
∑(Xi-µ)^2 / (n-1)
i=1

∑(X-µ)^2 / 4 = (1+64+49+1+1)/5 = 116/4 = 29

To find the variance for a set of data, follow these steps:

Step 1: Find the mean (average) of the data set.
To find the mean, add up all the numbers in the data set and divide by the total number of numbers.
Mean = (24 + 31 + 16 + 22 + 22) / 5 = 115/5 = 23

Step 2: Subtract the mean from each number in the data set and square the result.
(24 - 23)^2 = 1^2 = 1
(31 - 23)^2 = 8^2 = 64
(16 - 23)^2 = -7^2 = 49
(22 - 23)^2 = -1^2 = 1
(22 - 23)^2 = -1^2 = 1

Step 3: Calculate the sum of the squared differences.
1 + 64 + 49 + 1 + 1 = 116

Step 4: Divide the sum of the squared differences by the total number of numbers to get the variance.
Variance = 116 / 5 = 23.2

Therefore, the variance for the given set of data (24, 31, 16, 22, 22) is 23.2.

To find the variance for a set of data, you will need to follow these steps:

Step 1: Find the mean (average) of the data set.
To find the mean, sum up all the values in the data set and divide it by the total number of values.

Mean = (24 + 31 + 16 + 22 + 22) / 5 = 115 / 5 = 23

Step 2: Subtract the mean from each value in the data set.
Subtract the mean (23) from each value in the data set.

(24 - 23) = 1
(31 - 23) = 8
(16 - 23) = -7
(22 - 23) = -1
(22 - 23) = -1

Step 3: Square each result from step 2.
Square each of the results obtained in step 2.

1^2 = 1
8^2 = 64
(-7)^2 = 49
(-1)^2 = 1
(-1)^2 = 1

Step 4: Find the mean of the squared differences.
Sum up all the squared differences from step 3 and divide it by the total number of values.

Mean of squared differences = (1 + 64 + 49 + 1 + 1) / 5 = 116 / 5 = 23.2

Step 5: Find the variance.
The variance is the mean of the squared differences, which we obtained in step 4.

Variance = 23.2

Therefore, the variance for the given set of data: 24, 31, 16, 22, 22 is 23.2.