Find the mean and standard deviation for the data set
{6, 8, 7, 5, 10, 6, 9, 8, 4}
Please SHOW steps for everything
I answered this problem on Brainly for you. I'm @goddessboi there
mean: add 'em up and divide by 9.
Now that you have the mean, just apply the formula for std.
Sure! To find the mean and standard deviation for the given data set {6, 8, 7, 5, 10, 6, 9, 8, 4}, follow these steps:
Step 1: Find the mean.
- Add up all the numbers in the data set:
6 + 8 + 7 + 5 + 10 + 6 + 9 + 8 + 4 = 63
- Since there are 9 numbers in the data set, divide the sum by 9 to find the mean:
63 / 9 = 7
So, the mean of the data set is 7.
Step 2: Find the deviation for each number from the mean.
- Subtract the mean (7) from each number in the data set:
6 - 7 = -1
8 - 7 = 1
7 - 7 = 0
5 - 7 = -2
10 - 7 = 3
6 - 7 = -1
9 - 7 = 2
8 - 7 = 1
4 - 7 = -3
Step 3: Calculate the squared deviation for each number.
- Square each of the deviations calculated in step 2:
(-1)^2 = 1
1^2 = 1
0^2 = 0
(-2)^2 = 4
3^2 = 9
(-1)^2 = 1
2^2 = 4
1^2 = 1
(-3)^2 = 9
Step 4: Find the sum of the squared deviations.
- Add up all the squared deviations:
1 + 1 + 0 + 4 + 9 + 1 + 4 + 1 + 9 = 30
Step 5: Calculate the variance.
- Divide the sum of squared deviations (30) by the number of data points (9) to find the variance:
30 / 9 = 3.33 (rounded to two decimal places)
Step 6: Find the standard deviation.
- Take the square root of the variance calculated in step 5 to find the standard deviation:
√3.33 ≈ 1.82 (rounded to two decimal places)
So, the mean of the data set is 7 and the standard deviation is approximately 1.82.
To find the mean and standard deviation for a data set, follow these steps:
Step 1: Find the Mean (Average)
First, add up all the numbers in the data set:
6 + 8 + 7 + 5 + 10 + 6 + 9 + 8 + 4 = 63
Next, divide the sum by the total number of data points (which is 9 in this case):
63 / 9 = 7
So, the mean or average of the data set is 7.
Step 2: Find the Deviations
To find the deviation for each data point, subtract the mean from each value in the data set, one by one. The deviations are as follows:
6 - 7 = -1
8 - 7 = 1
7 - 7 = 0
5 - 7 = -2
10 - 7 = 3
6 - 7 = -1
9 - 7 = 2
8 - 7 = 1
4 - 7 = -3
Step 3: Square the Deviations
Next, square each of the deviations:
(-1)^2 = 1
(1)^2 = 1
(0)^2 = 0
(-2)^2 = 4
(3)^2 = 9
(-1)^2 = 1
(2)^2 = 4
(1)^2 = 1
(-3)^2 = 9
Step 4: Find the Variance
Now, find the average of the squared deviations:
(1 + 1 + 0 + 4 + 9 + 1 + 4 + 1 + 9) / 9 = 4
So, the variance for the data set is 4.
Step 5: Find the Standard Deviation
Lastly, find the square root of the variance to get the standard deviation:
√4 = 2
Therefore, the mean or average of the data set is 7, and the standard deviation is 2.