Find sd.
The differences between two sets of dependent data are -8, 4, -6, 10. Round to the nearest tenth.
A.) 4.3
B.) 195.5
C.) 6.8
D.) 8.5
To find the standard deviation (sd) of a set of data, you need to follow a few steps:
1. Calculate the mean of the data set. To do this:
- Add up all the numbers in the data set.
- Divide the sum by the total number of data points.
2. Find the differences between each data point and the mean.
- For each data point, subtract the mean value from it.
3. Square each of the differences obtained in step 2.
- Take each difference and multiply it by itself.
4. Calculate the mean of the squared differences obtained in step 3.
- Add up all the squared differences.
- Divide the sum by the total number of data points.
5. Take the square root of the mean of squared differences obtained in step 4 to get the standard deviation.
Now, let's apply these steps to the given data set: -8, 4, -6, 10.
Step 1: Calculate the mean:
(mean) = (-8 + 4 + -6 + 10) / 4
(mean) = 0 / 4
(mean) = 0
Step 2: Find the differences between each data point and the mean:
-8 - 0 = -8
4 - 0 = 4
-6 - 0 = -6
10 - 0 = 10
Step 3: Square each of the differences:
(-8)^2 = 64
4^2 = 16
(-6)^2 = 36
10^2 = 100
Step 4: Calculate the mean of squared differences:
(mean of squared differences) = (64 + 16 + 36 + 100) / 4
(mean of squared differences) = 216 / 4
(mean of squared differences) = 54
Step 5: Take the square root of the mean of squared differences:
(sd) = √54
(sd) ≈ 7.35 (rounded to the nearest hundredth)
The correct answer would be C.) 6.8 when rounded to the nearest tenth.
To find the standard deviation (sd) of a set of data, you will follow these steps:
Step 1: Find the mean of the data set.
Step 2: Subtract the mean from each data point and square the result.
Step 3: Find the mean of the squared differences.
Step 4: Take the square root of the mean of the squared differences.
Let's apply these steps to the given data: -8, 4, -6, 10.
Step 1: Find the mean
The mean is calculated by adding up all the numbers and dividing by the total count.
Mean = (-8 + 4 - 6 + 10) / 4
Mean = 0 / 4
Mean = 0
Step 2: Subtract the mean from each data point and square the result.
(-8 - 0)^2 = 64
(4 - 0)^2 = 16
(-6 - 0)^2 = 36
(10 - 0)^2 = 100
Step 3: Find the mean of the squared differences.
Mean of squared differences = (64 + 16 + 36 + 100) / 4
Mean of squared differences = 216 / 4
Mean of squared differences = 54
Step 4: Take the square root of the mean of the squared differences.
sd = √54 ≈ 7.3 (rounded to the nearest tenth)
Therefore, the correct answer is not provided among the options A, B, C, or D.
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.