Answer :
The mean of the given data set is approximately 25.8, and the standard deviation is approximately 10.
To find the mean, you sum up all the data points and then divide by the number of data points:
Mean = (10.8 + 15.8 + 20.8 + 25.8 + 30.8 + 35.8 + 40.8) / 7
Mean = 180.6 / 7
Mean ≈ 25.8
Step 2: Calculate the Standard Deviation
To find the standard deviation, you'll need to follow these steps:
1. Find the squared difference between each data point and the mean.
2. Calculate the average of these squared differences.
3. Take the square root of that average.
First, calculate the squared differences:
(10.8 - 25.8)² = 225
(15.8 - 25.8)² = 100
(20.8 - 25.8)² = 25
(25.8 - 25.8)² = 0
(30.8 - 25.8)² = 25
(35.8 - 25.8)² = 100
(40.8 - 25.8)² = 225
Now, calculate the average of these squared differences:
Average = (225 + 100 + 25 + 0 + 25 + 100 + 225) / 7
Average ≈ 100
Finally, take the square root of the average to find the standard deviation:
Standard Deviation ≈ √100
Standard Deviation ≈ 10
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Complete Question:
Find the mean and standard deviation for the following data set,
10.8 15.8 20.8 25.8 30.8 35.8 S 40.8
