Find the variance for the given sample data. Round your answer to one more decimal place than the original data.
7 7 2 5 1
To find the variance for the given sample data, follow these steps:
Step 1: Calculate the mean (average) of the data.
7 + 7 + 2 + 5 + 1 = 22
Mean = 22 / 5 = 4.4
Step 2: Calculate the squared difference for each data point from the mean.
For 7: (7 - 4.4)^2 = 7.84
For 7: (7 - 4.4)^2 = 7.84
For 2: (2 - 4.4)^2 = 5.76
For 5: (5 - 4.4)^2 = 0.36
For 1: (1 - 4.4)^2 = 11.56
Step 3: Calculate the sum of squared differences.
7.84 + 7.84 + 5.76 + 0.36 + 11.56 = 33.36
Step 4: Divide the sum of squared differences by the number of data points minus 1. This gives us the sample variance.
Sample variance = 33.36 / (5 - 1) = 33.36 / 4 = 8.34
Rounded to one more decimal place, the variance for the given sample data is 8.3.
To find the variance for the given sample data, you need to follow these steps:
1. Calculate the mean (average) of the sample data.
2. Subtract the mean from each individual data point and square the result.
3. Compute the sum of all the squared differences.
4. Divide the sum by the number of data points minus one (n-1) to get the variance.
5. Round the answer to one more decimal place than the original data.
Let's apply these steps to the given sample data: 7, 7, 2, 5, 1.
Step 1: Calculate the mean.
Mean = (7 + 7 + 2 + 5 + 1) / 5 = 22 / 5 = 4.4
Step 2: Subtract the mean from each data point and square the result.
Squaring the differences: (7 - 4.4)^2 = 5.76
(7 - 4.4)^2 = 5.76
(2 - 4.4)^2 = 5.76
(5 - 4.4)^2 = 0.36
(1 - 4.4)^2 = 11.56
Step 3: Compute the sum of all the squared differences.
Sum = 5.76 + 5.76 + 5.76 + 0.36 + 11.56 = 29.8
Step 4: Divide the sum by n-1 to get the variance.
Variance = Sum / (n - 1) = 29.8 / (5 - 1) = 29.8 / 4 = 7.45
Step 5: Round the answer to one more decimal place than the original data.
Rounding the variance to one more decimal place than the original data, we get: Variance ≈ 7.5
Therefore, the variance for the given sample data is 7.5 rounded to one decimal place.