Calculate SS, variance, and standard deviation for the following population of N _ 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.)
Well, well, well! Let's calculate the SS, variance, and standard deviation for that population of 7 scores.
First, we need to find the mean (average) of these scores. Adding them all up together, we get: 8 + 1 + 4 + 3 + 5 + 3 + 4 = 28. To find the mean, we divide this sum by the number of scores, which is 7. So, the mean is 28/7 = 4.
Now that we have the mean, let's find the SS (sum of squares). The SS is the sum of the squared differences between each score and the mean. Squaring each difference, we get: (8-4)^2 + (1-4)^2 + (4-4)^2 + (3-4)^2 + (5-4)^2 + (3-4)^2 + (4-4)^2. Simplifying this, we have: 16 + 9 + 0 + 1 + 1 + 1 + 0 = 28. So, the SS is 28.
Next up, we solve for the variance. The variance is the SS divided by the number of scores. In this case, it's 28/7 = 4. So, the variance is 4.
Lastly, we calculate the standard deviation. The standard deviation is the square root of the variance. Taking the square root of 4, we find that the standard deviation is 2.
So, to sum it up:
SS = 28
Variance = 4
Standard Deviation = 2
Voila! We've got our answers.
To calculate SS (sum of squares), variance, and standard deviation for this population, follow these steps:
Step 1: Calculate the mean (average) of the scores:
Mean = (8 + 1 + 4 + 3 + 5 + 3 + 4) / 7 = 4
Step 2: Subtract the mean from each score and square the result:
Squared differences = (8 - 4)^2, (1 - 4)^2, (4 - 4)^2, (3 - 4)^2, (5 - 4)^2, (3 - 4)^2, (4 - 4)^2
= 4^2, (-3)^2, 0^2, (-1)^2, 1^2, (-1)^2, 0^2
= 16, 9, 0, 1, 1, 1, 0
Step 3: Calculate the sum of squared differences:
SS = 16 + 9 + 0 + 1 + 1 + 1 + 0 = 28
Step 4: Calculate the variance:
Variance = SS / (N - 1) = 28 / (7 - 1) = 28 / 6 = 4.67
Step 5: Calculate the standard deviation:
Standard deviation = √(Variance) = √4.67 = 2.16
Therefore, for this population, the SS is 28, the variance is 4.67, and the standard deviation is 2.16.
To calculate SS (Sum of Squares), variance, and standard deviation for a given population, follow these steps:
1. Calculate the mean (μ) of the population by summing up all the scores and dividing by the total number of scores (N).
In this case, the sum of the scores is 8 + 1 + 4 + 3 + 5 + 3 + 4 = 28.
The total number of scores is 7.
Therefore, the mean (μ) is 28 / 7 = 4.
2. Calculate the deviation of each score from the mean (X - μ). Square each deviation to eliminate negative values.
The deviations of each score from the mean are:
8 - 4 = 4
1 - 4 = -3
4 - 4 = 0
3 - 4 = -1
5 - 4 = 1
3 - 4 = -1
4 - 4 = 0
Squaring each deviation, we get:
4² = 16
(-3)² = 9
0² = 0
(-1)² = 1
1² = 1
(-1)² = 1
0² = 0
3. Calculate the Sum of Squares (SS) by adding up all the squared deviations.
SS = 16 + 9 + 0 + 1 + 1 + 1 + 0 = 28
The Sum of Squares (SS) is 28.
4. Calculate the variance by dividing the Sum of Squares (SS) by the number of scores (N).
Variance = SS / N = 28 / 7 = 4
The variance is 4.
5. Calculate the standard deviation by taking the square root of the variance.
Standard Deviation = √Variance = √4 = 2
The standard deviation is 2.
Therefore, for the given population of scores: 8, 1, 4, 3, 5, 3, 4, SS = 28, variance = 4, and standard deviation = 2.
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(SS). Divide that by the number of scores to get variance.
Standard deviation = square root of variance