The following are all quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.



10,6,7,6,5,8

Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places

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.

To find the standard deviation of a population, you can use the following formula:

Σ(x - μ)² / N

Where:
Σ represents the sum of the values,
x represents each individual value,
μ represents the mean of the population,
N represents the total number of values.

First, calculate the mean (μ) of the population.
μ = (10 + 6 + 7 + 6 + 5 + 8) / 6
μ = 42 / 6
μ = 7

Next, calculate the squared differences between each value (x) and the mean (μ).
For each value:
(10 - 7)² = 9
(6 - 7)² = 1
(7 - 7)² = 0
(6 - 7)² = 1
(5 - 7)² = 4
(8 - 7)² = 1

Then, sum up all the squared differences:
Σ(x - μ)² = 9 + 1 + 0 + 1 + 4 + 1
Σ(x - μ)² = 16

Finally, divide the sum by the total number of values (N) and take the square root to find the standard deviation:
Standard deviation (σ) = √(Σ(x - μ)² / N)
Standard deviation (σ) = √(16 / 6)
Standard deviation (σ) ≈ √2.6667
Standard deviation (σ) ≈ 1.63

Therefore, the standard deviation of the population is approximately 1.63, rounded to two decimal places.

To find the standard deviation of a population, you can follow these steps:

Step 1: Calculate the mean of the population.
To find the mean, add up all the scores and divide it by the number of scores.

Mean = (10 + 6 + 7 + 6 + 5 + 8) / 6 = 42 / 6 = 7

Step 2: Calculate the deviation for each score.
Subtract the mean from each score to find the deviation of that score from the mean.

Deviation = Score - Mean

For the given scores, the deviations are:
10 - 7 = 3
6 - 7 = -1
7 - 7 = 0
6 - 7 = -1
5 - 7 = -2
8 - 7 = 1

Step 3: Square each deviation.
Square each deviation calculated in step 2.

Squared Deviation = Deviation^2

For the given scores, the squared deviations are:
3^2 = 9
(-1)^2 = 1
0^2 = 0
(-1)^2 = 1
(-2)^2 = 4
1^2 = 1

Step 4: Calculate the variance.
Add up all the squared deviations and divide it by the number of scores to find the variance.

Variance = (9 + 1 + 0 + 1 + 4 + 1) / 6 = 16 / 6 = 2.66 (rounded to two decimal places)

Step 5: Calculate the standard deviation.
Take the square root of the variance to find the standard deviation.

Standard Deviation = √Variance = √2.66 ≈ 1.63 (rounded to two decimal places)

Therefore, the standard deviation of the given population is approximately 1.63.