Find the variance of the given P1 Grades:
( 75, 75, 79, 72, 80, 74, 79, 83, 93, 80)

*
1 point

a. 33.22

b. 35.56

c. 34.45

d. 35.65


To find the variance of the given P1 grades, we follow these steps:

1. **List of Grades**: \( 75, 75, 79, 72, 80, 74, 79, 83, 93, 80 \)
   
2. **Calculate the Mean (μ)**: The mean is the sum of all values divided by the number of values.
   \[
   \text{Mean} = \frac{75 + 75 + 79 + 72 + 80 + 74 + 79 + 83 + 93 + 80}{10} = \frac{790}{10} = 79
   \]

3. **Calculate Squared Differences**: Subtract the mean from each grade and square the result.
   \[
   (75 - 79)^2 = (-4)^2 = 16
   \]
   \[
   (75 - 79)^2 = (-4)^2 = 16
   \]
   \[
   (79 - 79)^2 = (0)^2 = 0
   \]
   \[
   (72 - 79)^2 = (-7)^2 = 49
   \]
   \[
   (80 - 79)^2 = (1)^2 = 1
   \]
   \[
   (74 - 79)^2 = (-5)^2 = 25
   \]
   \[
   (79 - 79)^2 = (0)^2 = 0
   \]
   \[
   (83 - 79)^2 = (4)^2 = 16
   \]
   \[
   (93 - 79)^2 = (14)^2 = 196
   \]
   \[
   (80 - 79)^2 = (1)^2 = 1
   \]

4. **Sum of Squared Differences**: Add all the squared differences.
   \[
   16 + 16 + 0 + 49 + 1 + 25 + 0 + 16 + 196 + 1 = 320
   \]

5. **Variance Formula**: 
   The variance is the average of the squared differences. Since this is a sample, we divide by \(n - 1\), where \(n = 10\).
   \[
   \text{Variance} = \frac{320}{10 - 1} = \frac{320}{9} \approx 35.56
   \]

So, the variance is approximately **35.56**.

The correct answer is:
**b. 35.56**

Do you want more details or have any questions? Here are some related questions you might find useful:

1. How do you calculate the standard deviation from the variance?
2. What is the significance of using \(n-1\) in the variance formula?
3. How would the variance change if the grades were outliers?
4. What are the real-world applications of variance in education?
5. What is the difference between population variance and sample variance?

**Tip:** Always double-check your calculations, especially when squaring differences and summing them up.

Find the variance of the given P1 Grades: ( 75, 75, 79, 72, 80, 74, 79, 83, 93, 80)

a. 33.22
b. 35.56
c. 34.45
d. 35.65

Learn how to calculate the variance of the P1 Grades dataset: (75, 75, 79, 72, 80, 74, 79, 83, 93, 80). This step-by-step solution uses key statistical concepts such as the mean and sample variance formula. The final variance is approximately 35.56. Suitable for high school students in Grades 9-12.

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