Using the data below, calculate the variance 43,20,35,77,24,51,48,50,16 write your answer below to 2 decimal places 

To calculate the variance, follow these steps:

1. **Find the mean** (average) of the dataTo calculate the variance, follow these steps:

1. **Find the mean** (average) of the 
\[
\text{Mean} = \frac{43 + 20 + 35 + 77 + 24 + 51 + 48 + 50 + 16}{9} = \frac{364}{9} = 40.44
\]

2. **Find the squared differences** from the mean for each data point:
\[
(43 - 40.44)^2 = 6.57, \quad (20 - 40.44)^2 = 422.59, \quad (35 - 40.44)^2 = 29.63, \quad (77 - 40.44)^2 = 1331.86
\]
\[
(24 - 40.44)^2 = 273.13, \quad (51 - 40.44)^2 = 109.13, \quad (48 - 40.44)^2 = 57.11, \quad (50 - 40.44)^2 = 91.55, \quad (16 - 40.44)^2 = 604.95
\]

3. **Sum of squared differences**:
\[
6.57 + 422.59 + 29.63 + 1331.86 + 273.13 + 109.13 + 57.11 + 91.55 + 604.95 = 2926.52
\]

4. **Divide by the number of data points (n = 9)** to get the variance:
\[
\text{Variance} = \frac{2926.52}{9} = 325.17
\]

So, the variance is **325.17**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you calculate the standard deviation from the variance?
2. What is the difference between sample variance and population variance?
3. How does variance change if we add a constant to all data points?
4. How does the variance formula adjust for a sample rather than a full population?
5. What real-world situations require calculating variance?

**Tip**: Always check if you are calculating sample or population variance; the formula differs slightly!

Using the data below, calculate the variance 43,20,35,77,24,51,48,50,16 write your answer below to 2 decimal places.

Learn how to calculate the variance of the data set 43, 20, 35, 77, 24, 51, 48, 50, 16 with a detailed step-by-step solution. This problem covers key statistical concepts, including the mean and variance formulas, suitable for students in Grades 9-12.

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