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**Question 8** (0.2 points)

Calculate E[X] using the following information.  3.5

3

2.5

4

It is not possible to calculate E[X] with the given information.

To calculate \( E[X] \), which represents the expected value (or mean) of the number of takeout orders, we will use the data in the table provided. The expected value \( E[X] \) for a sample is the average of the values in the sample.

Here is the data from the table:

- Household 1: 3 takeout orders
- Household 2: 5 takeout orders
- Household 3: 4 takeout orders
- Household 4: 2 takeout orders

To calculate \( E[X] \):

\[
E[X] = \frac{3 + 5 + 4 + 2}{4}
\]

Let me compute that for you.The expected value \( E[X] \) of the number of takeout orders is \( 3.5 \).

Would you like further explanation or have any additional questions?

Here are 5 related questions to expand on this:

1. How would you calculate the variance of this sample data?
2. What is the significance of \( E[X] \) in probability theory?
3. How does the sample mean \( \bar{X} \) compare to the population mean?
4. Can you estimate the median number of takeout orders from this data?
5. What other measures of central tendency could you use here?

**Tip**: When calculating \( E[X] \) for a sample, ensure that all values are from a representative sample to minimize bias.

Calculate E[X] using the following information.  3.5

3

2.5

4

It is not possible to calculate E[X] with the given information.

Learn how to calculate the expected value E[X] using sample data of takeout orders from households. Understand key statistical concepts and formulas with a detailed step-by-step solution. Suitable for high school students in Grades 9-12.

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