How does this seem to compare with the 68-9599.7 rule? Determine what percentage of your data is within 2 standard deviations of the meanDoes this data seem to be normally distributed? Why or why not ### Descriptive Statistics: Times Eating Out Per Week#### Summary Statistics:- **Variable:** Times Eating Out Per Week- **Sample Size (N):** 30- **Mean:** 5.333- **Standard Error of Mean (SE Mean):** 0.598- **Standard Deviation (StDev):** 3.273- **Minimum:** 1.000- **First Quartile (Q1):** 2.750- **Median:** 5.000- **Third Quartile (Q3):** 7.000- **Maximum Observed:** 15.000This data represents the number of times individuals eat out per week. It provides a comprehensive overview of the central tendency and variability within the sample. The histogram mentioned would likely visualize these statistics, although it is not visible in this image. - **Mean** indicates the average times eating out per week.- **Standard Deviation** measures the data's dispersion from the mean.- **Quartiles** divide the data into four parts, with Q1 being the 25th percentile and Q3 the 75th percentile.The data can help in understanding eating out habits and potentially guide related lifestyle or economic studies.

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Description: How does this seem to compare with the 68-9599.7 rule? Determine what percentage of your data is within 2 standard deviations of the meanDoes this data seem to be normally distributed? Why or why not ### Descriptive Statistics: Times Eating Out Per W

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How does this seem to compare with the 68-9599.7 rule? Determine what percentage of your data is within 2 standard deviations of the mean

Does this data seem to be normally distributed? Why or why not

### Descriptive Statistics: Times Eating Out Per Week

#### Summary Statistics:

- **Variable:** Times Eating Out Per Week
- **Sample Size (N):** 30
- **Mean:** 5.333
- **Standard Error of Mean (SE Mean):** 0.598
- **Standard Deviation (StDev):** 3.273
- **Minimum:** 1.000
- **First Quartile (Q1):** 2.750
- **Median:** 5.000
- **Third Quartile (Q3):** 7.000
- **Maximum Observed:** 15.000

This data represents the number of times individuals eat out per week. It provides a comprehensive overview of the central tendency and variability within the sample. The histogram mentioned would likely visualize these statistics, although it is not visible in this image.

- **Mean** indicates the average times eating out per week.
- **Standard Deviation** measures the data's dispersion from the mean.
- **Quartiles** divide the data into four parts, with Q1 being the 25th percentile and Q3 the 75th percentile.

The data can help in understanding eating out habits and potentially guide related lifestyle or economic studies.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

To determine the percentage of the data which lies within 2 standard deviations of the mean, Chebyshev's inequality can be used.

$P (| X - μ | < k σ) \geq 1 - \frac{1}{k^{2}}$

For $k = 2$ we have

$P (| X - μ | < 2 σ) \geq 1 - \frac{1}{2^{2}} = 0.75$

Therefore, around 75% of the data are within 2 standard deviations of the mean.

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