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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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