Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are th statistics representative of the current population of all people? 9.2 8.9 10.2 9.5 9.5 10.4 9.6 10.1 9.5 9.5 9 0 The range of the sample data is 1.5 inches. (Type an integer or a decimal. Do not round.) The standard deviation of the sample data is (Round to two decimal places as needed.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Statistical Analysis of Foot Length Data
**Problem Statement:**
Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are the statistics representative of the current population of all people?
#### Foot Length Data (in inches):
9.2, 8.9, 10.2, 9.5, 10.4, 9.6, 10.1, 9.8, 9.5, 9.9, 9.5
1. **Range Calculation:**
The range of the sample data is calculated by subtracting the smallest value from the largest value in the dataset.
- Smallest value: 8.9 inches
- Largest value: 10.4 inches
\[
\text{Range} = 10.4 - 8.9 = 1.5 \text{ inches}
\]
The range of the sample data is **1.5 inches**.
2. **Standard Deviation Calculation:**
The standard deviation provides a measure of the dispersion or spread of the data points around the mean. Since the exact method to enter the standard deviation and the specific calculation method (population vs sample) is not provided, we'll denote that the standard deviation needs to be calculated and rounded to two decimal places, as specified.
- The standard deviation of the sample data (rounded to two decimal places) is to be calculated.
3. **Variance Calculation:**
The variance is the square of the standard deviation and represents the average of the squared differences from the mean.
#### Conclusion:
- Entry fields or placeholders specify where the calculated range and standard deviation should be typed.
- The data and required calculations allow the statistical analysis of foot lengths to determine the range and the variability within the dataset.
In a real-world application, confirming whether these statistics are representative of the current population would require updated and more comprehensive data from the current population, along with the appropriate sampling techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b7cc1c7-6b89-434c-9693-fee285d86a2f%2F100327e2-09d5-417d-a1c1-5eef2da5dcc7%2Fob4e99_processed.jpeg&w=3840&q=75)
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