Stats hw part 3 ---6. Use the following Stem and Leaf Plot to answer the following questions. Assume you have a sample and that the data is **not** bell-shaped.(Sample) Variable: Gas $ Key: 12 = 1.2```1 | 22 | 3 | 4 | 5 | 6 | 77 | 5 58 | 8 89 | 9```a. Use the above Stem and Leaf Plot and calculate the range.b. Use the above Stem and Leaf Plot and calculate the **Quadratic Mean**.c. **Calculate the upper fence**--- This section of text provides a stem and leaf plot for a dataset, which is useful for quickly visualizing the distribution of a sample of data, in this case, gas prices. Each number is split into a stem, representing the leading digits, and a leaf, representing the last digit. The key indicates how to interpret the plot numbers. Despite missing data in stems 2 through 5, the plot shows values ranging from $1.2 to $9.9.Questions prompt the calculation of the range, the quadratic mean (a measure of central tendency), and the upper fence (to detect potential outliers). --- **Question:**4. Estimate the standard deviation.d) Find the mean and standard deviation.e) Find the percentage of data that is 4 standard deviations away from the mean. Provide the percentage and interval. Also, quote *the proper theorem* that allows for this prediction. Express your final answer in a sentence.**Explanation:**This set of questions involves statistical concepts:- **Standard Deviation:** A measure of how spread out the numbers in a data set are.- **Mean:** The average of a data set.- **Theorem:** The use of a statistical theorem like Chebyshev’s Theorem or the Empirical Rule (68-95-99.7 rule) to determine the percentage of data within a certain number of standard deviations from the mean.These concepts are fundamental in understanding data distribution and variability.

Answered: e. Calculate the upper fence

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Stats hw part 3

**Question:**

4. Estimate the standard deviation.

d) Find the mean and standard deviation.

e) Find the percentage of data that is 4 standard deviations away from the mean. Provide the percentage and interval. Also, quote *the proper theorem* that allows for this prediction. Express your final answer in a sentence.

**Explanation:**

This set of questions involves statistical concepts:
- **Standard Deviation:** A measure of how spread out the numbers in a data set are.
- **Mean:** The average of a data set.
- **Theorem:** The use of a statistical theorem like Chebyshev’s Theorem or the Empirical Rule (68-95-99.7 rule) to determine the percentage of data within a certain number of standard deviations from the mean.

These concepts are fundamental in understanding data distribution and variability.

Expert Solution

Step 1

Part 3: c.

The samples from Stem and leaf plot is 12, 55, 55, 78, 78, 89.

The position of first quartile value for even sample size is,

$\begin{array}{rcl} First quartile (Q_{1}) & = & {[\frac{25}{100} (n + 1)]}^{t h} Data value \\ = & {[\frac{25}{100} (6 + 1)]}^{t h} Data value \\ = & 1 . 75^{t h} Data value \end{array}$

The first quartile is,

$\begin{array}{rcl} First quartile (Q_{1}) & = & 1^{s t} Data value + 0.75 (2^{n d} Data value - 1^{s t} Data value) \\ = & 12 + 0.75 (55 - 12) \\ = & 44.25 \end{array}$

The position of third quartile value for even sample size is,

$\begin{array}{rcl} Third quartile (Q_{3}) & = & {[\frac{75}{100} (n + 1)]}^{t h} Data value \\ = & {[\frac{75}{100} (6 + 1)]}^{t h} Data value \\ = & 5 . 25^{t h} Data value \end{array}$

The third quartile is,

$\begin{array}{rcl} Third quartile (Q_{3}) & = & 5^{t h} Data value + 0.25 (6^{t h} Data value - 5^{t h} Data value) \\ = & 78 + 0.25 (89 - 78) \\ = & 80.75 \end{array}$

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