Question: Use the applet Standard Deviation to study the effect that multiplying or dividing each number in a data set by the same number has on

Use the applet Standard Deviation to study the effect that multiplying or dividing each number in a data set by the same number has on the standard deviation. Begin by setting appropriate limits and plotting the given data on the number line provided in the applet.
0 1 1 1 2 2 3 4
a. Record the standard deviation. Then multiply each data item by 2, plot the new data items, and record the standard deviation. Repeat the process, first multiplying each of the original data items by 3 and then by 4. Describe what happens to the standard deviation as the data items are multiplied by ever higher numbers. Divide each standard deviation by the standard deviation of the original data set. Do you see a pattern? Explain.
b. Divide each of the original data items by 2, plot the new data, and record the standard deviation. Repeat the process, first dividing each of the original data items by 3 and then by 4. Describe what happens to the standard deviation as the data items are divided by ever higher numbers. Divide each standard deviation by the standard deviation of the original data set. Do you see a pattern? Explain.
c. Using your results from parts a and b, describe what happens to the standard deviation of a data set when each of the data items in the set is multiplied or divided by a fixed number n. Experiment by repeating parts a and b for other data sets if you need to.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a UseStandard deviation applet to obtain the standard deviation for the give set Dataset 0 1 1 1 2 2 3 4 Applet procedure Step 1 Select Add point and enter 0 Step 2 Click ok Step 3 Select Add point an... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics Questions!

Use the applet Standard Deviation to study the effect that an extreme value has on the standard deviation. Begin by setting appropriate limits and plotting the following data on the number line...

please solve all of these questions:- A qualitative variable with three classes (X, Y, and Z) is measured for each of 20 units randomly sampled from a target population. The data (observed class for...

find solutions:- A qualitative variable with three classes (X, Y, and Z) is measured for each of 20 units randomly sampled from a target population. The data (observed class for each unit) are as...

Consider the following two sample data sets. Sample A Sample B 121 171 158 171 152 170 173 184 163 168 169 171 157 85 145 190 183 185 165 172 196 140 173 206 170 159 172 172 174 169 161 187 100 199...

Use the applet Standard Deviation to determine whether an item in a data set may be an outlier. Begin by setting appropriate limits and plotting the given data on the number line provided in the...

Consider the following sample data set. 171 152 170 168 169 171 190 183 185 140 173 206 172 174 169 199 151 180 167 170 188 a. Construct a box plot. b. Identify any outliers that may exist in the...

Standard Deviation Standard deviation is a measure of the dispersion of a data set. In more layman's terms, it measures the general variation of the mean value and the other values in the data set. A...

answer asappp a. Use the data given to calculate annual returns for Bartman, Reynolds, and the Wiltor 5000 Index, and then calculate average returns over the 5-year period. (Hint: Remember returns...

Week 5 Lecture 13 This week we look at two different approaches to analyzing data and making inferences about the populations they come from. The first is confidence intervals, a range of values that...

You are an IT Manager for a small company and must create a program to track your companys personal computer inventory. Create a class that can be used for a Personal Computer. The class should have...

Recall that Table 14.6 (page 590) presents data concerning the need for labor in 16 U.S. Navy hospitals. This table gives values of the dependent variable Hours (monthly labor hours) and of the...

One of the most powerful tools in Excel for decision making is the IF function found in the Lookup & Reference section of the Function library. Yes No

Under what circumstances is the sign test preferred to the t-test for making inferences about the central tendency of a population?

In Canada, the Supreme Court recently ruled that employees can be tested for drugs only if management has reasonable cause to administer the test. An article in Chance (Vol. 28, 2015) focused on the...

The Journal of Research of the National Institute of Standards and Technology (November-December 2003) published a study of a double intrusion detection system with independent systems. If there is...

Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23. Recall that the level of support for corporate sustainability (measured on a...

5 Financial statements prepared on the basis inform users not only of transaction involving the payment and receipt of cash but also of obligations to pay cash in the future and of resources that...

Udala Uke's had the following transactions involving notes payable. July 1, 2021 Nov. 1, 2021 Dec. 31, 2021 Feb. 1. Apr. 1, 2022 2022 Borrows $42,000 from First National Bank by signing a nine-month,...

10. Cigar smoking: The data in the following table show the results of a national study of 137,243 U.S. men that investigated the association between cigar smoking and death from cancer. Note:...