**Exploring the Effect on Standard Deviation**In this problem, we will explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 13, 6, 12, 14.**(a)** Use the defining formula, the computation formula, or a calculator to compute $ s $. (Round your answer to one decimal place.)\[ s = 7.6 \]**(b)** Multiply each data value by 8 to obtain the new data set 40, 104, 48, 96, 112. Compute $ s $. (Round your answer to one decimal place.)\[ s = \]**(c)** Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant $ c $?- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation being $|c|$ times smaller.- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation increasing by $ c $ units.- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation remaining the same.- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation being $|c|$ times as large.**(d)** You recorded the weekly distances you bicycled in miles and computed the standard deviation to be $ s = 3.3 $ miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?- $ \bigcirc $ Yes- $ \bigcirc $ NoGiven $ 1 \text{ mile} \approx 1.6 \text{ kilometers} $, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)\[ s = \text{_____} \text{ km} \]**Need Help?**- Read It- Watch It

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In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 13, 6, 12, 14. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) S = 7.6 (b) Multiply each data value by 8 to obtain the new data set 40, 104, 48, 96, 112. Compute s. (Round your answer to one decimal place.) = S (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. Multiplying each data value by the same constant c results in the standard deviation increasing by c units. Multiplying each data value by the same constant c results in the standard deviation remaining the same. OMultiplying each data value by the same constant c results in the standard deviation being |c| times as large.

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 13, 6, 12, 14. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) S = 7.6 (b) Multiply each data value by 8 to obtain the new data set 40, 104, 48, 96, 112. Compute s. (Round your answer to one decimal place.) = S (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. Multiplying each data value by the same constant c results in the standard deviation increasing by c units. Multiplying each data value by the same constant c results in the standard deviation remaining the same. OMultiplying each data value by the same constant c results in the standard deviation being |c| times as large.

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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Concept explainers

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.

Topic Video

Question

**Exploring the Effect on Standard Deviation**

In this problem, we will explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 13, 6, 12, 14.

**(a)** Use the defining formula, the computation formula, or a calculator to compute $ s $. (Round your answer to one decimal place.)
\[ s = 7.6 \]

**(b)** Multiply each data value by 8 to obtain the new data set 40, 104, 48, 96, 112. Compute $ s $. (Round your answer to one decimal place.)
\[ s = \]

**(c)** Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant $ c $?

- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation being $|c|$ times smaller.
- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation increasing by $ c $ units.
- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation remaining the same.
- $ \bigcirc $ Multiplying each data value by the same constant $ c $ results in the standard deviation being $|c|$ times as large.

**(d)** You recorded the weekly distances you bicycled in miles and computed the standard deviation to be $ s = 3.3 $ miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

- $ \bigcirc $ Yes
- $ \bigcirc $ No

Given $ 1 \text{ mile} \approx 1.6 \text{ kilometers} $, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
\[ s = \text{_____} \text{ km} \]

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