Chapter 3: Q.3.67. (page 113)

In Exercises $3.65 - 3, 67$ , we have provided simple data sets for you to practice the basics of finding measures of variation . For each data set determine.
a) Range
b) sample standard deviation
$1, 2, 4, 4$

Short Answer

Expert verified

$a) R a n g e = 3 b) s a m p l e s \tan d a r d d e v i a t i o n = 1.5$

Step by step solution

Step 1. Given information.

We have given data : 1,2,4,4

Step 2. Range of the data.

$R a n g e = M a x . v a l u e - M i n . v a l u e R a n g e = 4 - 1 R a n g e = 3$

Step 3. Mean of the data.

$s = \sqrt{\frac{\sum_{} {x - x)^{2}}{n - 1}} M e a n, x = \frac{\sum_{} x}{n} M e a n = \frac{1 + 2 + 4 + 4}{4} M e a n = \frac{11}{4} M e a n = 2.75 s a m p i e s i z e, n = 4$

Step 4. Standard deviation of the data.

Variable $x$	Deviation from mean $x - x$	Squared deviation role="math" localid="1651598578463" ${(x - x)}^{2}$
$1$	$- 1.75$	$3.06$
$2$	$- 0.75$	$0.56$
$4$	$1.25$	$1.56$
$4$	$1.25$	$1.56$

Thus, the standard deviation is

$s = \sqrt{\frac{\sum_{} {(x - x)}^{2}}{n - 1}} = \sqrt{\frac{6.75}{4 - 1}} = \sqrt{2.25} = 1.5$

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In Exercises $3.65 - 3, 67$ , we have provided simple data sets for you to practice the basics of finding measures of variation . For each data set determine.
a) Range
b) sample standard deviation
$1, 2, 4, 4$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Range of the data.

Step 3. Mean of the data.

Step 4. Standard deviation of the data.

One App. One Place for Learning.

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In Exercises 3.65-3,67, we have provided simple data sets for you to practice the basics of finding measures of variation . For each data set determine.a) Rangeb) sample standard deviation1,2,4,4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Range of the data.

Step 3. Mean of the data.

Step 4. Standard deviation of the data.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises $3.65 - 3, 67$ , we have provided simple data sets for you to practice the basics of finding measures of variation . For each data set determine.
a) Range
b) sample standard deviation
$1, 2, 4, 4$