Chapter 3: Q.3.69. (page 113)

In Exercises $3.65 - 3.70$ , 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
$1, 9, 8, 4, 3$

Short Answer

Expert verified

$a) R a n g e = 8 b) s a m p l e s \tan d a r d d e v i a t i o n =$ $3.39$

Step by step solution

Step 1. Given information.

We have given data : 1,9,8,4,3

Step 2. Range of the data.

$R a n g e = M a x . v a l u e - M i n . v a l u e R a n g e = 9 - 1 R a n g e = 8$

Step 3. Mean of the data.

$s = \sqrt{\frac{\sum_{} {x - x)^{2}}{n - 1}} M e a n, x = \frac{\sum_{} x}{n} M e a n = \frac{1 + 9 + 8 + 4 + 3}{5} M e a n = \frac{25}{5} M e a n = 5 s a m p i e s i z e, n = 5$

Step 4. Standard deviation of the data.

Variable $x$	Deviation from mean $x - x$	Squared deviation ${(x - x)}^{2}$
$1 9 8 4 3$	$- 4 4 3 - 1 - 2$	$16 16 9 1 4 46$

Thus, the standard deviation is

$s = \sqrt{\frac{\sum_{} {(x - x)}^{2}}{n - 1}} = \sqrt{\frac{46}{5 - 1}} = \sqrt{11.5} = 3.39$

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In Exercises $3.65 - 3.70$ , 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
$1, 9, 8, 4, 3$

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

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In Exercises 3.65-3.70, 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 deviation1,9,8,4,3

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

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises $3.65 - 3.70$ , 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
$1, 9, 8, 4, 3$