Answered: Find the range, sample standard…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Find the range, sample standard deviation and inter-quartile range (IQR) of the following data set.

range = (Please enter an exact answer.)

standard deviation (ss) = (Round to one decimal place.)

IQR = (Please enter an exact answer.)

A new number, 252, is added to the data set above. Find the range, sample standard deviation and IQR of the new data set.

range = (Please enter an exact answer.)

standard deviation = (Round to one decimal place.)

IQR = (Please enter an exact answer.)

Which measure of spread is less affected by the addition of the extreme observation?

IQR
Range
standard deviation

Expert Solution

Step 1: Introduction

The formula's are

$r a n g e (R) = m a x i m u n v a l u e - m i n i m u m v a l u e s \tan d a r d d e v i a t i o n (s d) = \sqrt{\frac{\sum_{i = 1}^{n} {(x_{i} - x)}^{2}}{n - 1}} m e a n (x) = \frac{{\sum x_{i}}_{i = 1}^{n}}{n} I Q R = Q_{3} - Q_{1}$

Now, let us sort our data in ascending order,

21, 55, 55, 57, 58, 63, 70, 76, 81, 93

Now, let first calculate mean

$\begin{array}{rcl} m e a n (x) & = & \frac{21 + 55 + 55 + 57 + 58 + 63 + 70 + 76 + 81 + 93}{10} \\ = & 62.9 \end{array}$

Now, standard deviation

$\begin{array}{rcl} s d & = & \sqrt{\frac{{(21 - 62.9)}^{2} + . . . + {(93 - 62.9)}^{2}}{10 - 1}} \\ = & 19.42192 \end{array}$

$\begin{array}{rcl} R a n g e & = & 93 - 21 \\ = & 72 \end{array}$

$\begin{array}{rcl} Q_{1} & = & 55 \\ Q_{3} & = & 76 \\ I Q R & = & 76 - 55 \\ = & 21 \end{array}$

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