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Q.100

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Introductory Statistics

Found in: Page 152

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.
• μ = 1000 FTES
• median = 1,014 FTES
• σ = 474 FTES
• first quartile = 528.5 FTES
• third quartile = 1,447.5 FTES
• n = 29 years
Calculate the mean, median, standard deviation, the first quartile, the third quartile and the IQR. Round to one decimal place

Mean $= 1809.3$

Median $= 1812.5$

Standard deviation $= 151.2$

First quartile $= 1690$

Third quartile $= 1935$

$IQR = 245$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 : To find

The mean, median, standard deviation, the first quartile, the third quartile and the IQR.

Step 2: To calculating the mean value.

The mean is one of the measurements of central tendency in statistics. The mean is defined as the total of data values divided by the number of data values. The following is the formula for determining the mean:

Mean $= μ = \frac{\sum x}{N}$

Calculation: We are given below the data.

YEAR	TOTAL FTES (x)
$2005 - 2006$	$1585$
$2006 - 2007$	$1690$
$2007 - 2008$	$1735$
$2008 - 2009$	$1935$
$2009 - 2010$	$2021$
$2010 - 2011$	$1890$
	$\sum x = 10856$

$Mean = \frac{10856}{6} = 1809.3$

Step 3: To calculating median value

First arrange the data in the ascending order

$1585, 1690, 1735, 1890, 1935, 2021$

Since we have even number of observations, therefore, the median is:

Median $= \frac{1735 + 1890}{2} = 1812.5$

Hence the median value is = 1812.5

Step 4: To calculate the standard deviation value.

$\begin{aligned} Standard deviation & = \sqrt{\frac{(1585 - 1809.3)^{2} + (1690 - 1809.3)^{2} + \dots + (1890 - 1809.3)^{2}}{6}} \\ S D & = \sqrt{\frac{50310.49 + 14232.49 + \dots + 137193.3}{6}} \\ S D & = 151.2 \end{aligned}$

Step 5: To find first and third quartile values and IQR values

First we have to arrange the data in ascending order.

$1585, 1690, 1735, 1890, 1935, 2021$

$Q_{1} = 1690$ because it is middle term of the first $50 %$ of the data

$Q_{3} = 1935$ because it the middle term of the last $50 %$ of the data

Now, the interquartile range is calculated as:

$I Q R = Q_{3} - Q_{1} = 1935 - 1690 = 245$

Step 6: Final answer

Mean $= 1809.3$

Median $= 1812.5$

Standard deviation = $= 151.2$ $= 151.2$

First quartile $= 1690 .$

Third quartile $= 1935$

$IQR = 245$

Most popular questions for Math Textbooks

Use the following information to answer the next six exercises. Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

Interquartile range (IQR) = _____ – _____ = _____

The number of books checked out from the library from $25$ students are as follows:

$0; 0; 0; 1; 2; 3; 3; 4; 4; 5; 5; 7; 7; 7; 7; 8; 8; 8; 9; 10; 10; 11; 11; 12; 12$

Find the mode.

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:

median = _______

Use the following information to answer the next six exercises. Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

$70^{t h}$ percentile = _______

The following data are the shoe sizes of $50$ male students. The sizes are continuous data since shoe size is measured. Construct a histogram and calculate the width of each bar or class interval. Suppose you choose six bars.

$9; 9; 9.5; 9.5; 10; 10; 10; 10; 10; 10; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11.5; 11.5; 11.5; 11.5; 11.5; 11.5; 11.5 12; 12; 12; 12; 12; 12; 12; 12.5; 12.5; 12.5; 12.5; 14$

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