 # S O C In problem 3.11, you computed measures of central tendency for the number of cars per 1000 population for 15 nations. The scores are reproduced here. Compute the standard deviation for this variable, and write a paragraph summarizing the mean, median, and standard deviation. Nation Number of Motor Vehicles per 1000 population (2009) United States 786 Germany 588 Canada 608 Japan 588 Australia 703 Israel 330 Russia 271 Mexico 278 Tunisia 130 Bolivia 87 China 69 Niger 8 Kenya 25 Thailand 172 India 18 Mean = Median = Standard deviation = Source: World Bank, 2014. Retrieved from http://data.worldbank.org/indicator/lS.VEH.NVEH.P3 3.11 S O C The following table lists the approximate number of cars per 1000 population for 15 nations. Compute the mean and median for these data. Which is greater in value? Is there a positive skew in the data? How do you know? Nation Number of Motor Vehicles per 1000 population (2009) United States 786 Germany 588 Canada 608 Japan 588 Australia 703 Israel 330 Russia 271 Mexico 278 Tunisia 130 Bolivia 87 China 69 Niger 8 Kenya 25 Thailand 172 India 18 Mean = Median = ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 4, Problem 4.10P
Textbook Problem
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## S O C In problem 3.11, you computed measures of central tendency for the number of cars per 1000 population for 15 nations. The scores are reproduced here. Compute the standard deviation for this variable, and write a paragraph summarizing the mean, median, and standard deviation. Nation Number of Motor Vehicles per 1000 population (2009) United States 786 Germany 588 Canada 608 Japan 588 Australia 703 Israel 330 Russia 271 Mexico 278 Tunisia 130 Bolivia 87 China 69 Niger 8 Kenya 25 Thailand 172 India 18 Mean = Median = Standard deviation = Source: World Bank, 2014. Retrieved from http://data.worldbank.org/indicator/lS.VEH.NVEH.P33.11 S O C The following table lists the approximate number of cars per 1000 population for 15 nations. Compute the mean and median for these data. Which is greater in value? Is there a positive skew in the data? How do you know? Nation Number of Motor Vehicles per 1000 population (2009) United States 786 Germany 588 Canada 608 Japan 588 Australia 703 Israel 330 Russia 271 Mexico 278 Tunisia 130 Bolivia 87 China 69 Niger 8 Kenya 25 Thailand 172 India 18 Mean = Median =

Expert Solution
To determine

To find:

The standard deviation for the given variable

### Explanation of Solution

Given:

The following table shows the number of cars per 1000 population for 15 nations.

 Nation Number of Motor Vehicles per 1000 population (2009) United States 786 Germany 588 Canada 608 Japan 588 Australia 703 Israel 330 Russia 271 Mexico 278 Tunisia 130 Bolivia 87 China 69 Niger 8 Kenya 25 Thailand 172 India 18

Formula used:

Let the data values be Xi’s.

The formula to calculate median for odd number of terms is given by,

Median=(Number of terms+1)2

The formula to calculate mean is given by,

X¯=i=1NXiN

The formula to calculate standard deviation is given by,

s=(XiX¯)2N

Where, N is the population size.

Calculation:

Arrange the data in the increasing order.

The data in increasing order is given by,

 S. No Income 1 8 2 18 3 25 4 69 5 87 6 130 7 172 8 271 9 278 10 330 11 588 12 588 13 608 14 703 15 786

The number of terms is 15, which is odd.

The median for the odd number of terms is given by,

Median=(Number of terms+1)2

Substitute 15 for number of terms in the above mentioned formula,

Median=(15+1)2=162=8

The median income corresponding to 8th number is 271.

The size of the population is 15.

The mean is given by,

X¯=i=1NXiN

Substitute 15 for N, 786 for X1, 588 for X2 and so on in the above mentioned formula,

X¯=786+588+...+1815=466115=310.73 ……(1)

Consider the following table of sum of squares,

 (Xi) (Xi−X¯) (Xi−X¯)2 786 475.27 225881.6 588 277.27 76878.65 608 297.27 88369.45 588 277.27 76878.65 703 392.27 153875.8 330 19.27 371.3329 271 −39.73 1578.473 278 −32.73 1071.253 130 −180.73 32663.33 87 −223.73 50055.11 69 −241

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