Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
3rd Edition
ISBN: 9781259969454
Author: William Navidi Prof.; Barry Monk Professor
Publisher: McGraw-Hill Education
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Question
Chapter 3.3, Problem 36E

a)

To determine

To find the first and third quartiles of the given data.

a)

Expert Solution
Check Mark

Answer to Problem 36E

First quartile = 2 and third quartile = 18.25

Explanation of Solution

Formula:

First quartile Q1:

  Q1=14(n+1)thvalue

Third quartile Q3:

  Q3=34(n+1)thvalue

Calculation:

Data sorted in ascending order:

    x
    1315
    1416
    1418
    1419
    2520
    2623
    2733
    2850
    2958
    210100

Here, n = 24

First need to find First quartile and third quartile

First Quartile:

   Q 1 = 1 4 (30+1) th value Q 1 = 1 4 (31) th value Q 1 = (7.75) th valueQ1=2+0.75×(22)Q1=2

First quartile is 2

Third quartile:

   Q 3 = 3 4 (n+1) th value Q 3 = 3 4 (30+1) th value Q 3 = 3 4 (31) th value Q 3 = (23.25) th valueQ3=18+0.25×(1918)Q3=18.25

Third quartile is 18.25

b)

To determine

To find median of the data.

b)

Expert Solution
Check Mark

Answer to Problem 36E

Median is 5.5

Explanation of Solution

Formula:

  median=( n+12)thvalue

Calculation:

  median=( 30+1 2)thvaluemedian=(15.5)thvaluemedian=5+62median=5.5

c)

To determine

To find upper and lower outlier boundaries

c)

Expert Solution
Check Mark

Answer to Problem 36E

Lower outlier boundary is -22.375

Upper outlier boundary is 42.625

Explanation of Solution

  Q1=2Q3=18.25

Formula:

IQR:

  IQR=Q3Q1

Calculation:

  IQR = Q3Q1IQR = 7.5-3IQR = 4.25

Therefore,

  Lower outlier limit = Q11.5 × IQRLower outlier limit = 21.5×16.25Lower outlier limit = -22.375AndUpper outlier limit = Q3+1.5 × IQRUpper outlier limit = 18.25+1.5×16.25Upper outlier limit = 42.625

d)

To determine

To find the list of outlier countries.

d)

Expert Solution
Check Mark

Answer to Problem 36E

The outlier countries are Japan, France and United states.

Explanation of Solution

Outliers are those values which are less than Q1-1.5 x IQR and greater than Q3+1.5 x IQR.

Here

Lower outlier boundary is -22.375

Upper outlier boundary is 42.625

There is no any value less than -22.375. But there are three values larger than 42.625 which are 50, 58 and 100. Hence outlier points are 50, 58 and 100. Corresponding countries to the outlier points are Japan, France and United states.

e)

To determine

To construct a boxplot from given data

e)

Expert Solution
Check Mark

Explanation of Solution

Boxplot:

  Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561, Chapter 3.3, Problem 36E

f)

To determine

To find shape of the distribution

f)

Expert Solution
Check Mark

Answer to Problem 36E

The shape of the distribution is positively-skewed.

Explanation of Solution

Here, median is close to first quartile. Hence the shape of the distribution is positively-skewed.

g)

To determine

To find 45th percentile

g)

Expert Solution
Check Mark

Answer to Problem 36E

45th percentile is 2.54

Explanation of Solution

  PercentilePosition=(n+1)P100PercentilePosition=(30+1)×45100PercentilePosition=10.54

Therefore,

  P45=2+0.54×(32)P45=2.54

h)

To determine

To find 88th percentile

h)

Expert Solution
Check Mark

Answer to Problem 36E

88th percentile is 39.44

Explanation of Solution

  PercentilePosition=(n+1)P100PercentilePosition=(30+1)×88100PercentilePosition=27.28

Therefore,

  P88=33+0.28×(5027)P88=39.44

i)

To determine

To find percentile rank of 20 nuclear reactors

i)

Expert Solution
Check Mark

Answer to Problem 36E

Percentile rank of 20 nuclear reactor is 80%.

Explanation of Solution

Formula:

  Percentilerankofx=no.ofvaluesbelowxn×100

Calculation:

  Percentilerankof20=2430×100Percentilerankof20=80%

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Chapter 3 Solutions

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

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