Concept explainers
a)
To find the first and third quartiles of the given data.
a)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
First quartile = 1414.75 and third quartile = 2931
Explanation of Solution
Formula:
First quartile Q1:
Third quartile Q3:
Calculation:
Data sorted in ascending order:
135 | 1229 | 1658 | 2128 | 2486 | 3843 |
559 | 1339 | 1686 | 2155 | 2561 | 3968 |
700 | 1359 | 1704 | 2166 | 2831 | 4055 |
984 | 1366 | 1730 | 2218 | 2915 | 4392 |
1090 | 1431 | 1803 | 2273 | 2979 | 4472 |
1127 | 1433 | 1808 | 2320 | 3329 | 4809 |
1128 | 1507 | 1880 | 2321 | 3336 | 5434 |
1176 | 1526 | 2015 | 2395 | 3375 | 8460 |
1177 | 1592 | 2071 | 2427 | 3637 | |
1211 | 1598 | 2096 | 2459 | 3672 |
Here, n = 58
First need to find First quartile and third quartile
First Quartile:
First quartile is 1414.75
Third quartile:
Third quartile is 2931.
b)
To find median of the data.
b)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
Median is 2083.5
Explanation of Solution
Formula:
Calculation:
c)
To find upper and lower outlier boundaries.
c)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
Lower outlier boundary is -859.625
Upper outlier boundary is 5205.375
Explanation of Solution
Formula:
IQR:
Calculation:
Therefore,
d)
To find the 135 and 559 are outliers or not.
d)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
135 and 559 are not outliers.
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 -859.625
Upper outlier boundary is 5205.375
135 and 559 are within
e)
To find the 8460 and 5434 are outliers or not.
e)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
The 8460 and 5434 are outliers.
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 -859.625
Upper outlier boundary is 5205.375
8460 and 5434 are greater than upper outlier limit 5205.375. Hence both are outliers.
f)
To construct a boxplot from given data
f)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Boxplot from given data:
g)
To find shape of the distribution
g)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
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.
h)
To find 15st percentile
h)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
15st percentile is 1176.85
Explanation of Solution
Therefore,
i)
To find 65th percentile
i)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
65th percentile is 2406.2
Explanation of Solution
Therefore,
j)
To find percentile rank for 1433 words
j)
![Check Mark](/static/check-mark.png)
Answer to Problem 38E
Percentile rank for 1433 words is 25.86%
Explanation of Solution
Formula:
Calculation:
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Chapter 3 Solutions
ELEMENTARY STATISTICS(LL)(FD)
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
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