EBK STATISTICS FOR ENGINEERS AND SCIENT
4th Edition
ISBN: 9780100274389
Author: Navidi
Publisher: YUZU
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Textbook Question
Chapter 1, Problem 16SE
The article “Hydrogeochemical Characteristics of Groundwater in a Mid-Western Coastal Aquifer System” (S. Jeen. J. Kim, et al., Geosciences Journal, 2001:339–348) presents measurements of various properties of shallow groundwater in a certain aquifer system in Korea. Following are measurements of electrical conductivity (in microsiemens per centimeter) for 23 water samples.
2099 528 2030 1350 1018 384 1499
1265 375 424 789 810 522 513
488 200 215 486 257 557 260
461 500
- a. Find the mean.
- b. Find the standard deviation.
- c. Find the
median . - d. Construct a dotplot.
- e. Find the 10% trimmed mean.
- f. Find the first
quartile . - g. Find the third quartile.
- h. Find the
interquartile range . - i. Construct a boxplot.
- j. Which of the points, if any, are outliers?
- k. If a histogram were constructed, would it be skewed to the left, skewed to the right, or approximately symmetric?
a.
Expert Solution
To determine
Find the mean.
Answer to Problem 16SE
The mean is 740.0.
Explanation of Solution
Given info:
The data shows that the measurements of the electrical conductivity.
Calculation:
Step by step procedure for finding the mean concentration using Minitab software is follows:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Measurements.
- Choose option statistics, and select Mean.
- Click OK.
Output using Minitab software is,
From the output the mean is 74.0.
b.
Expert Solution
To determine
Find the standard deviation.
Answer to Problem 16SE
The standard deviation is 550.
Explanation of Solution
Calculation:
Step by step procedure for finding the mean concentration using Minitab software is follows:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Measurements.
- Choose option statistics, and select Standard deviation.
- Click OK.
Output using Minitab software is,
From the output the standard deviation is 550.
c.
Expert Solution
To determine
Compute the median.
Answer to Problem 16SE
The median is 513.
Explanation of Solution
Calculation:
Step by step procedure for finding the median concentration is follows:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Measurements.
- Choose option statistics, and select Median.
- Click OK.
Output using Minitab software is,
From the output the median is 513.
d.
Expert Solution
To determine
Construct a dotplot.
Answer to Problem 16SE
The dotplot is,
Explanation of Solution
Calculation:
Step by step procedure to constructing dotplot using Minitab procedure is follows:
- Choose Graph > Dotplot.
- Choose One Y-Simple and then click OK.
- In Graph variables, enter Measurements.
- Click OK.
e.
Expert Solution
To determine
Compute the 10% trimmed mean.
Answer to Problem 16SE
The 10% trimmed mean is 657.16.
Explanation of Solution
Calculation:
The sample size n is 23.
Trimmed mean:
The trimmed mean is a measure of center that is designed to be unaffected by outliers.
The 10% of the value is,
Therefore, trim the highest 2 and lowest 2 observations from the given data.
The observations after trimmed values are,
| n | Measurements |
| 1 | 257 |
| 2 | 260 |
| 3 | 375 |
| 4 | 384 |
| 5 | 424 |
| 6 | 461 |
| 7 | 486 |
| 8 | 488 |
| 9 | 500 |
| 10 | 513 |
| 11 | 522 |
| 12 | 528 |
| 13 | 557 |
| 14 | 789 |
| 15 | 810 |
| 16 | 1018 |
| 17 | 1265 |
| 18 | 1350 |
| 19 | 1499 |
| Total | 12,486 |
| Mean |
From the table, the trimmed mean is 657.16.
f.
Expert Solution
To determine
Compute the first quartile.
Answer to Problem 16SE
The first quartile of the concentrations is 384.
Explanation of Solution
Calculation:
Step by step procedure for finding the first quartile of the concentration is follows:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Measurements.
- Choose option statistics, and select First quartile.
- Click OK.
Output using Minitab software is,
From the output the first quartile is 384.
g.
Expert Solution
To determine
Compute the third quartile.
Answer to Problem 16SE
The third quartile is 1,018.
Explanation of Solution
Calculation:
Step by step procedure for finding the third quartile of the concentration is follows:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Measurements.
- Choose option statistics, and select Third quartile.
- Click OK.
Output using Minitab software is,
From the output the third quartile is 1,018.
h.
Expert Solution
To determine
Compute the interquartile range.
Answer to Problem 16SE
The interquartile range is 634.
Explanation of Solution
Calculation:
Step by step procedure for finding the third quartile of the concentration is follows:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Measurements.
- Choose option statistics, and select Interquartile range.
- Click OK.
Output using Minitab software is,
From the output the interquartile range is 634.
i.
Expert Solution
To determine
Construct a boxplot for the concentrations.
Answer to Problem 16SE
The boxplot for the given data is,
Explanation of Solution
Calculation:
Step by step procedure to constructing boxplot using Minitab procedure is follows:
- Choose Graph > Boxplot or Stat > EDA > Boxplot.
- Under One Y, choose Simple. Click OK.
- In Graph variables, enter Measurements.
- Click OK.
j.
Expert Solution
To determine
Identify the points in any outliers.
Answer to Problem 16SE
The points 2,030 and 2,099 are outliers.
Explanation of Solution
Calculation:
Outlier:
If the sample contain a few points that are much larger or smaller than the rest then the points are called outliers.
From the boxplot, it can be concluded that there are two outliers. They are 2,030 and 2,099.
k.
Expert Solution
To determine
Identify it is skewed to the left, skewed to the right or approximately symmetric if histogram were constructed.
Answer to Problem 16SE
The histogram is skewed to the right.
Explanation of Solution
Calculation:
Left and Right skewed:
If the sample is left skewed then the median is closer to the third quartile than to the first quartile and if the sample is right skewed then the median is closer to the first quartile than to the third quartile.
From the boxplot, it is observed that the median is closer to the first quartile than to the third quartile. That is, the data is skewed to the right.
Therefore, the histogram is skewed to the right.
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Chapter 1 Solutions
EBK STATISTICS FOR ENGINEERS AND SCIENT
Ch. 1.1 - Each of the following processes involves sampling...Ch. 1.1 - If you wanted to estimate the mean height of all...Ch. 1.1 - True or false: a. A simple random sample is...Ch. 1.1 - A sample of 100 college students is selected from...Ch. 1.1 - A certain process for manufacturing integrated...Ch. 1.1 - Refer to Exercise 5. True or false: a. If the...Ch. 1.1 - To determine whether a sample should be treated as...Ch. 1.1 - A medical researcher wants to determine whether...Ch. 1.1 - A medical researcher wants to determine whether...Ch. 1.2 - True or false: For any list of numbers, half of...
Ch. 1.2 - Is the sample mean always the most frequently...Ch. 1.2 - Is the sample mean always equal to one of the...Ch. 1.2 - Is the sample median always equal to one of the...Ch. 1.2 - Find a sample size for which the median will...Ch. 1.2 - For a list of positive numbers, is it possible for...Ch. 1.2 - Is it possible for the standard deviation of a...Ch. 1.2 - In a certain company, every worker received a...Ch. 1.2 - In another company, every worker received a 5%...Ch. 1.2 - A sample of 100 adult women was taken, and each...Ch. 1.2 - In a sample of 20 men, the mean height was 178 cm....Ch. 1.2 - Each of 16 students measured the circumference of...Ch. 1.2 - Refer to Exercise 12. a. If the measurements for...Ch. 1.2 - There are 10 employees in a particular division of...Ch. 1.2 - Quartiles divide a sample into four nearly equal...Ch. 1.2 - In each of the following data sets, tell whether...Ch. 1.3 - The weather in Los Angeles is dry most of the...Ch. 1.3 - Forty-five specimens of a certain type of powder...Ch. 1.3 - Refer to Table 1.2 (in Section 1.2). Construct a...Ch. 1.3 - Following are measurements of soil concentrations...Ch. 1.3 - A certain reaction was run several times using...Ch. 1.3 - Sketch a histogram for which a. The mean is...Ch. 1.3 - The figure below is a histogram showing the...Ch. 1.3 - The histogram below presents the compressive...Ch. 1.3 - Refer to Table 1.4 (in Section 1.3). a. Using the...Ch. 1.3 - Refer to Table 1.5 (in Section 1.3). a. Using the...Ch. 1.3 - The following table presents the number of...Ch. 1.3 - Which of the following statistics cannot be...Ch. 1.3 - A sample of 100 resistors has an average...Ch. 1.3 - Following are boxplots comparing the amount of...Ch. 1.3 - Following are summary statistics for two data...Ch. 1.3 - Match each histogram to the box plot that...Ch. 1.3 - Prob. 17ECh. 1.3 - Match each scatterplot to the statement that best...Ch. 1.3 - Prob. 19ECh. 1 - A vendor converts the weights on the packages she...Ch. 1 - Refer to Exercise 1. The vendor begins using...Ch. 1 - The specification for the pull strength of a wire...Ch. 1 - A coin is tossed twice and comes up heads both...Ch. 1 - The smallest number on a list is changed from 12.9...Ch. 1 - There are 15 numbers on a list, and the smallest...Ch. 1 - There are 15 numbers on a list, and the mean is...Ch. 1 - The article The Selection of Yeast Strains for the...Ch. 1 - Concerning the data represented in the following...Ch. 1 - True or false: In any boxplot, a. The length of...Ch. 1 - For each of the following histograms, determine...Ch. 1 - In the article Occurrence and Distribution of...Ch. 1 - The article Vehicle-Arrival Characteristics at...Ch. 1 - The cumulative frequency and the cumulative...Ch. 1 - The article Hydrogeochemical Characteristics of...Ch. 1 - Water scarcity has traditionally been a major...Ch. 1 - Prob. 18SECh. 1 - The article The Ball-on-Three-Ball Test for...
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