Concept explainers
Videos
a.
Arrange the data and obtain Xmin and Xmax.
a.
Answer to Problem 99CE
The value of Xmin is 0.9.
The value of Xmax is 11.9.
Explanation of Solution
Calculation:
The data state to choose a dataset to prepare a brief descriptive report.
Here, the data chosen is Data set A.
The Data set A represents the percentage of sales in selected industries.
The data set A of sales percent can be sorted either ascending or descending.
Here, the data is sorted in the ascending order.
Sorting:
Software procedure:
Step-by-step procedure to sort the data using the MINITAB software is given below:
- Choose Data > Sort.
- In columns to sort by, enter Percent.
- Under Columns to sort , Choose specified columns.
- In columns, enter the percent and choose increasing option.
- In storage location for current columns, choose “specified columns of the current worksheet”.
- In columns, enter “sorted percent”.
- Click ok.
Thus, the sorted data has been stored in the column of sorted percent.
Minimum and Maximum:
Step-by-step procedure to find the minimum and maximum using the MINITAB software using the given below:
- Choose Calc>calculator.
- In store result in variable box, enter Minimum.
- Under Expression, enter “MIN(Percent)”.
- Click ok.
- Choose Calc>calculator.
- In store result in variable box, enter Maximum.
- Under Expression, enter “MAX(Percent)”.
- Click ok.
Data display:
Step-by-step procedure to display the data using the MINITAB software using the given below:
- Choose data> display data.
- Select the columns to display as Minimum, Maximum.
- Click ok.
Output using the MINITAB software is given below:
Thus, the value of Xmin is 0.9 and the value of Xmax is 11.9.
b.
Construct a histogram.
b.
Answer to Problem 99CE
Histogram:
Output obtained from MINITAB software is:
Explanation of Solution
Calculation:
Software procedure:
- Step by step procedure to draw the Histogram using MINITAB software is given below:
- Choose Graph > Histogram.
- Choose Simple, and then click OK.
- In Graph variables, enter the Percent.
- Click OK.
Thus, the histogram has been obtained.
By observing the graph, it is clear that the curve is right skewed. Hence, it is appropriate to conclude that the data is approximately right skewed. Thus, the data set A for percent of sales is approximately right skewed.
c.
Find the
c.
Answer to Problem 99CE
The mean score is 3.55.
The median score is 3.
Explanation of Solution
Mean and median:
Software procedure:
Step-by-step procedure to find the mean, the median using the MINITAB software is given below:
- Choose Stat > Basic Statistics > Display
Descriptive Statistics . - In Variables enter the columns Percent.
- Choose option statistics, and select Mean, Median.
- Click OK.
Output using the MINITAB software is given below:
- Thus, the mean and the median for the data set A are 3.55 and 3 respectively.
Shape of the distribution:
- For symmetric data, the mean, the median and the
mode are equal. - For positively skewed data, the mean exceeds the median.
- For negatively skewed data, the mean is lower than the median.
From the value of mean, median, it is observed that the value of mean is greater than that of the median.
Thus, the data is said to be right skewed or positively skewed.
d.
Find the standard deviation for data set A.
d.
Answer to Problem 99CE
The standard deviation for data set A is 2.749.
Explanation of Solution
Standard deviation:
Software procedure:
Step-by-step procedure to find the mean and standard deviation using the MINITAB software is given below:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Percent.
- Choose option statistics, and select Standard deviation.
- Click OK.
Output using the MINITAB software is given below:
- Thus, the standard deviation have been obtained.
e.
Standardize the data and identify the outliers and unusual observations.
e.
Answer to Problem 99CE
The standardized values of dataset A are given below:
| -0.9640 | -0.6366 | 0.3456 | 0.3820 | -0.6730 | 0.0909 |
| 0.7093 | -0.0182 | -0.0182 | -0.9276 | -0.1637 | -0.2001 |
| 1.4005 | -0.9640 | -0.8912 | -0.0182 | 3.0375 | -0.6002 |
| -0.8185 | 1.0367 | -0.2001 | -0.4547 | 0.2728 | -0.6366 |
| -0.8912 | -0.5638 | -0.5638 | 0.4911 | -0.3820 | 2.8192 |
There are one outlier in the dataset.
Explanation of Solution
Standardized values:
Software procedure:
Step-by-step software procedure to obtain standardized values using EXCEL software is as follows:
- Open an EXCEL file.
- Enter the data in the column A in cells A1 to A32.
- In cell B1, enter the formula “=STANDARDIZE(A1, 3.55, 2.749)”.
- Select “ENTER” option.
- Select and copy the cell B1 and drag till the 30nd cell.
- Output using EXCEL software is given below:
Thus, the standardized values have been obtained using EXCEL.
The outliers in the data set A can be identified using
Empirical Rule:
The Empirical Rule for a Normal model states that:
- Within 1 standard deviation of mean, 68.26% of all observations will lie.
- Within 2 standard deviations of mean, 95.44% of all observations will lie.
- Within 3 standard deviations of mean, 99.73% of all observations will lie.
Empirical rule using MEGASTAT:
Software procedure:
Step-by-step software procedure to obtain Empirical rule using Mega Stat software is as follows:
- Open an EXCEL file.
- Enter the data in the column A in cells A1 to A30.
- From the Add-Ins, Select Mega Stat >Descriptive statistics.
- A dialogue box appears.
- In Input
range box, select the input range from Sheet1!$A$1:$A$30. - From the list box, select Empirical rule.
- Click “OK”.
Output obtained using MEGA STAT is as follows:
The upper and lower bounds for the intervals indicated by the Empirical rule have been obtained.
Based on the z-scores, the observation has one outlier, that is, the observations with values 11.9 do not lie within the 3-standard deviations limits (–4.697 to 11.797). there is no unusual observation in the data set A.
f.
Find the
f.
Answer to Problem 99CE
The Q1 (25th percentile) is 1.775, Q2 (50th percentile) is 3 and Q3 (75th percentile) is 4.525.
The boxplot for the data set A is:
Explanation of Solution
Quartiles:
Software procedure:
Step-by-step procedure to find the Quartiles using the MINITAB software:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns Percent.
- Choose option statistics, and select First Quartile, Median and Third Quartile.
- Choose option Graphs, and select boxplot of data.
- Click OK.
Output using the MINITAB software is given below:
- Thus, the Quartiles and boxplot have been obtained.
Observation:
From the boxplot, it is observed that the data set has two outliers within it. The boxplot disclosed that the median is closer to the first quartile, Q1 than it is to the third quartile, Q3, suggesting that the data is right skewed. The whiskers on the two sides are close in length, although it appears that the left whisker is slightly longer.
Want to see more full solutions like this?
Chapter 4 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
- 9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forwardSuppose that you buy a lottery ticket, and you have to pick six numbers from 1 through 50 (repetitions allowed). Which combination is more likely to win: 13, 48, 17, 22, 6, 39 or 1, 2, 3, 4, 5, 6? barrow_forward2 Make a histogram from this data set of test scores: 72, 79, 81, 80, 63, 62, 89, 99, 50, 78, 87, 97, 55, 69, 97, 87, 88, 99, 76, 78, 65, 77, 88, 90, and 81. Would a pie chart be appropriate for this data? ganizing Quantitative Data: Charts and Graphs 45arrow_forward
- 10 Meteorologists use computer models to predict when and where a hurricane will hit shore. Suppose they predict that hurricane Stat has a 20 percent chance of hitting the East Coast. a. On what info are the meteorologists basing this prediction? b. Why is this prediction harder to make than your chance of getting a head on your next coin toss? U anoiaarrow_forward6. Show that one cannot find independent, identically distributed random variables X and Y such that X-YE U(-1, 1). 7 Consider al onarrow_forward2 Which situation is more likely to produce exactly 50 percent heads: flipping a coin 10 times or flipping a coin 10,000 times?arrow_forward
- 2. Let X1, X2..... X, be independent random variables with expectation 0 and finite third moments. Show, with the aid of characteristic functions, that E(X₁ + X₂++X)³ = EX² + EX²++ EX₁₂-arrow_forward21 Check out the sales of a particular car across the United States over a 60-day period in the following figure. 800- 700- 600- Number of items sold 400 500- Line Graph of Sales 3001 16 12 18 24 30 36 42 48 54 60 60 Day a. Can you see a pattern to the sales of this car across this time period? b. What are the highest and lowest numbers of sales, and when did they occur? c. Can Can you estimate the average of all sales over this time period?arrow_forward11 Bob has glued himself to a certain slot machine for four hours in a row now with his bucket of coins and a bad attitude. He doesn't want to leave because he feels the longer he plays, the better chance he has t win eventually. Is poor Bob right?arrow_forward
- 7 You feel lucky again and buy a handful of instant lottery tickets. The last three tickets you open each win a dollar. Should you buy another ticket because you're "on a roll"?arrow_forward5 Suppose that an NBA player's free throw shooting percentage is 70 percent. a. Explain what this means as a probability. b. What's wrong with thinking that his chances of making his next free throw are 50-50 (because he either makes it or he doesn't)? 78 PART 2 Probability.arrow_forwardA couple has conceived three girls so far with a fourth baby on the way. Do you predict the newborn will be a girl or a boy? Why?arrow_forward
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning