All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learn how to construct and interpret summarization procedures for qualitative data such as: frequency and relative frequency distributions, bar graphs and pie charts. Learn how to construct and interpret tabular summarization procedures for quantitative data such as: frequency and relative frequency distributions, cumulative frequency and cumulative relative frequency distributions.
Learn how to construct a dot plot, a histogram, and an ogive as graphical summaries of quantitative data. Learn how the shape of a data distribution is revealed by a histogram. Learn how to recognize when a data distribution is negatively skewed, symmetric, and positively skewed. Be able to use and interpret the exploratory data analysis technique of a stem-and-leaf display.
Learn how to construct and interpret cross tabulations and scatter diagrams of bivariate data. Solutions: 1. Class Frequency Percent Frequency A. Yes Categorical b. CSI had the largest viewing audience. Desperate Housewives was in second place.
Most common: Smith, Johnson and Williams 6. ABC is a close third with The fact that the three networks are so close is surprising. FOX, the newest television network, does not have the history to compete with the other three networks in term of the top rated shows in television history.
Rating Frequency Relative Frequency Outstanding 19 0. Comparing these ratings with previous results will show whether or not the restaurant is making improvements in its ratings of food quality. Position Frequency Relative Frequency Pitcher 17 0.
Infielders 16 or Where do you live now? What do you consider the ideal community? Suburb living is steady, but the trend would be that living in the city would decline while living in small towns and rural areas would increase. Both countries show pessimism and relatively low confidence in how the banks are handling the credit problems in the financial markets.
Class Frequency Percent Frequency 6. Waiting Time Frequency Relative Frequency 0 - 4 4 0. Salary Frequency 1 3 7 5 1 2 1 Total 20 b. Salary Percent Frequency 5 15 35 25 5 10 5 Total Salary Cumulative Percent Frequency Less than or equal to 5 Less than or equal to 20 Less than or equal to 55 Less than or equal to 80 Less than or equal to 85 Less than or equal to 95 Less than or equal to Total d.
There is skewness to the right. A class size of 10 results in 10 classes. The general shape of the distribution is skewed to the right. A variety of comparisons are possible depending upon when the study is done. Spending Frequency Percent 3 12 6 24 5 20 5 20 3 12 1 4 0 0 1 4 1 4 Total 25 The distribution shows a positive skewness. Histogram of Off-Course Income Note: The first class is labeled and provides the golfers who had an off-course income in the range 0 to or less than Off-course income is skewed to the right.
The majority of the computer users are in the 3 to 6 hour range. Usage is somewhat skewed toward the right with 3 users in the 12 to Rotating the stem-and-leaf display counter clockwise shows a histogram that is slightly skewed to the left but is roughly symmetric. There are a couple of outliers. Observations such as the following can be made using the stem-and-leaf display. Most frequent age group: with 9 runners c.
Category A values for x are always associated with category 1 values for y. Category B values for x are usually associated with category 1 values for y. Category C values for x are usually associated with category 2 values for y.
There is a negative relationship between x and y; y decreases as x increases. Graduate The first five give the percent frequency distribution of income for each educational level. The total row provides an overall percent frequency distribution for household income. The second row, labeled H. Graduate, is the percent frequency distribution for households headed by high school graduates.
The fourth row, labeled Bachelor's Degree, is the percent frequency distribution for households headed by bachelor's degree recipients. The percent frequency histogram for high school graduates. Yes, there is a positive relationship between education level and income.
The first five columns give the percent frequency distributions for each income level. The percent frequency distribution in the "Total" column gives the overall percent frequency distributions for educational level. From that percent frequency distribution we see that The column percentages show that The row percentages show that These percentages are different because they came from different percent frequency distributions and provide different kinds of information.
Compare the "under 25" percent frequency distributions to the "Total" percent frequency distributions. We see that for this low income level the percentage with lower levels of education is higher than for the overall population and the percentage with higher levels of education is lower than for the overall population. Compare the " or more" percent frequency distribution to "Total" percent frequency distribution.
We see that for this high income level the percentage with lower levels of education is lower than for the overall population and the percentage with higher levels of education is higher than for the overall population. From the comparisons it is clear that there is a positive relationship between household incomes and the education level of the head of the household.
The crosstabulation of condition of the greens by gender is below. So, for the low handicappers, the men show a higher percentage who think the greens are too fast.
So, for the higher handicap golfers, the men show a higher percentage who think the greens are too fast. This is an example of Simpson's Paradox. At each handicap level a smaller percentage of the women think the greens are too fast. But, when the crosstabulations are aggregated, the result is reversed and we find a higher percentage of women who think the greens are too fast. The hidden variable explaining the reversal is handicap level. Fewer people with low handicaps think the greens are too fast, and there are more men with low handicaps than women.
The right margin shows the frequency distribution for the fund type variable and the bottom margin shows the frequency distribution for the 5 year average return variable. Higher returns are associated with International Equity funds and lower returns are associated with Fixed Income funds. Higher expense ratios are associated with Domestic Equity funds and lower expense ratios are associated with Fixed Income fund The scatter diagram is shown below: b.
There is some indication that higher 5-year returns are associated with higher net asset values. Higher fuel efficiencies are associated with midsize cars. In fact, for these data compact cars had the lowest fuel efficiencies. Higher fuel efficiencies are associated with front wheel drive cars. Rear wheel drive cars had somewhat lower fuel efficiencies than four wheel drive cars.
Higher fuel efficiencies are associated with cars that use regular fuel. Higher fuel efficiencies are associated with smaller displacement engines and lower fuel efficiencies are associated with larger displacement engines. The scatter diagram is shown below: d. The scatter diagram shows that lower fuel efficiencies are associated with larger displacement engines. It is easier to see the relationship between the two variables using the scatter diagram.
Business Administration is the most popular major selected by incoming freshmen, Frequency distribution and percent frequency distribution of sales by division. This is considered General Motors most important division. General Motors would be almost certain to maintain these two divisions. At the time it was doubtful than General Motors would be able to maintain all three of the other divisions. The distribution is skewed to the right. The most frequent range is 3. General Electric had an unusually high dividend yield of 9.
Class Frequency 1 3 6 10 7 2 1 Total 30 The distribution if nearly symmetrical. It could be approximated by a bell-shaped curve.
The average SAT score looks to be a little over Sweeney University of Cincinnati Thomas A. Data and Statistics Descriptive Statistics: Tabular and Graphical Methods Descriptive Statistics: Numerical Methods Introduction to Probability Discrete Probability Distributions Continuous Probability Distributions Sampling and Sampling Distributions Interval Estimation Hypothesis Testing Statistical Inference about Means and Proportions with Two populations Simple Linear regression Multiple Regression Regression Analysis: Model Building Decision Analysis Data and Statistics The population is all visitors coming to the state of Hawaii.
Since airline flights carry the vast majority of visitors to the state, the use of questionnaires for passengers during incoming flights is a good way to reach this population. The questionnaire actually appears on the back of a mandatory plants and animals declaration form that passengers must complete during the incoming flight.
A large percentage of passengers complete the visitor information questionnaire. Questions 1 and 4 provide quantitative data indicating the number of visits and the number of days in Hawaii. Questions 2 and 3 provide qualitative data indicating the categories of reason for the trip and where the visitor plans to stay.
The two populations are the population of women whose mothers took the drug DES during pregnancy and the population of women whose mothers did not take the drug DES during pregnancy. It was a survey. Thus, a rough estimate would be In many situations, disease occurrences are rare and affect only a small portion of the population.
Large samples are needed to collect data on a reasonable number of cases where the disease exists. Descriptive Statistics: Tabular and Graphical Methods Waiting Time Frequency Relative Frequency 4 0.
Category A values for x are always associated with category 1 values for y. Category B values for x are usually associated with category 1 values for y. Category C values for x are usually associated with category 2 values for y. Gas Oil Propane Other Total or before 40 12 5 7 24 26 2 2 0 54 37 38 1 0 6 82 48 70 2 0 1 Total 17 7 14 b. Gas Oil Propane Other or before Crosstabulation of row percentages.
Gas Oil Propane Other Total or before Observations from the column percentages crosstabulation For those buildings using electricity, the percentage has not changed greatly over the years. For the buildings using natural gas, the majority were constructed in or before; the second largest percentage was constructed in Most of the buildings using oil were constructed in or before.
All of the buildings using propane are older. In the period or before most used natural gas. From , it is fairly evenly divided between electricity and natural gas. Since almost all new buildings are using electricity or natural gas with natural gas being the clear leader.
The average air quality is about the same. But, the variability is greater in Anaheim. Thus, half of , or 2. No outliers. If you know the change in either, you will have a good idea of the stock market performance for the day.
Introduction to Probability 4. Requirement 4. Use the relative frequency method. Divide by the total adult population of Age Number Probability 18 to 24 Mutually exclusive events are dependent. Yes, the probability of default is greater than. So, if an accident leads to a fatality, the probability a small car was involved is. We should display the offer that appeals to female visitors. Discrete Probability Distributions 2. Continuous The expected value of a 3 - point shot is higher.
So, if these probabilities hold up, the team will make more points in the long run with the 3 - point shot. Since the shipment is large we can assume that the probabilities do not change from trial to trial and use the binomial probability distribution. Continuous Probability Distributions 2. The z value corresponding to a cumulative probability of. The area to the left of z is 1 -. Reducing the process standard deviation causes a substantial reduction in the number of defects.
Sampling and Sampling Distributions 3. The probability of spending this much or less is only. Interval Estimation 7. Section 8. As the confidence level increases, there is a larger margin of error and a wider confidence interval.
This modest positive skewness in the data set can be expected to exist in the population. Regardless of skewness, this is a pretty small data set. Consider using a larger sample next time.
Hypothesis Testing 1. There is no statistical evidence that the new bonus plan increases sales volume. We can conclude that the new bonus plan increases the mean sales volume. A mistake could be implementing the plan when it does not help.
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