Intro to Statistics MCCC Ch. 2

Class width is found by -------.

subtracting a lower class limit from the next consecutive lower class limit

Look at #50 chart and answer the questions: In what way might the graph be deceptive? How much greater is the braking distance of Car A than the braking distance of Car C?

By starting the horizontal axis at 100, the graph cut off portions of the bars. The braking distance of Car A is about 30% greater than the braking distance of Car C.

Look at #5 chart and answer the question: Does the frequency distribution appear to have a normal distribution?

No, the distribution does not appear to be normal.

Look at the #42 charts and answer the questions: Is there strong evidence suggesting that the data are not from a population having a normal distribution?

No, the distribution is not dramatically far from being a normal distribution with a "bell" shape, so there is not strong evidence against a normal distribution.

Look at #38 chart and question and answer the questions: Construct a scatterplot on the calculator. Does there appear to be a correlation between the president's height and his opponent's height?

No, there does not appear to be a correlation because there is no general pattern to the data.

Why is it important to learn about bad graphs?

So that we can critically analyze a graph to determine whether it is misleading.

Look at the #43 charts and answer the question: Which graph is more effective in showing the relative importance of the causes of work-related deaths?

The Pareto chart is better because it more clearly draws attention to the main cause of work-related death.

Look at #25 chart and answer the questions: Construct a histogram on the calculator. Are the data reported or measured?

The data appears to be measured. The heights occur with roughly the same frequency.

Look at #7 charts and answer the question: Do cigarette filters appear to be effective?

Yes, because the relative frequency of the higher tar classes is greater for nonfiltered cigarettes.

A - is a graph of each data value plotted as a point.

dotplot

A(n) - distribution has a "bell" shape.

normal

A -- histogram has the same shape and horizontal scale as a histogram but the vertical scale is marked with relative frequencies instead of actual frequencies.

relative frequency

In a -- distribution, the frequency of a class is replaced with a proportion or percent.

relative frequency

The bars in a histogram -.

touch

Which characteristic of data is a measure of the amount that the data values vary? a. variation b. distribution c. time d. center

variation

Look at #51 chart and answer the questions: Compare the results.

The distribution of pulse rates for men is concentrated, centered around 60, whereas the distribution of pulse rates for women is more spread out, centered around 70.

Look at #28 chart and answer the questions: Construct a histogram on the calculator. Does the histogram appear to depict data that have a normal distribution?

The histogram appears to roughly approximate a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is symmetric.

Look at #10 charts and answer the two questions: Based on the distribution, do the weights appear to be reported or actually measured? What can be said about the accuracy of the results?

The weights appear to be reported because there are disproportionately more 0s and 5s. They are likely not very accurate because they appear to be reported.

Look at #40 and answer the questions: Construct a time-series graph (line graph) on the calculator. What is the trend? How does this trend compare to the trend for drive-in movie theaters?

There appears to be an upward trend, unlike drive-in movie theatres, which have a downward trend.

Look at #49 chart and answer the question: Does the graph distort the data? Why or why not?

Yes, because the graph incorrectly uses objects of volume to represent the data.

Look at the #41 charts and answer the questions: Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution? Are there any outliers?

Yes, the population appears to have a normal distribution because the dotplot resembles a "bell" shape. Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes.

Look at #26 chart and answer the questions: Construct a histogram on the calculator. Do the data appear to have a distribution that is approximately normal?

Yes. It is approximately normal.

In a graph, if one or both axes begin at some value other than zero, the differences are exaggerated. This bad graphing method is known as ---.

a nonzero axis

Which of the following is NOT true about statistical graphs? a. They utilize areas or volumes for data that are one-dimensional in nature. b. Similar graphs can be constructed in order to compare data sets. c. They can be used to identify extreme data values. d. They can be used to consider the overall shape of the distribution.

a.

Look at #29 chart and answer the questions: Construct a histogram on the calculator. Do the data appear to have a distribution that is approximately normal?

No, it is not symmetric

Look at #39 chart and answer the questions? Construct a scatterplot on the calculator. Is there a relationship between cigarette tar and CO?

Yes, as the amount of tar increases the amount of carbon monoxide also increases.

Look at #6 chart and answer the question: Does the frequency distribution appear to have a normal distribution? Explain.

Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.

The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal distribution? 0.39 0 0 0.28 0 0.56 0 0.18 0 0 1.36 0 0.16 0 0.01 0 0.16 0 0.11 0.42 0 0.01 0 0.27 0 0.11 0 0 0.15 0 Find the frequencies for daily rainfall in ranges: 0.00-0.19 0.20-0.39 0.40-0.59 0.60-0.79 0.80-0.99 1.00-1.19 1.20-1.39 Does the frequency distribution appear to be roughly a normal distribution?

0.00-0.19----------- 24 0.20-0.39------------ 3 0.40-0.59------------ 2 0.60-0.79------------ 0 0.80-0.99------------ 0 1.00-1.19------------ 0 1.20-1.39----------- 1 No, the distribution is not symmetric, the frequencies do not start off low.

Look at #23 chart and answer the question: The histogram represents - debate team members.

11

Look at #2 chart and answer the questions: What is the class width? What are the class midpoints? What are the class boundaries?

3 51, 54, 57, 60, 63, 66, 69 49.5, 52.5, 55.5, 58.5, 61.5, 64.5, 67.5, 70.5

Look at #4 chart and answer the questions: What is the class width? What are the class midpoints? What are the class boundaries?

3 6.45, 9.45, 12.45, 15.45, 18.45 4.95, 7.95, 10.95, 13.95, 16.95, 19.95

Look at #3 chart and answer the questions: What is the class width? What are the class midpoints? What are the class boundaries?

3 65.45, 68.45, 71.45, 74.45, 77.45, 80.45, 83.45, 86.45, 89.45, 92.45 63.95, 66.95, 69.95, 72.95, 75.95, 78.95, 81.95, 84.95, 87.95, 90.95, 93.95

Look at the #44 charts and answer the questions: If someone would like to get a job, what seems to be the most effective approach?

Help-wanted ads (H)

A bar chart and a Pareto chart both use bars to show frequencies of categories of categorical data. What characteristic distinguishes a Pareto chart from a bar chart, and how does that characteristic help us in understanding the data?

In a Pareto chart, the bars are always arranged in descending order according to frequencies. The Pareto chart helps us understand data by drawing attention to the more important categories, which have the highest frequencies.

Listed below are blood groups of O, A, B, and AB of randomly selected blood donors. Construct the relative frequency distribution. A O O O O A A O A O O A A O O AB O A B A AB O A O B O O AB A A AB A O A B O AB O O O Find the relative frequency for O, A, B, AB

O: 47.5% A: 32.5% B: 7.5% AB:12.5%

Which of the following is a common distortion that occurs in graphs? a. Using bars to represent the frequency of data values. b. Using points above the class midpoints at the heights of the class frequencies. c. Labeling both axes d. Using a two-dimensional object to represent data that are one-dimensional in nature.

d.

We utilize statistical - to look for the features that reveal some useful or interesting characteristics of the data set.

graphs

- are sample values that lie very far away from the majority of the other sample values.

outliers

When drawings of objects are used to depict data, false impressions can be made. These drawings are called -.

pictographs

A - is a plot of paired data (x,y) and is helpful in determining whether there is a relationship between the two variables.

scatterplot

A histogram aids in analyzing the - of the data.

shape of the distribution

The data represents the body mass index (BMI) values for 20 females. Construct a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0. Does the frequency distribution appear to be roughly a normal distribution? 17.7 33.5 26.9 22.5 24.9 28.9 22.8 18.3 27.8 22.6 19.2 22.4 21.2 37.7 40.4 27.7 44.9 30.3 29.1 21.7 Find the frequency for body mass indexes between: 15.0-20.9 21.0-26.9 27.0-32.9 33.0-38.9 39.0-44.9 Does the frequency distribution appear to be roughly a normal distribution?

15.0-20.9 ---------- 3 21.0--26.9 ---------- 8 27.0-32.9 -------------- 5 33.0-38.9 ---------- 2 39.0-44.9 -----------2 No, although the frequencies start low, increase to some maximum, then decrease, the distribution is not symmetric.

Look at #24 chart and answer the questions: What is the class width? What are the approximate lower and upper class limits of the first class?

20 Lower class: 105 Upper class: 125

After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?

If percentages are used, the sum should be 100%. If proportions are used, the sum should be 1.

Use the given qualitative data to construct the relative frequency distribution. The 2445 people aboard a ship that sank include 325 male survivors, 1661 males who died, 322 female survivors, and 137 who died. Find the relative frequency for male survivors, males who died, female survivors, and females who died.

Male Survivors: 13.3% Males who died: 67.9% Female survivors: 13.2% Females who died: 5.6%

Among fatal plane crashes that occurred during the past 70 years, 269 were due to pilot error, 54 were due to other human error, 665 were due to weather, 85 were due to mechanical problems, and 479 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it? What is the relative frequency for pilot error, other human error, weather, mechanical problems, and sabotage? Round to one decimal point. What is the most serious threat to aviation safety, and can anything be done about it?

Pilot Error: 17.3% Other Human Error: 3.5% Weather: 42.8% Mechanical problems: 5.5% Sabotage: 30.9% Weather is the most serious threat to aviation safety. Weather monitoring systems could be improved. Whi

Look at the #45 charts and answer the questions: Compare the pie chart found above to the Pareto chart given on the left. Can you determine which graph is more effective in showing the relative importance of job sources?

The Pareto char is more effective.

Look at the #46 charts and answer the questions: Applying a loose interpretation of the requirements for a normal distribution, does the data appear to be normally distributed? Why or why not?

The frequency polygon appears to roughly approximate a normal distribution because the frequencies increase to a maximum, then decrease, and the graph is roughly symmetric.

Look at #47 charts and answer the question: Applying a strict interpretation of the requirements for a normal distribution, do the depths appear to be normally distributed? Why or why not?

The frequency polygon does not appear to approximate a normal distribution because the frequencies do not increase to a maximum and then decrease, and the graph is not symmetric.

Look at #48 chart and answer the questions: What impression does the graph create? Does the graph depict the data fairly?

The graph creates the impression that men have salaries that are more than twice the salaries of women. No, because the vertical scale does not start at zero.

Look at #27 chart and answer the questions: Construct a histogram on the calculator. Does the histogram appear to depict data that have a normal distribution?

The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric.

Look at #30 charts and answer the questions: Construct a histogram on the calculator. Does the histogram appear to depict data that have a normal distribution?

The histogram appears to roughly approximate a normal distribution. The frequencies generally increase to a maximum and then decrease and the histogram is symmetric.

Look at #31 chart and answer the questions: Construct a histogram on the calculator. Which part of the histogram depicts flights that arrived early, and which part depicts flights that arrived late?

The two leftmost bars depict flights that have arrived early, and the other bars to the right depict flights that arrived late.

The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set?

With a data set that is so small, the true nature of the distribution cannot be seen with a histogram.

Look at #11 at the charts and answer the question: Does the result appear to have a normal distribution? Why or why not?

Yes, because the frequencies start low, reach a maximum, then become low again, and are roughly symmetric about the maximum frequency.

The heights of the bars of a histogram correspond to - values.

frequency

A -- helps us understand the nature of the distribution of a data set.

frequency distribution

A(n) -- uses line segments to connect points located directly above class midpoint values.

frequency polygon