Stat 2.2 & 2.3 HW
Which of the following is true about statistical graphs?
- Similar graphs can be constructed in order to compare data sets. - They can be used to consider the overall shape of the distribution. - They can be used to identify extreme data values.
The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. What are the approximate lower limits of the first class? 105-125 | 5 125-145 | 1 145-165 | 5 185-205 | 5 205-225 | 3 225-245 | 2
105
The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. What are the approximate upper limits of the first class? 105-125 | 5 125-145 | 1 145-165 | 5 185-205 | 5 205-225 | 3 225-245 | 2
125
The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. How many team members are included in the histogram? x | y 120 | 5 140 | 2 160 | 4 180 | 1 200 | 1 220 | 2 240 | 2
17
The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. What is the class width? 105-125 | 5 125-145 | 1 145-165 | 5 185-205 | 5 205-225 | 3 225-245 | 2
20
The data represents the heights of eruptions by a geyser. Use the heights to construct a stem-plot. 62, 39, 50, 90, 80, 50, 40, 70, 50, 67, 77, 54, 51, 69, 60, 60, 74, 70, 45, 81
3 | 9 4 | 0 5 5 | 0 0 0 1 4 6 | 0 0 2 7 9 7 | 0 0 4 7 8 | 0 1 9 | 0
Construct a stem-and-leaf plot of the test scores 67, 72, 85, 75, 89, 89, 87, 90, 99, 100.
6 | 7 7 | 2 5 8 | 5 7 9 9 9 | 0 9 10 | 0
Heights of adult males are normally distributed. If a large sample of heights of adult males is randomly selected and the heights are illustrated in a histogram, what is the shape of that histogram?
Bell-shaped
A study was conducted to determine how people get jobs. The table lists data from 400 randomly selected subjects. If someone would like to get a job, what seems to be the most effective approach? Job Sources vs frequency Help-wanted ads (H) - 268 Executive search firms (E) - 59 Networking (N) - 28 Mass mailing (M) - 45
Help-wanted ads (H)
If we have a large voluntary response sample consisting of weights of subjects who chose to respond to a survey posted on the Internet, can a graph help to overcome the deficiency of having a voluntary response sample?
No, a graph cannot help to overcome the deficiency. If the sample is a bad sample, there are no graphs or other techniques that can be used to salvage the data.
The table below shows the frequency distribution of the rainfall on 52 consecutive Sundays in a certain city. Do the data appear to have a distribution that is approximately normal? Class v frequency 0-0.19 - 26 0.20-0.39 - 12 0.40-0.59 - 3 0.60-0.79 - 1 0.80-0.99 - 6 1.00-1.19 - 1 1.20-1.39 - 3
No, it is not symmetric.
Why is it important to learn about bad graphs?
So that we can critically analyze a graph to determine whether it is misleading Your answer is correct.
A study was conducted to determine how people get jobs. The table below lists data from 400 randomly selected subjects. Job Sources vs frequency Help-wanted ads (H) - 18 Executive search firms (E) - 42 Networking (N) - 289 Mass mailing (M) - 69 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 chart is more effective.
The last digit of the heights of 63 statistics students were obtained as part of an experiment conducted for a class. What can be concluded from the distribution of the digits? Specifically, do the heights appear to be reported or actually measured? Digit v Frequency 0 - 15 1 - 4 2 - 3 3 - 5 4 - 5 5 - 16 6 - 4 7 - 3 8 - 4 9 - 4
The data appears to be reported. Certain heights occur a disproportionate number of times.
Listed below are body temperatures (°F) of healthy adults. Why is it that a graph of these data would not be very effective in helping us understand the data? 98.6 98.6 98.0 98.0 99.0 98.4 98.4 98.4 98.4 98.6
The data set is too small for a graph to reveal important characteristics of the data.
The given data represent the number of people from a town, aged 25-64, who subscribe to a certain print magazine. Age vs people 25-34 | 90 35-44 | 278 45-54 | 713 55-64 | 602 Does the graph suggest that the distribution is skewed? If so, how?
The distribution appears to be skewed to the left (or negatively skewed).
The given data represents a frequency distribution of the F-scale intensities of recent tornadoes. Tornado F-Scale vs Frequency 0 | 23 1 | 16 2 | 1 3 | 2 4 | 2 Does the graph suggest that the distribution is skewed? If so, how?
The distribution appears to be skewed to the right (or positively skewed).
The graph to the right compares teaching salaries of women and men at private colleges and universities. What impression does the graph create? Does the graph depict the data fairly? If not, construct a graph that depicts 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.
The table shows the magnitudes of the earthquakes that have occurred in the past 10 years. Does the histogram appear to be skewed? If so, identify the type of skewness. Earthquake magnitude Frequency 5.0-5.9 14 6.0-6.9 12 7.0-7.9 8 8.0-8.9 5 9.0-9.9 2
The histogram has a longer right tail, so the distribution of the data is skewed to the right.
The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Does the histogram appear to depict data that have a normal distribution? Weight (g) Frequency 6.000-6.049 3 6.050-6.099 4 6.100-6.149 8 6.150-6.199 10 6.200-6.249 12 6.250-6.299 5 6.300-6.349 4 6.350-6.399 1
The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric.
How does the stem-and-leaf plot show the distribution of these data?
The lengths of the rows are similar to the heights of bars in a histogram; longer rows of data correspond to higher frequencies.
If we collect a large sample of blood platelet counts and if our sample includes a single outlier, how will that outlier appear in a histogram?
The outlier will appear as a bar far from all of the other bars with a height that corresponds to a frequency of 1.
The data represents the heights of eruptions by a geyser. 62, 39, 50, 90, 80, 50, 40, 70, 50, 67, 77, 54, 51, 69, 60, 60, 74, 70, 45, 81 Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest.
The values closest to the middle are 60 inches and 62 inches.
Given below are the numbers of indoor movie theaters, listed in order by row for each year. What is the trend? How does this trend compare to the trend for drive-in movie theaters? Year vs Number_of_Indoor_Theaters 1 20595 2 21248 3 21907 4 22359 5 23740 6 23842 7 24789 8 27200 9 26995 10 30651 11 31050 12 31450 13 36448 14 34550 15 34490 16 36338 17 35361
There appears to be an upward trend, unlike drive-in movie theaters, which have a downward trend.
The accompanying data represent women's median earnings as a percentage of men's median earnings for recent years beginning with 1989. Is there a trend? How does it appear to affect women? Year Median Earnings 1989 - 59.2 1990 - 60.1 1991 - 62.5 1992 - 61.9 1993 - 62.7 1994 - 61.9 1995 - 61.9 1996 - 65.5 1997 - 67.5 1998 - 65.6 1999 - 62.9 2000 - 63.3 2001 - 61.7 2002 - 65.2 2003 - 63.9 2004 - 66.7 2005 - 68.8
There is a general upward trend though there have been some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.
Which of the following is NOT true about statistical graphs?
They utilize areas or volumes for data that are one-dimensional in nature.
Which of the following is a common distortion that occurs in graphs?
Using a two-dimensional object to represent data that are one-dimensional in nature
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.
The graph to the right uses cylinders to represent barrels of oil consumed by two countries. Country A: 19.8 (shown way bigger) Country B: 5.7 Does the graph distort the data or does it depict the data fairly? Why or why not? If the graph distorts the data, construct a graph that depicts the data fairly.
Yes, because the graph incorrectly uses objects of volume to represent the data.
The frequency distribution below represents frequencies of actual low temperatures recorded during the course of a 31-day month. Do the data appear to have a distribution that is approximately normal? Class v Frequency A: 39-44 | 1 B: 45-50 | 1 C: 51-56 | 8 D: 57-62 | 9 E: 63-68 | 7 F: 69-74 | 2 G: 75-80 | 3
Yes, it is approximately normal.
In a study of retractions in biomedical journals, 416 were due to error, 224 were due to plagiarism, 847 were due to fraud, 289 were due to duplications of publications, and 271 had other causes. Among such retractions, does misconduct (fraud, duplication, plagiarism) appear to be a major factor?
Yes, misconduct appears to be a major factor because the majority of retractions were due to misconduct.
The data table to the right represents the volumes of a generic soda brand. Are there any outliers? Volumes of Soda (oz) 70, 75, 70, 75, 50, 70, 80, 70, 65, 85, 80, 65, 70, 75
Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes.
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
A _______ is a graph of each data value plotted as a point.
dotplot
The heights of the bars of a histogram correspond to _______ values.
frequency
A(n) _______ uses line segments to connect points located directly above class midpoint values.
frequency polygon
We utilize statistical _______ to look for features that reveal some useful or interesting characteristics of the data set.
graphs
A(n) _______ distribution has a "bell" shape.
normal
When drawings of objects are used to depict data, false impressions can be made. These drawings are called _______.
pictographs
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
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 distribution
The bars in a histogram _______.
touch
