Chapter two 2.1

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

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

graphs

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males (1000 cells/uL): 0-99, 100-199, 200-299, 300-399, 400-499, 500-599, 600-699 Frequency: 3, 49, 76, 25, 0, 1, 0

lower class limits: 0, 100, 200, 300, 400, 500, 600 upper class limits: 99, 199, 299, 399, 499, 599, 699 class width: 100 class midpoints: 49.5, 149.5, 249.5, 349.5, 449.5, 549.5, 649.5 class boundaries: -0.5, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5 number of individuals: 153

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was won: 25-34, 35-44, 45-54 , 55-64, 65-74, 75-84, 85-94 Frequency: 29, 34, 16, 3, 5, 1, 2

lower class limits: 25, 35, 45, 55, 65, 75, 85 upper class limits: 34, 44, 54, 64, 74, 84, 94 class width: 10 (34-25+1) class midpoints: 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5 class boundaries: 34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5 (don't forget to find the lowest class boundary which is 24.5) number of individuals included included in the summary: 90

Which characteristic of data is a measure of the amount that the data values​ vary?

variation

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.

A frequency table of grades has five classes​ (A, B,​ C, D,​ F) with frequencies of 2​, 11​, 17​, 6​, and 2 respectively. Using​ percentages, what are the relative frequencies of the five​ classes?

(divide each frequency by the total of frequencies then multiplay by 100) 5.26% 28.95% 44.74% 15.79% 5.26%

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 24.928.9 22.8 18.3 27.8 22.619.2 22.4 21.2 37.7 40.427.7 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

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

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?

21, 6, 2, 0, 0, 0, 1 No, the distribution is not symmetric and the frequencies do not start off low.

Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution. Begin with a lower class limit of 3.220 ​in, and use a class width of 0.010 in. The screws were labeled as having a length of 3 1/4 in.

3.220-3.229 3.230-3.239 and so on

Refer to the table summarizing service times​ (seconds) of dinners at a fast food restaurant. How many individuals are included in the​ summary? Is it possible to identify the exact values of all of the original service​ times?

47 individuals are included in the summary (add up all numbers in the frequency column) No. The data values in each class could take on any value between the class​ limits, inclusive.

Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. Construct a frequency distribution with 10 classes. Based on the​ distribution, do the weights appear to be reported or actually​ measured? What can be said about the accuracy of the​ results?

8, 2, 2, 1, 3, 10, 1, 0, 3, 1The 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.

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? Construct a​ time-series graph.

A Graph

The last digit of the heights of 65 statistics students were obtained as part of an experiment conducted for a class. Use the following frequency distribution to construct a histogram. What can be concluded from the distribution of the​ digits? Specifically, do the heights appear to be reported or actually​ measured?

A Graph

The table shows the magnitudes of the earthquakes that have occurred in the past 10 years. Use the frequency distribution to construct a histogram. Does the histogram appear to be​ skewed? If​ so, identify the type of skewness.

A graph

The table available below shows the drive through service times​ (seconds) for lunches at a fast food restaurant. Use the data to construct a histogram. Begin with a lower class limit of 70 seconds and use a class width of 40 seconds. Does the histogram appear to be​ skewed? If​ so, identify the type of skewness.

A graph The histogram has a longer right tail, so the distribution of the data is skewed to the right.

Construct a​ stem-and-leaf plot of the test scores 67, 72, 86, 75, 89, 89, 88, 90, 98, 100. How does the​ stem-and-leaf plot show the distribution of these​ data?

A graph The lengths of the rows are similar to the heights of bars in a​ histogram; longer rows of data correspond to higher frequencies.

What is a scatterplot and how does it help​ us?

A scatterplot is a graph of paired​ (x, y) quantitative data. It provides a visual image of the data plotted as​ points, which helps show any patterns in the data

In a study of retractions in biomedical​ journals: 405 were due to​ error, 194 were due to​ plagiarism, 888 were due to​ fraud, 291 were due to duplications of​ publications, and 273 had other causes. Does the Pareto chart (above) showing such retractions, appear to show misconduct​ (fraud, duplication,​ plagiarism) as a major​ factor? Please explain.

B Graph from high to low Yes, misconduct appears to be a major factor because the majority of retractions were due to misconduct.

The table provided below shows paired data for the heights of a certain​ country's presidents and their main opponents in the election campaign. Construct a scatterplot. Does there appear to be a​ correlation? Does there appear to be a correlation between the​ president's height and his​ opponent's height?

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

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?

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

The table lists weights​ (pounds) and highway mileage amounts​ (mpg) for seven automobiles. Use the sample data to construct a scatterplot. Use the first variable for the​ x-axis. Based on the​ scatterplot, what do you conclude about a linear​ correlation? Is there a linear relationship between weight and highway​ mileage?

D graph Yes, as the weight increases the highway mileage decreases.

The data table to the right represents the volumes of a generic soda brand. Are there any​ outliers?

D graph Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes.

Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant​ criteria?

No, the distribution does not appear to be normal

Why is it important to learn about bad​ graphs?

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

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 histogram to the right represents the weights​ (in pounds) of members of a certain​ high-school programming team.How many team members are included in the​ histogram?

The sample size can be found by adding the heights of all the bars in the histogram.

In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coefficient as being​ linear?

The term linear refers to a straight line, and r measures how well a scatterplot fits a straight-line pattern.

Which of the following is NOT true about statistical​ graphs?

They utilize areas or volumes for data that are​ one-dimensional in nature.

The population of ages at inauguration of all US Presidents who had professions in the military is 62, 46, 68, 64, and 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. 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. Does the graph distort the​ data? Why or why​ not? If the graph does not depict the data​ fairly, which graph below​ does?

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

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

For a data set of brain volumes (cm3​) and IQ scores of sevenmales, the linear correlation coefficient is r equals=0.814 Use the table available below to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical​ values, what do you conclude about a linear​ correlation?

critical value is the # of people Since the correlation coefficient r is in the right tail above the positive critical value ​,there is sufficient evidence to support the claim of a linear correlation.

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

n a​ _______ distribution, the frequency of a class is replaced with a proportion or percent.

relative frequency

A histogram aids in analyzing the​ _______ of the data.

shape of the distribution