Elementary stats

The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the mean, median, and mode time. 34.0, 33.2, 37.0, 29.4, 23.6, 25.9

Mean: 30.52 mpg Median: 31.3 mpg No mode

A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The concrete is poured into casting cylinders and allowed to set for 28 days. The concrete's strength of nine randomly selected casts (in psi). Compute the mean, median, and mode time. 3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780

Mean: 3670 Median: 3830 Mode: 4090

The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan's Statistic course. Compute the mean, median, and mode time. 60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9

Mean: 93.1 Median: 87.9 No mode

The Gini Index is a measure of how evenly income is distributed within a country, ranging from 0-100. An index of 0 suggests income is distributed with perfect equality. The higher the number, the worse the income inequality. The data below represent the Gini Indec for a random sample of countries. (a) Construct a frequency distribution (b) Construct a relative frequency distribution (c) Construct a frequency histogram of the data (d) Construct a relative frequency histogram of the data (e) Describe the shape of the distribution. (f) Repear parts (a)-(e) using a class width of 10. (g) Does one frequency distribution provide a better summary of the data than the other?

(a) In notebook (b) In notebook (c) In notebook (d) In notebook (e) Skewed right (f) Skewed right (g) Answers may vary. However, the summary with a class width of 5 seems superior.

The following frequency histogram represents the IQ scores of a random sample of seventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. (a) How many students were sampled? (b) Determine the class width. (c) Identify the classes and their frequencies. (d) Which class has the highest frequency? (e) Which class has the lowest frequency? (f) What percent of students had an IQ of at least 130? (g) Did any students have an IQ of 165?

(a) 200 (b) 10 (c) 60-69, 2; 70-79, 3; 80-89, 13; 90-99, 42; 100-109, 58; 110-119, 40; 120-129, 31; 130-139, 8; 140-149, 2; 150-159, 1 (d) 100-109 (e) 150-159 (f) 5.5% (g) No

An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The following frequency histogram given the results. (a) What was the most frequent outcome of this experiment? (b) What was the least frequent? (c) How many times did we observe a 7? (d) How many more 5's were observed than 4's? (e) Determine the percentage of a time a 7 was observed. (f) Describe the shape of the distribution.

(a) 8 (b) 2 (c) 15 (d) 4 (e) 15% (f) Bell-shaped

The USA Today- type chart shows the top responses to the question, "Who's the most difficult to 'sell yourself to'" (a) What was the most common response? (b) The survey is of 1053 adults. How many stated their significant other is most difficult to "sell yourself" to? (c) Explain why this graphic cannot be displayed as a pie chart.

(a) Boss (b) 158 (c) Values do not sum to one. That is, there is no "whole"

State whether you would except a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right. (a) annual household incomes in the United States (b) Scores on a standardized exam such as the SAT (c) Number of people living in a household (d) Ages of patients diagnosed with Alzheimer's disease

(a) Likely skewed right. Most household incomes will be to the left (perhaps in the $50,000 to $150,000 range), with fewer higher incomes to the right (in the millions). (b) Likely bell-shaped. Most scores will occur near the middle range, with scores tapering off equally in both directions. (c) Likely skewed right. Most households will have, say 1 to 4 occupants, with fewer households having a higher number of occupants. (d) Likely skewed left. Most Alzheimer's patients will fall in older-aged categories, with fewer patients being younger.

The ______ ______ is the difference between consecutive lower-class limits

Class width

The categories by which data are grouped are called ____

Classes

True or false A data set will always have exactly one mode.

False

True or false The shape of the distribution shown is best classified as uniform.

False This would be classified as bell-shaped

True or false Suppose the first class of a frequency distribution is 0-9.9 and the second class is 10-19.9. Then, the class width is 9.9.

False The class width would be 10-0=10

The median for the given set of six ordered data values is 26.5. What is the missing value? 7 12 21 _____ 41 50

x = 32

Find the population mean or sample mean as indicated. Sample: 20, 13, 4, 8, 10

x̄ = 11

The _____ class limit is the smallest value within the class and the _____ is the largest value within the class

lower, upper

A frequency distribution lists the _____ of occurrences of each category of data, while a relative frequency distribution lists the ______ of occurrences of each category of data.

number, proportion

Resistance and Sample size 3.1 #31

sample of size 5: all data recorded correctly: x=99.8; M=100; 106 recorded as 160: x=110.6; M=100 Sample of size 12: All data recorded correctly: x=100.4; M=101; 106 recorded as 160: x=104.9; M=101 Sample size of 30: All data recorded correctly: x=100.6; M=99; 106 recorded as 160: x=102.4; M =99 For each sample size, the mean becomes larger, but the median remains constant. As the sample size increases, the effect of the misrecorded data on the mean decreases.

What does it mean if a statistic is resistant?

A statistic is resistant if it is not sensitive to extreme values. Median is resistant Mean is not resistant

Determine the level of measurement of each variable Researchers want to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in women (27-44 years of age). To make this determination, they look at 7373 cases of hypertension in these women and find that those who consume at lease 1000 micrograms per day (ug/d) of total folate had a decreased risk of hypertension compared with those who consume less than 200 ug/d.

Population: women 27-44 years of age with hypertension Sample: 7373 women 27 to 44 years of age with hypertension

Classify the variable as qualitative or quantitative Nation of origin

Qualitative

Classify the variable as qualitative or quantitative Phone number

Qualitative

Find the population mean or sample mean as indicated. Population: 3, 6, 10, 12, 14

μ = 9

A histogram of the download time of a movie, in minutes, for 30 randomly selected movies is shown. The mean download time is 39.007 minutes and the median download time is 39.065 minutes. Identify the shape of the distribution, Which measure of central tendency better described the "center" of the distribution?

The distribution is symmetric. The mean is the better measure of central tendency.

What does it mean if a distribution is said to be "skewed left"?

The left tail (smaller values) is much longer than the right tail (larger values).

Mr. Zuro finds the mean height of all 14 students in his statistics class to be 68.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 65 inches tall. What is the mean height of the 15 students in the class including Danielle?

The mean height of the 15 students in the class is 67.8 inches.

A histogram of a set of data indicated that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?

The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. Since distribution is skewed right, mean will be larger than median.

According to MarketWatch, the mean net worth of all individuals in the United States in 2016 was $629,100, while the median net worth was $97,300. (a) Which measure do you believe better describes the typical individual's net worth? Support your opinion. (b) What shape would expect the distribution of net worth to have? Why? (c) What do you think causes the disparity in the two measures of central tendency?

?

A survey of U.S. adults and teens (ages 12-17) was administered by Pew Research, to determine the number of texts sent in a single day. (a) Construct a relative frequency distribution for adults (b) Construct a relative frequency distribution for teens (c) Construct a side-by-side relative frequency bar graph. (d) Compare the texting habits of adults and teens

(a) In notebook (b) In notebook (c) In notebook (d) In notebook

The table shows the movement of Walt Disney stock for 30 randomly selected trading days. "Up" means the stock price increased in value for the day, "Down" means the stock price decreased in value for the day, and "No change" means the stock price closed at the same price it closed for the previous day. (a) Construct a frequency distribution (b) Construct a relative frequency distribution (c) Construct a frequency bar graph (d) Construct a pie chart

(a) In notebook (b) In notebook (c) In notebook (d) In notebook

Use the data in problem 21 (a) Construct a relative frequency distribution (b) Frequency histogram (c) Relative frequency histogram (d) What percentage of players had a sprint speed between 24 and 25.9 ft/sec? What percentage of players had a spring speed less than 24 ft/sec?

(a) In notebook (b) In notebook (c) In notebook (d) The percentage of players with a sprint speed between 24 and 25.9 feet per second is 18.94%. The percentage of players with a sprint speed less than 23.9 feet per second is 3.28%.

The following time-series plot shows the annual unemployment and inflation rates for the years 2001 through 2017. (a) Estimate the unemployment rate in 2012. (b) In what year was the unemployment rate highest? (c) In what year was the inflation rate highest? (d) In what year were the unemployment rates and inflation rate furthest apart? (e) The misery index is defined as the sum of the unemployment rate and the inflation rate. According to the misery index, which year was more "miserable", 2008 or 2011? (f)

(a) 9% (b) 2010 (c) 2008 (d) 2009 (e) 2011 (f) Declining due to the decreases in unemployment

In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, "How often do you wear a seat belt when riding in a car driven by someone else" (a) Construct a relative frequency distribution (b) What percentage of respondents answered "always"? (c) What percentage of respondents answered "never" or "rarely"? (d) Construct a frequency bar graph (e) Construct a relative frequency bar graph (f) Construct a pie chart (g) Suppose that a representative from the Centers for Disease Control says, "52.7%" of college students surveyed always wear a seat belt." Is this a descriptive or inferential statement?

(a) In notebook (b) 52.7% (c) 9.4% (d) In notebook (e) In notebook (f) In notebook (g) This is a descriptive statement because it is reporting a result of the sample.

A sample of 30 registered voters was surveyed in which the respondents were asked, "Do you consider your political views to be conservative, moderate, or liberal?" The results of the survey are shown in the table. (a) Determine the mode political view. (b) Do you think it would be a good idea to rotate the choices conservative, moderate, or liberal in the question? Why?

(a) Moderate (b) Yes, to avoid response bias

The following Pareto chart shows the position played by the most valuable player (MVP ) in the National League since 1931. (a) Which position had the most MVPs? (b) How many MVP's played first base (1B) (c) How many more MVP's played first base (1B) than third base (3B) (d) There are three outfield (OF) positions. Given this, how might the graph be misleading?

(a) OF (b) 15 (c) 5 (d) Each of these positions should be reported as MVPs, rather than treating the three positions as a single position.

The Fair Isaacs Corporation has devised a model that is used to determine credit worthiness of individuals, called a FICO score. FICO scores range in value from 300 to 850, with a higher score indicating a more creditworthy individual. The distribution of FICO scores is skewed left with a median score of 723. (a) Do you think the mean FICO score is greater than, less than, or equal to 723? (b) What proportion of individuals have a FICO score above 723?

(a) The mean will be less than 723 because in left-skewed distributions, the mean is usually less than the median (b) 50%

Determine whether the quantitative variable is discrete or continuous High temperature on a randomly selected day in Memphis, Tennessee

Continuous

The US Department of Housing and Urban Development (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the median?

HUD uses the median because the data are skewed.

Determine the level of measurement of each variable Nation of origin

Nominal

Determine whether 0.366 is a parameter or statistic Ty Cobb is one of major league baseball's greatest hitters of all time, with a career batting average of 0.366.

Parameter

Classify the variable as qualitative or quantitative Student ID number

Qualitative

Classify the variable as qualitative or quantitative Grams of carbohydrates in a doughnut

Quantitative

Classify the variable as qualitative or quantitative Number of unpopped kernels in a bag of microwave popcorn

Quantitative

Determine whether 13.3% is a parameter or statistic In a national survey on substance abuse, 13.3% of 12th graders reported using illicit drugs within the past month.

Statistic

Determine whether 32% is a parameter or statistic In a national survey of 1300 high school students (grades 9 to 12), 32% of respondents reported that someone had bullied them at school.

Statistic

Compute the trimmed mean for the data in problem 25. Is the trimmed mean resistant?

The trimmed mean is 0.875. The trimmed mean is resistant only if the extreme observations is the highest or lowest value.

A professor has recorded exam grades for 20 students in his​ class, but one of the grades is no longer readable. If the mean score on the exam was 82 and the mean of the 19 readable scores is 84, what is the value of the unreadable​ score?

The unreadable score is 44.

What type of variable is required when drawing a time-series plot? Why do we draw time-series plots?

Time-series plots are drawn with quantitative variables. They are drawn to see trends in the data.

True or false There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others

True