Ch. 3 HW & Test

A concrete mix is designed to withstand 3000 lbs per sq in (psi) of pressure. The data represent the strength of 9 randomly selected casts (in psi): 3970, 4080, 3200, 3200, 2930, 3840, 4100, 4050, 3570 A. Compute the mean strength of the concrete. a. The mean strength of the concrete is ___ psi of pressure. b. The mean doesn't exist. B. Compute the median strength of the concrete. a. The median strength of the concrete is ___ psi of pressure. b. The median doesn't exist. C. Compute the mode strength of the concrete. a. The mode of the strengths of the concrete is ___ psi of pressure. b. The mode doesn't exist.

A. a. 3660 B. a. 3840 C. a. 3200

Determine whether the given value is a statistic or a parameter: In a study of 3151 professors at a college, it's found that 40% own a computer. a. Parameter b/c the value is a numerical measurement describing a characteristic of a population. b. Statistic b/c the value is a numerical measurement describing a characteristic of a population. c. Parameter b/c the value is a numerical measurement describing a characteristic of a sample. d. Statistic b/c the value is a numerical measurement describing a characteristic of a sample.

a. Parameter b/c the value is a numerical measurement describing a characteristic of a population.

The table shows the frequency of cremation burials found in 12 archaeological sites. Determine the sample standard deviation. 85, 57, 52, 525, 44, 262, 2482, 41, 381, 77, 436, 112

x bar = 4554/12 = 379.5 std dev. = 684.0

During one year, the number of motorcycle accidents in a region were tabulated by day of the week for paved roads and dirt roads and resulted in this data. ....M - T - W - R - F - Sa - Su P 76, 105, 76, 96, 111, 85, 64 D 72, 42, 52, 54, 60, 81, 103 A. The range of paved road accidents is: The range of dirt road accidents is: B. The standard deviation for the number of accidents on - paved roads: - dirt roads:

A. Paved: 47 Dirt: 61 B. Paved roads: 17.1 x bar = 613/7 = 87.57142857 1753.714286 /6 = 292.2857143 sq rt = 17.09636553 Dirt roads: 20.7 x bar = 464/7 = 66.28571429 2581.428571 /6 = 430.2380952 sq rt = 20.74218154

Use the data set to complete a-c. 0,0,2,4 A. Determine the mean. B. Determine the median. C. Determine the mode. a. The mode(s) is/are ___ b. The data set has no mode.

A. 1.5 B. 1 C. a. 0

The table lists the lengths (yd) of the 1st 9 holes of a gold course: 471, 458, 316, 542, 408, 260, 402, 187, 440. A. The population mean of the hole lengths for all 9 holes is: B. The population standard deviation of the hole lengths for all 9 holes is:

A. 387.1 B. 105.9 sum = 3484 x bar = 3484/9 = 387.111111 ** DIVIDE BY n (9), NOT by n-1!

Each year, tornados that touch down are recorded. The table gives the # of tornadoes that touched down during each month of 1 year. A. Find the range. B. Find the standard deviation.

A. range = 205 B. std. dev. = 55.08 x bar = 80.5

One year, the max winds for 9 storms were recorded. HA - 120 TSB - 45 HC - 160 HD - 110 TSE - 70 HF - 140 TSG - 60 TSH - 70 HI - 145 Consider these cyclones a population of interest. A. The pop mean is rep'd by ___ and is equal to ___. B. The pop std dev is rep'd by ___ and is equal to ___. C. The pop median is rep'd by ___ and is equal to ___. D. The mode is: E. The IQR is:

A. µ, 102.2 B. sigma, 39.6 C. Greek n, 110 D. 70 E. 70

Consider the following 4 data sets: -- Data Set I -- 4,4,4,4,4,4 -- Data Set II -- 2,4,5,6,3,4 -- Data Set III -- 2,2,2,6,6,6 -- Data Set IV -- 3,3,5,7,3,3 A. Compute the mean of each data set. B. Which data set appears to have the least variation? Which data set appears to have the greatest variation? The data set (I, II, III, IV) appears to have the least variation. The data set (I, II, III, IV) appears to have the most variation. C. Compute the range of each data set. D. Use the defining formula to compute the sample standard deviation of each data set.

A. (all of them are 4) B. I has the least variation, since it only has 4's. III has the most variation, because it only has 2 numbers (2 & 6), but are both far away from the sample mean, 4. C. Set I: 0 Set II: 4 Set III: 4 Set IV: 4 D. Set I: 0.0 Set II: 1.4 Set III: 2.2 Set IV: 1.7

A study is published with information about ages of people in a particular region. A sample of 5 residents from the region have the following ages, in years: 45, 34, 63, 82, 3. A. Determine the range of these ages. B. Find the sample standard deviation of these ages by using the defining formula, where n is the sample size and (x w/ line over it) is the sample mean.

A. 79 B. x bar (mean) = 45.4 s = 29.9

The data show the # of vacation days used in a recent year by a sample of 12 employees: 8,9,8,8,9,8,9,10,2,7,9,6 A. Obtain the quartiles. B. Determine the IQR. C. Find the 5 # summary.

A. Q1 = 7.5 Q2 = 8 Q3 = 9 B. 1.5 C. 2, 7.5, 8, 9, 20

The data shows the # hrs of TV watched/day by a sample of 11 people: 5,2,0,4,5,1,10,6,7,2,6 A. Obtain the quartiles. B. Calculate the IQR. C. Find the 5 # summary.

A. Q1 =2 Q2 = 5 Q3 =6 B. IQR = 4 C. 0,2,5,6,10

It was reported in 2004 the mean net worth of families in a certain region was $460.6 thousand, and the median net worth was $96.8 thousand. Which measure of center do you think is more appropriate? Explain. a. The mean, b/c it's not strongly affected by the relatively few families w/ extremely low net worth. b. The mean, b/c it takes into account each family's net worth in the region. c. The mean, b/c it's not strongly affected by the relatively few families w/ extremely high net worth. d. The median, b/c it's not strongly affected by the relatively few families w/ extremely low net worth. e. The median, b/c it's not strongly affected by the relatively few families w/ extremely high net worth. f. The median, b/c it takes into account each family's net worth in the region.

e. The median, b/c it's not strongly affected by the relatively few families w/ extremely high net worth.

The data set shows the additional sleep in hours obtained by a sample of 10 patients given a certain medication. 1.1, 0.8, 1.5, 0.4, 0.3, 3.7, 3.5, 1.3, 5.2, 2.6 a. Find n b. Compute ∑xi = c. Determine the sample mean.

a. 10 (n = sample size) b. 20.4 (summation of x variables) c. 2.04 (average of the sample data)

Consider the data set 2,3,4,5,6,7,8,9,10. A. Obtain the mean and median of the data. B. Replace the 10 in the data set by 100 and again compute the mean and median. C. Which center of measure works better here? a. The mean works better since it's more typical of most of the data. b. Both centers of measure work equally well here. They're both typical of most of the data. c. The median works better here since it's more typical of most of the data.

A. mean: 6 median: 6 B: mean: 16 median: 6 C. c. The median works better here since it's more typical of most of the data.

A census bureau collects info about the ages of people in a country. A. Identify the variable: a. The age of each person in the country b. The avg. age of people in the country c. The median age of people in the country d. The age of people in different countries Identify the population: a. All people b. All people living in the country c. All adults living in the country B. A sample of 6 residents yielded the data: 38,20,5,28,19,37 - The mean and median of these data are: (statistics/parameters) - The sample mean = - The sample median = C. By consulting the most recent census data, we found the mean age and median age of all residents are 35.8 and 35.5 years. Decide whether those descriptive measures are parameters or stats, and use statistical notation to express the results. - The mean & median age of all residents are (parameters/stats) - The population mean is (variable) - The population median is (variable)

A. a. The age of each person in the country b. All people living in the country B. 147/6 = 24.5 stats x bar = 24.5 M = 24 C. parameters pop mean = µ pop median = "Greek n"

In 2000, for a certain region, 29.8% of incoming college freshman characterized their political views as liberal, 47.2% as moderate, and 23.0% as conservative. For this year, a random sample of 400 incoming college freshman yielded the frequency distribution for political views shown: Political view // Freq Liberal - 111 Moderate - 213 Conservative - 76 A. Choose the correct answer. Select ALL that apply. a. The mode is conservative. b. The mode is moderate. c. The mode is liberal. d. There is no mode. B. Would it be appropriate to use either the mean or the median as a measure of center? a. The median would be an appropriate measure of center b/c it's not strongly affected by the relatively large gap b/w the smallest & largest frequencies. b. Either the mean or the median would be an appropriate measure of center since they're approximately the same. c. The mean would be an appropriate measure of center b/c the political views of freshman in the sample is very similar to the percentages of all freshman. d. Since the data is qualitative, neither the mean nor the median can be used as a measure of center.

A. b. The mode is moderate. B. d. Since the data is qualitative, neither the mean nor the median can be used as a measure of center.

An insurance company crashed 4 cars of the same model at 5 mph. The costs of repair for each were $420, $442, $451, and $218. A. Find the mean. B. Find the median. C. Find the mode.

A. $382.75 B. $431.00 C. The mode doesn't exist.

The following table gives the horsepower for each of 7 vacuum cleaners tested: 2.50, 2.00, 1.25, 1.50, 2.50, 2.25, 1.75. Determine the range and sample standard deviation.

A. 1.25 B. sum = 13.75 x bar (mean) = 1.96428571 s= 0.488

Simple data set: 3,0,1,2,5 A. Find the population mean: B. Find the population std. dev:

A. 2.2 B. 1.7

Consider the data set: 10, 11, 12, 13, 14, 15, 16, 17, 18. A. Use the defining formula to obtain the sample standard deviation. s=____ B. Replace the 18 in the data set by 188 and again use the defining formula to compute the sample standard deviation.

A. 2.739 B. 58.212

Each year, a magazine compiles a list of the 400 richest people in a country. As of 2008, the top 10 on the list are shown: Person//Wealth ($ billions) A - 51.1 B - 42.8 C - 33.6 D - 30.5 E - 30.2 F - 20.2 G - 20.2 H - 18.9 I - 18.8 J - 18.8 A. The mean is $___ billion. B. The median is $__ billion. C. Select the correct choice and fill in the box. a. The mode is $__billion. b. The modes are $__billion. c. The data set has no mode.

A. 28.51 B. 25.2 C. b. The modes are $18.8, 20.2 billion

A pro hockey player played 20 seasons. The data shows the # of games in which he played during each of his 20 seasons: 35,65,76,74,73,66,43,74,67,80,67,69,65,82,77,69,68,80,79,79 A. Obtain and interpret the quartiles. a. The quartiles suggest that 25% of the seasons have less than 66.5 games played, 25% are between 66.5-71, 25% are between 71-78, and 25% are 78+. b. The quartiles suggest that 33% of the seasons have less than 66.5, 33% are b/w 66.5-78, and 33% are 78+. c. The quartiles suggest that all the seasons fall b/w 66.5-78. d. The quartiles suggest that the average of the games played each season is 71. B. Determine and interpret the IQR. a. The number of games played in the middle 50% of the seasons span ~11.5. b. The average of the 1st and 3rd quartiles is 11.5. c. The approx. difference b/w each quartile is 11.5 d. The data roughly span 11.5 games played. C. Find & interpret the 5# summary. a. The 1st quarter has the greatest variation. The middle 50% has the next largest, the last has the least. b. The 1st quarter has the most seasons recorded. The last has the least. c. The middle 50% has the greatest variation in the data set. The 1st and 4th have the least. d. There aren't as many seasons in the 4th quarter as there are in the 1st. D. Identify potential outliers, if any. E. Construct and interpret a boxplot. a. The 2 potential outliers are relatively close to the other data points. Most seasons fall w/i the 1st quarter, b/w 61.5-71. b. The 2 potential outlying seasons fall far from the rest of the data. The other seasons vary 65-82. The majority of the seasons had b/w 66.5-78 games played. c. The 2 potential outliers fall far from the rest of the data. The other seasons vary 60-77 games. The majority of seasons had b/w 61.5-73 games played. d. Most seasons had ~71 games played. The highest # of games played was 87, and the lowest was 30.

A. Q1 = 66.5 Q2 = 71 Q3 = 78 a. The quartiles suggest that 25% of the seasons have less than 66.5 games played, 25% are between 66.5-71, 25% are between 71-78, and 25% are 78+. B. IQR = 11.5 a. The number of games played in the middle 50% of the seasons span ~11.5. C. sum = 35,66.5,71,78,82 a. The 1st quarter has the greatest variation. The middle 50% has the next largest, the last has the least. D. 33, 43 E. b. The 2 potential outlying seasons fall far from the rest of the data. The other seasons vary 65-82. The majority of the seasons had b/w 66.5-78 games played.

For the data set 6, 1, 9, 2, 8, determine the: A. range B. sample standard deviation

A. range = 8 B. std. dev. = 3.6 x bar = 5.2

A. Which measure of variation is preferred when the mean is used as a measure of center? B. Which measure of variation is preferred when the median is used as a measure of center? mode, variance, IQR, std. dev.

A. std. dev. B. IQR

A stats center compiles data on the length of stay by patients in short-term hospitals. A random sample of 21 patients yielded the data on length of stay (in days). 24, 6, 6, 11, 4, 10, 49, 22, 23, 16, 14, 6, 13, 1, 12, 24, 6, 13, 6, 19, 22 Aa. Obtain and interpret the quartiles. Ab. Interpret the quartiles. a. The quartiles suggest that the average length of stay is 13 days. b. The quartiles suggest that 33% of patients stayed less than 6 days, 33% stayed 6-22 days and 33% stayed more than 22 days. c. The quartiles suggest that 25% of the patients stayed less than 6 days, 25% stayed 6-13 days, 25% stayed 13-22 days and 25% stayed more than 22 days. d. The quartiles suggest that all the patients stayed 6-22 days. Ba. Determine the IQR. Bb. Interpret the IQR. a. The data spun roughly 16 days. b. The average of Q1 and Q3 = 16. c. The length of stay in the middle 50% of patients spans roughly 16 days. d. The approx. difference b/w each quartile is 16. Ca. Find & interpret the 5 # summary. Cb. Interpret a. The 4th quarter has the greatest variation. The middle 50% has the next largest, and the 1st has the least. b. The 1st quarter has the most patients recorded. The 4th has the least. c. There aren't as many patients in the 4th quarter as there are in the 1st. d. The middle 50% has the greatest variation in the data set. The 1st and 4th quarters have the same. D. Identify potential outliers, if any. Ea. Construct and interpret a boxplot. Choose the correct boxplot below. Eb. Interpret the boxplot. a. The potential outlier is relatively close to the other data points. Most stays fall w/ the 1st quarter of the plot, b/w 9-19.5. b. Most stays were ~19.5 days. The longest was 36, and shortest was 1.5. c. the 2 potential outliers fall far from the rest of the data. The other observations vary from 6.05-30.2 days. The majority of the stays were b/w 11.3-28.1. d. The potential outlying observation falls far from the rest of the data. The other stays vary from 1-24 days. The majority of the stays were between 6-22 days.

Aa. Q1 = 6 Q2 = 13 Q3 = 22 Ab. c. The quartiles suggest that 25% of the patients stayed less than 6 days, 25% stayed 6-13 days, 25% stayed 13-22 days and 25% stayed more than 22 days. Ba. IQR = 16 Bb. c. The length of stay in the middle 50% of patients spans roughly 16 days. Ca. 1, 6, 13, 22, 49 Cb. a. The 4th quarter has the greatest variation. The middle 50% has the next largest, and the 1st has the least. D. 49 Ea. Has one outlier Eb. d. The potential outlying observation falls far from the rest of the data. The other stays vary from 1-24 days. The majority of the stays were between 6-22 days.

An article by a researcher reported on a long-term study of the effects of hurricanes on tropical streams in forests. The study shows that 1 particular hurricane had a significant impact on stream water chemistry. The table shows a sample of 10 ammonia fluxes in the 1st year after the hurricane (in kg/hectare/year): 179, 156, 90, 86, 55, 177, 176, 95, 97, 148 Aa. Obtain the quartiles. Ab. Interpret the quartiles. a. The quartiles suggest that all the samples contain b/w 90-176 units. b. The quartiles suggest that 33% of the samples contain less than 90 units, 33% contain 90-176, and 33% contain 176+. c. The quartiles suggest that the average sample contains 122.5. d. The quartiles suggest that 25% of the samples contain less than 90, 25% contain 90-122.5, 25% contain 122.5-176 and 25% contain 176+. Ba. Determine the IQR. Bb. Interpret the IQR. a. The # of units contained in the middle 50% of the samples spans roughly 86 units. b. The approx. difference b/w each quartile is 86. c. The data span roughly 86 units. d. The average of the 1st quartile and the 3rd quartile is 86. Ca. Find the 5 # summary. Cb. Interpret the 5 # summary. a. There aren't as many samples in the 4th quarter as there are in the 1st. b. The middle 50% has the least variation. The 1st and 4th quarters have the greatest. c. The middle 50% has the greatest variation. The 1st has the next largest, the last has the least. d. The 1st quarter has the most samples recorded. The last has the least. D. Identify the potential outliers, if any. Ea. Choose the correct boxplot. Eb. Interpret the boxplot. a. The samples range from 55-179 units each. The majority of the samples contain 90-176. b. Most samples fall w/i the 1st quarter, b/w 85-122.5. c. Most samples had ~90 units. The highest # of units sampled was 189, the lowest was 45. d. The samples vary from 49.5-161.1 units. The majority of the samples had b/w 81-158.4 units.

Aa. Q1 = 90 Q2 = 122.5 Q3 = 176 Ab. d. The quartiles suggest that 25% of the samples contain less than 90, 25% contain 90-122.5, 25% contain 122.5-176 and 25% contain 176+. Ba. IQR = 86 Bb. a. The # of units contained in the middle 50% of the samples spans roughly 86 units. Ca. 55, 90, 122.5, 176, 179 Cb. c. The middle 50% has the greatest variation. The 1st has the next largest, the last has the least. D. There are no potential outliers. Ea. right skewed Eb. a. The samples range from 55-179 units each. The majority of the samples contain 90-176.

The data represents the # of chips per cookie in a random sample of a name brand and a store brand. Name brand: 23, 32, 29, 28, 26, 23, 22, 28, 31, 25, 22, 24, 35 Store brand: 20, 26, 18, 15, 16, 21, 24, 27, 33, 28, 23, 31, 20 A. Make boxplots for the data sets. Choose the correct one. B. Compare the data sets. a. Overall the 2 brands are fairly similar. The store brand appears to have slightly more chips/cookie, and less variation b/w cookies than the name brand. b. Overall the 2 brands are fairly similar. The name brand appears to have slightly more chips/cookie, and less variation b/w cookies than the store brand. c. The store brand has more chips/cookie overall, but the name brand has less variation b/w cookies. d. The name brand has more chips/cookie overall, but the store brand has less variation b/w cookies.

B. b. Overall the 2 brands are fairly similar. The name brand appears to have slightly more chips/cookie, and less variation b/w cookies than the store brand.

Name and describe the 3 most important measures of center. a. The sample size, median and mode are the most important. The sample size of a data set is the difference b/w the highest and lowest value in its ordered list. The median is its most frequently occurring value. The mode is the sum of the observations divided by the # of obs. b. The mean, median, and mode are the most important. The mean is the product of the obs. divided by the # of obs. The median is the lowest value in its ordered list. The mode is the least frequently occurring value. c. The mean, sample size and mode are the most important. The mean is the sum of the obs. divided by the middle value in its ordered list. The sample size is the # of obs. The mode is its highest value in its ordered list. d. The mean, median and mode are the most important. The mean is its arithmetic average. The median is the middle value in its ordered list. The mode is the most frequently occurring value.

d. The mean, median and mode are the most important. The mean is its arithmetic average. The median is the middle value in its ordered list. The mode is the most frequently occurring value.