Unit 1 Stats Test
The following list shows the selling prices of 8 houses in a certain town. What is the median selling price of the houses in the list?
$283,300 To find the median of the list of data, first order the data from least to greatest: 250,600; 275,800; 275,800; 281,900; 284,700; 295,000; 302,100; 305,400. Since there are 8 values, an even number, the median is the average of the 2 values in the middle of the ordered list: 281,900+284,7002=566,6002=$283,300281,900+284,7002=566,6002=$283,300. The median selling price of the houses is $283,300
A researcher is studying a group of field mice. The distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. Which of the following is closest to the proportion of field mice with a weight greater than 33 grams?
0.023 The z-score associated with a weight of 33 grams is 2. The area under the curve to the right of 2 in a standard normal distribution is approximately 0.023.
At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?
0.17 The correct z-score is −0.95z=240−27638=−0.95. The area under the standard normal curve to the left of that value is approximately 0.17.
For a certain online store, the distribution of number of purchases per hour is approximately normal with mean 1,200 purchases and standard deviation 200 purchases. For what proportion of hours will the number of purchases at the online store exceed 1,400 ?
16% By the empirical rule, 68% of the number of purchases in an hour will be between 1,000 and 1,400, so 100%−68%=32%100%−68%=32% of the number of purchases in an hour will fall outside of the interval. Since the normal distribution is symmetric around the mean, half of 32%, which is 16%, of the number of purchases in an hour will exceed 1,400.
Shalise competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes. Shalise completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percent of the participants had finishing times greater than Shalise's for each puzzle?
16% on the small puzzle and 84% on the large puzzle According to the empirical rule, approximately 68% of the completion times are within one standard deviation of the mean of 60 minutes for the smaller puzzle. By symmetry, 16% of the remaining completion times are less than 45 minutes and 16% of the completion times are greater than 75 minutes. For the large puzzle, the empirical rule guarantees that approximately 68% of the times will be within 1 standard deviation of the mean of 180 minutes. By symmetry, 16% of the remaining times are less than 140 minutes, and 16% of the times are greater than 220 minutes. Therefore 84% of the times will be greater than Shalise's time of 140 minutes on the large puzzle.
A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm)(mm) and standard deviation 1.4 mmmm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?
20.6 mm This value is an outlier, because it is located more than 2 standard deviations below the mean. Of the five values that are listed in the options, this value is the greatest value that is an outlier.
The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution?
26 Inches Since 10% of the salmon are longer than 30 inches, then 90% of the salmon are less than or equal to 30 inches. From the standard normal table, approximately 90% of the area under the curve falls at or below the z-score of 1.282, so this value can be substituted into the formula for a z-score (z=x−μσ=30−μ3.5=1.282)(z=x−μσ=30−μ3.5=1.282) and then solved for μμ.
The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon?
35 The value 35 is the third quartile, meaning at least 25% of the cars get 35 miles per gallon or more.
An amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. The following boxplot shows the heights of a sample of people who entered the amusement park on one day.
50% The median appears to be halfway between 46 and 50 at 48. So approximately 50% of the people met the height requirement.
A market researcher asked a group of men and women to choose their favorite color design from a sample of advertisements. The results are shown in the following table. Which of the following statements is not supported by the table?
For men, the number who chose a design with black was greater than the number who chose a design with blue.
A sample of 100 students from Liberty High School and a sample of 60 students from Central High School were asked what they planned to do after graduation. Responses fell into five categories: four-year university (4Y), community college (CC), join the workforce (W), join the military (M), or undecided (UD). The results are shown in the following bar chart. Which of the following statements is supported by the bar chart?
For the category undecided, the number of students from Liberty High School was 4 greater than the number of students from Central High School.
In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity. Which of the following statements is supported by the bar chart?
Grade 12 had the least relative frequency of participating students.
The following pie chart summarizes the results of a survey given to airlines about the primary reason for flight delays. Which of the following statements is supported by the pie chart?
More delays were caused by weather than by all other reasons combined.
The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm. Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR1.5×IQR rule for outliers, is there evidence to support the claim?
No, because 43 is not greater than (Q3+1.5×IQR)(Q3+1.5×IQR).
Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. Is Roger's claim correct?
No, only the mean is likely to change greatly.
The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream. Which of the following statements is not supported by the table?
One-half of the students chose vanilla or chocolate.
The following list shows the number of video games sold at a game store each day for one week. 15, 43, 50, 39, 22, 16, 20 Which of the following is the best classification of the data in the list?
Quantitative and discrete The number of games sold is quantitative because it is measurable. The number of games sold is also a whole number, and whole numbers are discrete.
The following bar chart shows the relative frequency of days of rain for 30 days in four regions of a certain state. Which of the following statements is not supported by the bar chart?
Region C had more than 25 days of rain.
The following table summarizes the number of pies sold at a booth one day at a local farmers market. Which of the following statements is supported by the table?
The combined percentage of key lime pies sold and pumpkin pies sold was less than 50%. The number of key lime pies sold is 12 and the number of pumpkin pies sold is 18. The combined total is 30, which is equal to approximately 33% of the pies sold. Therefore, the combined percentage is less than 50%
Which of the following describes a continuous variable?
The diameters of the tree trunks at an evergreen farm
The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town. Which of the following statements is supported by the table?
The number of people affiliated with the independents is 100 20% of 500 is 100
Which of the following statements is true about a distribution that appears to have a gap when displayed as a histogram?
The distribution has a region between two data values where no data were observed. A gap is a region of a distribution between two data values where there are no observed data.
The following dotplot shows the scores of 25 people who played an online trivia game. Which of the following statements is the best description of the distribution of scores?
The distribution is skewed right
One statistic calculated for pitchers in baseball is called the earned run average, or ERA. The following boxplots summarize the ERA for pitchers in two leagues, A and B. Based on the boxplots, which of the following statistics is the same for both leagues?
The interquartile range
The following histogram shows the ages, in years, of the people who attended a documentary at a movie theater. Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages?
The mean is most likely less than the median because the distribution is skewed to the left
One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distributions of the root-mean-square times for two sources of disturbances. Based on the histograms, which of the following correctly compares the two distributions?
The median of the earthquake disturbances is less than the median of the mining disturbances.
Data will be collected on the following variables. Which variable can be considered discrete.
The number of books a person finished reading last month The number of books is a counting number which, like all whole numbers, is discrete.
A child psychologist asked 100 five year olds and 50 ten year olds to name their favorite color. Their results are shown in the following table. Which of the following statements is supported by the table?
The percentage of five year olds who selected red or blue as their favorite color is greater than the percentage of ten year olds who selected red or blue as their favorite color.
The following table shows summary statistics for the number of hours a group of students spent playing video games last Monday and last Saturday. Based on the summary statistics, which of the following gives the best comparison of the range and the interquartile range (IQR)(IQR) of the two days?
The range and IQR of hours played on Monday are both less than the range and IQR of hours played on Saturday. The range (maximum minus minimum) is 12 hours played on Monday and 17 hours played on Saturday. The IQR (Q3 minus Q1) is 3 hours played on Monday and 4 hours played on Saturday.
The following histogram summarizes the amount spent on plane tickets to travel home, in dollars, for a group of 30 college students. If the interval size is decreased from $200 to $100, which of the following must remain the same on the new histogram?
The sum of the frequencies
Data were collected on 100 United States coins minted in 2018. Which of the following represents a quantitative variable for the data collected?
The value of the coin
At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th77th percentile of the distribution?
There were 770 entries with a score less than or equal to 68.
The following table shows data for the 8 longest roller coasters in the world as of 2015. Which of the following variables is categorical?
Type
Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?
What are the colors of the cars in the lot?
The distribution of the number of transactions per day at a certain automated teller machine (ATM)(ATM) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of the following represents the parameters of the distribution?
μ=80;σ=10
A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean?
∑(x−x¯)2=(86−84)2+(81−84)2+(87−84)2+(82−84)2