Intro to stats: Module 4, Examining Distributions Checkpoint 1
The boxplots below display annual incomes (in thousands of dollars) of households in two cities. Which city has greater variability in income?
Statstown Correct. The city whose boxplot appears "longer" is the city whose incomes had more variability. In this case, Statstown has more variability, since we see the Statstown boxplot extends more on either side than the Medianville plot.
The boxplots below show the real estate values of single-family homes in two neighboring cities (in thousands of dollars). Which city has the greater percentage of households with real estate values above $85,000?
Both cities have the same percentage of households with real estate values above $85,000. Correct. Correct. In this case, the median for each city is 85,000
The boxplots below show the real estate values of single-family homes in two neighboring cities (in thousands of dollars). Which city has a greater percentage of homes with real estate values between 55,000 and 55,000 and 85,000?
Tinytown Correct. Values between 55,000 and 85,000 include less than a fourth of the homes in Bigburg but more than a fourth of the households in Tinytown because of how the medians and the first quartiles compare for the two cities.
The boxplots below show the real estate values of single-family homes in two neighboring cities (in thousands of dollars). Which city has more households?
impossible to tell, Correct. A boxplot only displays the five-number summary of a dataset. A boxplot doesn't indicate how many data values might have been in the dataset. So, in this case, the boxplots only indicate the income levels for the households in the city, but not how many households there might be in the city.
Based on the results of a nation-wide study, the number of contacts programmed into cell phones are summarized on the following boxplot: Which of the following is true about this data?
impossible to tell. Given only the 5-number summary, it is impossible to determine which way the data is skewed. Even if we know there are outliers, we would need to know the mean or see the histogram to determine if there are outliers.
The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, only 0.15% of people have an IQ over what score?
145 Correct. The standard deviation rule tells us that for distributions that have the normal shape, approximately 99.7% of the observations will fall within 3 standard deviations of the mean. In this case the mean is 100, and the standard deviation is 15; therefore, approximately 99.7% of the observations (IQ scores) fall between 100 − 3 * 15 and 100 + 3 * 15 or between 55 and 145. Approximately 100% − 99.7% = 0.3% of the observations fall outside this interval. Since the normal shape is symmetric, approximately 0.15% of the observations fall above 145.
Based on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot: Which interval contains the greatest amount of data?
50-100 Correct. This interval stretches from Q1 to well above the median, so we can be sure that it contains more than 25% of the data. No other interval has more than 25% of the data, so this is the best answer.
The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, what range of IQ scores do many (68%) people have?
Between 85 and 115 Correct. The standard deviation rule tells us that for distributions that have the normal shape, approximately 68% of the observations fall within 1 standard deviation of the mean. Indeed, 85 = 100 − 1 * 15 and 115 = 100 + 1 * 15 are exactly 1 standard deviations below and above the mean, respectively.
The histogram below shows the times, in minutes, required for 25 rats in an animal behavior experiment to successfully navigate a maze. Which of the following are the appropriate numerical measures to describe the center and spread of the above distribution?
The median and the IQR
A student survey was conducted at a major university, and data were collected from a random sample of 750 undergraduate students. One variable that was recorded for each student was the student's answer to the question "With whom do you find it easiest to make friends? Opposite sex/same sex/no difference." These data would be best displayed using which of the following?
pie chart
