MATH 1680.150 Exam 1 Review
How could we identify which variable has more dispersion?
Dispersion is the degree to which the data are spread out. The more spread a set of data has, the higher the interquartile range will be.
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 87 and 113? (b) What percentage of people has an IQ score less than 87 or greater than 113? (c) What percentage of people has an IQ score greater than 126?
mean = 100 sd = 13 The empirical rule says that if a distribution is roughly bell shaped, the following is true. · Approximately 68% of the data will lie within 1 standard deviation of the mean. · Approximately 95% of the data will lie within 2 standard deviations of the mean. · Approximately 99.7% of the data will lie within 3 standard deviations of the mean. (a) In the 1st sd of the mean: mean + sd = 113 mean - sd = 87 Since an IQ score between 87 and 113 will lie within 1 sd of the mean, *the percentage of people having an IQ score between 87 and 113 is 68%* (b) *The percentage of people has an IQ score less than 87 or greater than 113 is 100% - 68% = 32%* (c) At the right 2nd sd of the mean: mean + 2sd = 126 The right section of the right 2nd sd ( the outside section of the right 2nd sd) will indicate the number of people having an IQ score greater than 126. According to the empirical rule, approximately 95% of the data will lie within 2 standard deviations of the mean. Therefore, the percentage of the section lying outside the 2nd sd is 100% - 95% = 5% Since the number of people having an IQ score greater than 126 lies on the right outer section of the 2nd sd, *the percentage of people whose IQ is greater than 126 is 5%/2 = 2.5%*
A student wanted to compare two types of commuting options. One type is carpooling and the other is taking a commuter train. It is a common belief that carpooling saves more time. This belief is tested by having 10 students commute to school by each mode of transportation and record the time of arrival at school each morning. A coin flip was used to determine which type of transportation that a student would use first. Results indicated that there was no difference in the two types of transportation. (1) What type of experimental design is this? A. Observational study B. Matched pair C. Completely randomized assignment D. Survey (2) What is the response variable in this experiment? A. The types of transportation B. The coin flip C. The time of arrival D. The students (3) What is the treatment? A. The coin flip B. The time of arrival C. The types of transportation D. The students (4) What are the experimental units? A. The students B. The time of arrival C. The types of transportation D. The coin flip (5) Why is a coin used to decide the transportation that a student would use first? A. To introduce an element of chance into the experiment B. To eliminate bias as to which transportation was used first C. To show that the experiment is fair D. None of the above
*(1) What type of experimental design is this?* A. Observational study *B. Matched pair* C. Completely randomized assignment D. Survey *(2) What is the response variable in this experiment?* A. The types of transportation B. The coin flip *C. The time of arrival* D. The students *(3) What is the treatment?* A. The coin flip B. The time of arrival *C. The types of transportation* D. The students *(4) What are the experimental units? A. The students* B. The time of arrival C. The types of transportation D. The coin flip *(5) Why is a coin used to decide the transportation that a student would use first?* A. To introduce an element of chance into the experiment *B. To eliminate bias as to which transportation was used first* C. To show that the experiment is fair D. None of the above
How to identify the outliers with Q1, Q2, Q3?
- *Calculate the interquartile range IQR* = Q3 - Q1 - *Calculate the lower and upper fence:* Lower fence = Q1 - 1.5 x IQR Upper fence = Q3 + 1.5 x IQR - *Check if there is any data point its under the lower fence or higher the upper fence:* A data point is considered an outlier using this method if it is less than the lower fence or greater than the upper fence.
What are the five-number summary of a data set?
- The smallest number of the data set - Q1 - Median (Q2) - Q3 - The largest number of the data set *NOTICE: Be sure to first list the data in ascending order.*
[T/F] The standard deviation can be negative.
False Explain: There is no way that the calculation of the population or sample standard deviation can produce a negative number. This makes intuitive sense because the standard deviation measures the spread of the data from the mean.
[T/F] A data set will always have exactly one mode.
False Explain: The mode of a variable is the most frequent observation of the variable that occurs in the data set. To compute the mode, tally the number of observations that occur for each data value. The data value that occurs most often is the mode. A set of data can have no mode, one mode, or more than one mode. If no observation occurs more than once, the data have no mode.
What is a Pareto chart?
*A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.* Explain: A Pareto chart helps prioritize categories for decision making purposes.
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2400 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 2600 grams and a standard deviation of 410 grams. 1) If a 33-week gestation period baby weighs 1850 grams and a 40-week gestation period baby weighs 2050 grams, find the corresponding z-scores. 2) Which baby weighs less relative to the gestation period?
1) *The sign of the z-score indicates whether the value is above (+) or below (-) the mean.* The z-score of the 33-week gestation period baby is z = (1850 - 2450)/700 = -0.79 => The 33-week gestation period baby weighs 0.79 standard deviations below the mean. The z-score of the 40-week gestation period baby is z = (2050 - 2600)/410 = -1.34 => The 40-week gestation period baby weighs 1.34 standard deviations below the mean. 2) *To identify which one is less relative, compare their z-scores. The smaller the value is, the less relative it is. (In more relative cases, the larger values indicates that it is more relative than the other)* The baby born in week 40 does since its z-score is smaller. *CAUTION: If two z-scores are both negative, the one whose absolute value is larger is less relative*
What is a bar graph?
A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the category's frequency or relative frequency. Explain: A bar graph is a clear way to compare the frequencies or relative frequencies of different categories by comparing the heights of the corresponding bars.
A graph is an ogive of a standardized test's scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. (a). Find and interpret the percentile rank of a test score with a value of 120. (the respectively vertical axis value is 50%) (b) Find and interpret the percentile rank of a test score with a value of 140. (the respectively vertical axis value is 90%)
A graph is an ogive of a standardized test's scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. *(a). Find and interpret the percentile rank of a test score with a value of 120.* A test score of 120 corresponds to the *50*th percentile rank since this percentage of test scores are *less than or equal to* a test score with a value of 120. *(b) Find and interpret the percentile rank of a test score with a value of 140.* A test score of 140 corresponds to the *90*th percentile rank since this percentage of test scores are *less than or equal to* a test score with a value of 140.
Explain the meaning of the following percentiles in parts (1) and (2). (1) The 10th percentile of the weight of males 36 months of age in a certain city is 12.0 kg. A. 10% of males weigh 12.0 kg or more, and 90% of 36-month-old males weigh less than 12.0 kg. B. 10% of males weigh 12.0 kg or less, and 90% of 36-month-old males weigh more than 12.0 kg. C. 10% of 36-month-old males weigh 12.0 kg or less, and 90% of 36-month-old males weigh more than 12.0 kg. D. 10% of 36-month-old males weigh 12.0 kg or more, and 90% of 36-month-old males weigh less than 12.0 kg. (2) The 95th percentile of the length of newborn females in a certain city is 53.3 cm. A. 95% of newborn females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm. B. 95% of newborn females have a length of 53.3 cm or more, and 5% of newborn females have a length that is less than 53.3 cm. C. 95% of females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm. D. 95% of females have a length of 53.3 cm or more, and 5% of newborn females have a length that is less than 53.3 cm.
Explain the meaning of the following percentiles in parts (1) and (2). (1) The 10th percentile of the weight of males 36 months of age in a certain city is 12.0 kg. A. 10% of males weigh 12.0 kg or more, and 90% of 36-month-old males weigh less than 12.0 kg. B. 10% of males weigh 12.0 kg or less, and 90% of 36-month-old males weigh more than 12.0 kg. *C. 10% of 36-month-old males weigh 12.0 kg or less, and 90% of 36-month-old males weigh more than 12.0 kg.* D. 10% of 36-month-old males weigh 12.0 kg or more, and 90% of 36-month-old males weigh less than 12.0 kg. (2) The 95th percentile of the length of newborn females in a certain city is 53.3 cm. *A. 95% of newborn females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm.* B. 95% of newborn females have a length of 53.3 cm or more, and 5% of newborn females have a length that is less than 53.3 cm. C. 95% of females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm. D. 95% of females have a length of 53.3 cm or more, and 5% of newborn females have a length that is less than 53.3 cm. Explain: The kth percentile of a set of data is a value such that k percent of the observations are less than or equal to the value.
A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why? A. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. B. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail. C. 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. D. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail.
A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why? A. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. B. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail. *C. 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.* D. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail. Explain: When data are either skewed left or skewed right, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. If the distribution of the data is skewed right, there are large observations in the right tail. These observations tend to increase the value of the mean, while having little effect on the median.
A mutual fund rating agency ranks a fund's performance by using one to five stars. A one-star mutual fund is in the bottom 20% of its investment class; a five-star mutual fund is in the top 20% of its investment class. Interpret the meaning of a four-star mutual fund. A. A four-star fund is in the 3rd quintile of the funds. That is, it is above the bottom 60%, but below the top 40% of the ranked funds. B. A four-star fund is in the 5th quintile of the funds. That is, it is above the bottom 60%, but below the top 20% of the ranked funds. C. A four-star fund is in the 4th quintile of the funds. That is, it is above the bottom 60%, but below the top 40% of the ranked funds. D. A four-star fund is in the 4th quintile of the funds. That is, it is above the bottom 60%, but below the top 20% of the ranked funds. E. A four-star fund is in the 5th quintile of the funds. That is, it is above the bottom 80%, but below the top 20% of the ranked funds. F. A four-star fund is in the 3rd quintile of the funds. That is, it is above the bottom 40%, but below the top 40% of the ranked funds.
A mutual fund rating agency ranks a fund's performance by using one to five stars. A one-star mutual fund is in the bottom 20% of its investment class; a five-star mutual fund is in the top 20% of its investment class. Interpret the meaning of a four-star mutual fund. A. A four-star fund is in the 3rd quintile of the funds. That is, it is above the bottom 60%, but below the top 40% of the ranked funds. B. A four-star fund is in the 5th quintile of the funds. That is, it is above the bottom 60%, but below the top 20% of the ranked funds. C. A four-star fund is in the 4th quintile of the funds. That is, it is above the bottom 60%, but below the top 40% of the ranked funds. *D. A four-star fund is in the 4th quintile of the funds. That is, it is above the bottom 60%, but below the top 20% of the ranked funds.* E. A four-star fund is in the 5th quintile of the funds. That is, it is above the bottom 80%, but below the top 20% of the ranked funds. F. A four-star fund is in the 3rd quintile of the funds. That is, it is above the bottom 40%, but below the top 40% of the ranked funds. Explain: The five star rating system represents percentiles. The kth percentile, denoted Pk, of a set of data is a value such that k percent of the observations are less than or equal to the value. In this case the percentiles are quintiles. Quintiles divide data sets in fifths, or five equal parts. A four-star fund is in the 4th quintile of the funds. It is above the bottom 60%, but below the top 20% of the ranked funds.
Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The following table represents the standing height of males aged 20 years or older for various age groups in a certain city in 2015. Based on the percentile measurements of the different age groups, what might you conclude?
At each percentile, compare the height values for each age group and make the appropriate conclusion. Keep in mind that adults in a given age range were in all of the previous age ranges at earlier points in time. At each percentile, the heights generally decrease as the age increases. Assuming that an adult male does not grow after age 20, the percentiles imply that adults born in 1990 are generally taller than adults at the same age who were born in 1950.
Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range? A. The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation. B. The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it increases as the dispersion of the data increases. C. The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it is resistant to extreme values. D. The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it is resistant to extreme values. E. The interquartile range is preferred when the data are not skewed or no have outliers. An advantage of the standard deviation is that it uses all the observations in its computation. F. The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it increases as the dispersion of the data increases.
Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range? *A. The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.* B. The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it increases as the dispersion of the data increases. C. The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it is resistant to extreme values. D. The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it is resistant to extreme values. E. The interquartile range is preferred when the data are not skewed or no have outliers. An advantage of the standard deviation is that it uses all the observations in its computation. F. The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it increases as the dispersion of the data increases. Explain: The interquartile range, IQR, is the range of the middle 50% of the observations in a data set. That is, the IQR is the difference between the first and third quartiles. The interquartile range is not affected by extreme values. Therefore, when the distribution of data is highly skewed or contains extreme observations, it is best to use the interquartile range as the measure of dispersion because it is resistant. The standard deviation describes how far, on average, each observation is from the mean. It is affected by extreme values, but the advantage that it has over the interquartile range is that it uses all the observations in its computation.
[T/F] The standard deviation is a resistant measure of spread.
False Explain: Extreme values are far from the mean, and will increase the standard deviation greatly. If the standard deviation was a resistant measure, then extreme data values would not affect it very much.
For a distribution that is symmetric, the left whisker is (1) For a distribution that is skewed right, the median is (2) For a distribution that is skewed left, the left whisker is (3) A. the same length as the right whisker. B. longer than the right whisker. B. shorter than the right whisker. D. left of center of the box. E. right of center of the box. F. center of the box.
For a distribution that is symmetric, the left whisker is *the same length as the right whisker*. For a distribution that is skewed right, the median is *left of center* of the box. For a distribution that is skewed left, the left whisker is *longer than the right whisker*.
Which histogram depicts a higher standard deviation?
Histogram whose distribution has more dispersion (larger range)
Suppose you are interested in comparing brand A interior enamel paint to brand B interior enamel paint. Design an experiment to determine which paint is better for painting ceilings. A. Completely randomized design because experimental units are paired up and there are only two levels of treatment. B. Matched-pairs design because experimental units are paired up and there are only two levels of treatment.
Suppose you are interested in comparing brand A interior enamel paint to brand B interior enamel paint. Design an experiment to determine which paint is better for painting ceilings. A. Completely randomized design because experimental units are paired up and there are only two levels of treatment. *B. Matched-pairs design because experimental units are paired up and there are only two levels of treatment.*
The U.S. 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? A. HUD uses the median because the data are skewed left. B. HUD uses the median because the data are symmetrical. C. HUD uses the median because the data are skewed right. D. HUD uses the median because the data are bimodal.
The U.S. 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? A. HUD uses the median because the data are skewed left. B. HUD uses the median because the data are symmetrical. *C. HUD uses the median because the data are skewed right.* D. HUD uses the median because the data are bimodal. Explain: HUD uses the median because the data are skewed to the right, and the median is better for skewed data.
Suppose the first class in a frequency table of quantitative data is 0 - 4 and the second class is 5 - 9. What is the class midpoint of the first class?
The class midpoint of the first class is 2.5
The cumulative relative frequency for the last class must always be 1. Why? A. The last class must always have at least one value in it. B. All the observations are less than or equal to the last class. C. All the observations are less than the last class.
The cumulative relative frequency for the last class must always be 1. Why? A. The last class must always have at least one value in it. *B. All the observations are less than or equal to the last class.* C. All the observations are less than the last class. Explain: The cumulative relative frequency displays the proportion (or percentage) of observations less than or equal to the class. Since all the observations are less than or equal to the last class, the cumulative relative frequency for it must be 1, or 100%.
The standard deviation is used in conjunction with the __(1)__ to numerically describe distributions that are bell shaped. The __(2)__ measures the center of the distribution, while the standard deviation measures the __(3)__ of the distribution. (1) mean | range | mode | variance | median (2) standard variation | variance | range | mean (3) center | range | spread
The standard deviation is used in conjunction with the *mean* to numerically describe distributions that are bell shaped. The *mean* measures the center of the distribution, while the standard deviation measures the *spread* of the distribution. Explain: Recall that the mean of a variable is computed by determining the sum of all the values of the variable in the data set and dividing by the number of observations. The standard deviation describes how far, on average, each observation is from the mean. Note that the standard deviation and the mean are the most popular methods for numerically describing the distribution of a variable. This is because these two measures are used for most types of statistical inference. Therefore, the standard deviation is used in conjunction with the mean to numerically describe distributions that are bell shaped and symmetric. The mean measures the center of the distribution, while the standard deviation measures the spread of the distribution.
The sum of the deviations about the mean always equals A. one B. zero C. negative one
The sum of the deviations about the mean always equals *zero*.
The sum of the deviations about the mean always equals to A. one B. negative one C. zero
The sum of the deviations about the mean always equals to A. one B. negative one *C. zero*
To help assess student learning in her music theory courses, a music professor at a community college implemented pre- and post-tests for her music theory students. A knowledge-gained score was obtained by taking the difference of the two test scores. (1) What type of experimental design is this? A. Completely randomized assignment B. Observational study C. Survey D. Matched pair (2) What is the response variable in this experiment? A. Total in test scores B. The score on the pretest C. Difference in test scores D. The score on the posttest (3) What is the treatment? A. Music theory course B. Type of school C. Background of student D. Music theory scores
To help assess student learning in her music theory courses, a music professor at a community college implemented pre- and post-tests for her music theory students. A knowledge-gained score was obtained by taking the difference of the two test scores. *(1) What type of experimental design is this?* A. Completely randomized assignment B. Observational study C. Survey *D. Matched pair* *(2) What is the response variable in this experiment?* A. Total in test scores B. The score on the pretest *C. Difference in test scores* D. The score on the posttest *(3) What is the treatment?* *A. Music theory course* B. Type of school C. Background of student D. Music theory scores
[T/F] When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.
True Explain: The standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Q1 = 272.8, Q2 = 387.9, Q3 = 528.3 (a) Interpret these results. (b) Determine and interpret the interquartile range. (c) The violent-crime rate in a certain state of the country in that year was 1 comma 459. Would this be an outlier? (d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Q1 = 272.8, Q2 = 387.9, Q3 = 528.3 *(a) Interpret these results.* *Q1:* 25% of the states have a violent-crime rate that is 272.8 crimes per 100,000 population or less. *Q2:* 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. *Q3:* 75% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or less. *(b) Determine and interpret the interquartile range.* The interquartile range is 528.3 - 272.8 = *255.5 crimes per 100,000 population. The middle 50% of all observations have a range of 255.5 crimes per 100,000 population.* *Hints:* The interpretation of the interquartile range is similar to that of the range and standard deviation. That is, the more spread a set of data has, the higher the interquartile range will be. *(c) The violent-crime rate in a certain state of the country in that year was 1459. Would this be an outlier?* The lower fence is 272.8 - 1.5 x 255.5 = -110.45 crimes per 100,000 population. The upper fence is 528.3 + 1.5 x 255.5 = 911.55 crimes per 100,000 population. Since violent-crime rate in a certain state of the country in that year is greater than the upper fence (1459>911.55), *it is an outlier*. *(d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?* The difference between Q 1 and Q 2 is quite a bit less than the difference between Q 2 and Q 3 (387.9-272.8>528.3-387.9). In addition, the outlier in the right tail of the distribution implies that the distribution is skewed right. Thus, *the distribution of violent-crime rates is skewed right*.
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Q1 = 273.8, Q2 = 387.9, Q3 = 528.3 Provide an interpretation of these results. Choose the correct answer below. A. 75% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. 25% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or less. B. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or more. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or more. 75% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or more. C. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or less.
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Q1 = 273.8, Q2 = 387.9, Q3 = 528.3 Provide an interpretation of these results. Choose the correct answer below. A. 75% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. 25% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or less. B. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or more. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or more. 75% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or more. *C. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or less.*
What are the advantages of having a pre-survey with open questions to assist in constructing a questionnaire that has closed questions? A. The researcher can possibly eliminate the need for closed questions. B. The researcher can learn common answers. C. The researcher can possibly create the option to use open questions. D. The researcher can get an idea of how large the sample needs to be.
What are the advantages of having a pre-survey with open questions to assist in constructing a questionnaire that has closed questions? A. The researcher can possibly eliminate the need for closed questions. *B. The researcher can learn common answers.* C. The researcher can possibly create the option to use open questions. D. The researcher can get an idea of how large the sample needs to be. Explain: A presurvey could give the researcher an idea of what the most common responses are from a population. The researcher could then use these responses as the answers to closed questions in the actual survey.
What can be said about a set of data with a standard deviation of 0? A. For every positive value, there is a corresponding negative value (as in 4 and -4; 6 and -6). B. All the observations are 0. C. All the observations are the same value.
What can be said about a set of data with a standard deviation of 0? A. For every positive value, there is a corresponding negative value (as in 4 and -4; 6 and -6). B. All the observations are 0. *C. All the observations are the same value.* Explain: If every positive value has a corresponding negative value, then the mean of the data would be 0, but the standard deviation would not be 0. Remember that if any data value differs from the mean, then the standard deviation will not be 0. Think about what a set of data would look like if no data value differed from the mean.
What does it mean if a statistic is resistant? A. Extreme values (very large or small) relative to the data affect its value substantially. B. Extreme values (very large or small) relative to the data do not affect its value substantially. C. An estimate of its value is extremely close to its actual value. D. Changing particular data values affects its value substantially.
What does it mean if a statistic is resistant? A. Extreme values (very large or small) relative to the data affect its value substantially. *B. Extreme values (very large or small) relative to the data do not affect its value substantially.* C. An estimate of its value is extremely close to its actual value. D. Changing particular data values affects its value substantially. Explain: A statistic is resistant if it is not sensitive to extreme values.
What makes the range less desirable than the standard deviation as a measure of dispersion? A. The range describes how far, on average, each observation is from the mean. B. The range is biased. C. The range does not use all the observations. D. The range is resistant to extreme values.
What makes the range less desirable than the standard deviation as a measure of dispersion? A. The range describes how far, on average, each observation is from the mean. B. The range is biased. *C. The range does not use all the observations.* D. The range is resistant to extreme values. Explain: The range of a variable is the difference between the largest data value and the smallest data value. The range is less desirable than the standard deviation as a measure of dispersion because it is computed using only two values in the data set (the largest and smallest).
Another measure of central tendency is the trimmed mean. It is computed by determining the mean of a data set after deleting the smallest and largest observed values. Is the trimmed mean resistant to changes in the extreme values in the given data?
Yes, because changing the extreme values does not change the trimmed mean.
