Statistics Chapter 3

A professor grades 120 research papers and reports that the average score was an 80%. What do we know about the sum of the differences of these 120 scores from their mean of 80%? The sum of the differences is minimal. The sum of the differences is 80%, the same as the mean. The sum of the differences is equal to zero. It is impossible to know without knowing each of the 120 scores.

The sum of the differences is equal to zero.

Which of the following will decrease the value of the mean? deleting a score below the mean adding a score below the mean adding a score exactly equal to the mean none of the above

adding a score below the mean

Which of the following can be used to estimate the median? the 50th percentile of a relative percentage distribution the 50th percentile of a cumulative percentage distribution the mean the mode

the 50th percentile of a cumulative percentage distribution

Which type of mean is used to describe a portion of individuals in a given population? sample mean population mean restricted mean none of the above

sample mean

What terms refer to each of the following measures, respectively: mean, median, and mode. middle, most, and average average, middle, and most average, most, and middle most, average, and middle

average, middle, and most

The mean would be used to describe which of the following variables? rankings distance traveled in miles gender model of car

distance traveled in miles

A researcher records the following scores: 5, 3, 7, 6, 2, 8, 0, and 1. In terms of these data, the sum of the squared differences of scores from their mean is 0 8 32 60

60

A researcher records the following data for the number of different food items chosen by seven participants in a buffet-style setting: 1, 6, 2, 5, 4, 3, and 7. Is the mean equal to the median in this example? Yes. No; the median is larger than the mean. No; the mean is larger than the median. There is not enough information to answer this question.

Yes

A researcher records 17 scores. What is the median position of these scores? the 9th score in numeric order the average of the 9th and 10th scores in numeric order the average of the 8th and 9th scores in numeric order It's not possible to know this without the raw scores.

the 9th score in numeric order

Which of the following statements about a weighted mean is true. The weighted mean is always equal to the arithmetic mean. The weight mean can only be reported id the sample size is equal in each group. The weighted mean is used to compute the combined mean for two or more samples of scores in which the number of scores in each sample is disproportionate or unequal. The weighted mean is heavier than an arithmetic mean.

The weighted mean is used to compute the combined mean for two or more samples of scores in which the number of scores in each sample is disproportionate or unequal.

The median would be used to describe which of the following variables? gender ethnicity rankings brand name

rankings

A researcher asks participants to estimate the height (in inches) of a statue that was in a waiting area. The researcher records the following estimates: 40, 46, 30, 50, and 34. If the researcher removes the estimate of 40 (say, due to an experimenter error), then the value of the mean will decrease increase remain the same become negative

remain the same

The mode can be used with the mean to describe which of the following variables? rankings gender volume in a container all of the above

volume in a container

The ________ is an arithmetic mean of a weighted or disproportionate set of scores. mean weighted mean median mode

weighted mean

A researcher selects a sample of 6 males and 11 females. She asks participants to rate the likelihood they would do female-stereotyped jobs (such as nursing or school teaching) on a scale from 1 = not likely at all to 5 = very likely. Men indicated that they would be less likely to do these jobs (M = 2.1) compared with women (M = 4.3). What is the weighted mean for this entire sample of 17 participants? 2.1 4.3 3.2 3.5

3.5

The ________ is the sum of all scores (in a sample or population) divided by the number of scores summed. mode median mean range

mean

A researcher measures the mean time (in seconds) it takes two groups of children to complete an activity task. She finds that Group A (M = 22 seconds) completed the task more quickly than Group B (M = 36 seconds). She then computes a weighted mean for both groups combined and calculates = 26. Based on the information provided, which group had a larger sample size Group A Group B The sample size is equal in both groups. It is not possible to know this without knowing the sample size for each group.

Group A

A researcher reports, "the average patron (n = 22) in a local bar consumed more than twice the number of drinks (per day) on weekends (M = 5.4 drinks) compared to weekdays (M = 2.3 drinks)." Although not stated directly, how do we know that the patrons in this study constitute a sample, and not a population of patrons at this local bar? We can't know for sure because this was not stated directly. The notation for a sample mean was used. The notation for sample size was used. both B and C

both B and C

A researcher asks participants to estimate the calories they consume in a meal. The researcher records the following estimates: 450, 426, 310, 500, and 220. If the researcher removes the estimate of 220 (perhaps because the participant drops out of the study), then the value of the mean will decrease increase remain the same become negative

increase

The ________ is the middle value in a distribution of scores that are listed in numeric order. mean median mode range

median

The sum of the squared differences of scores from their mean is minimal zero negative negligible

minimal

A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different hospitals had the highest overall rates of hospital admissions. Which measure of central tendency did this researcher use to describe these data? mean median mode range

mode

The distribution of personal income for U.S. citizens is positively skewed. If the median annual income is $44,000, this implies that the mean annual income is smaller larger the same There is not enough information to answer this question.

larger

The size of a population is symbolized as ________, whereas the size of a sample is symbolized as ________. μ; M M; μ n; N N; n

N; n

#22 When would a researcher calculate a population mean? when data are measured for of a portion of individuals from a population when the sample mean it not available when data are measured for all members of a population when it is not possible to measure all data in a population

when data are measured for all members of a population

The fact that the sum of the differences of scores from their mean is zero best illustrates that the mean is at the center of a distribution the mean is the "balance point" of a distribution the mean is equal to zero the mean can never be negative

the mean is the "balance point" of a distribution

A staff member records the number of victories (per 10-game season) for a new football coach during his first three seasons with a team. The coach won 1, 3, and 8 games respectively over the three seasons. Which conclusion is appropriate? The football coach won an average of four games per season. The football coach won a median of three games per season. The football coach won 40% of his games during his first three seasons. All of the above

All of the above

The mathematical term ∑x is the numerator for the population mean the sample mean Both A and B None; this term is not in the numerator for any calculation.

Both A and B

Which of the following is NOT a characteristic of the mean? Add a score above the mean and the mean will increase. Add a score below the mean and the mean will decrease. Delete a score below the mean and the mean will increase. Delete a score above the mean and the mean will increase.

Delete a score above the mean and the mean will increase.

A researcher records the following data for the number of complaints filed (per day) following a controversial policy change at a local business: 3, 8, 5, 0, 4, 6, 2, 1, 1, 4, 2, and 0. Is the mean equal to the median in this example? Yes. No; the median is larger than the mean. No; the mean is larger than the median. There is not enough information to answer this question.

No; the mean is larger than the median.

A researcher records the following data for the number of times an interviewer is interrupted during a series of interviews: 0, 0, 3, 2, 5, 3, 0, 8, 0, 2, 1, and 1. Is the mode equal to the median in this example? Yes. No; the median is larger than the mode. No; the mode is larger than the median. There is not enough information to answer this question.

No; the median is larger than the mode.

A researcher records the following data for the time (in seconds) it takes five rats to cross an electrical grid to obtain reinforcement on the other side: 12, 9, 13, 4, and 12. Is the mean equal to the mode in this example? Yes. No; the mode is larger than the mean. No; the mean is larger than the mode. There is not enough information to answer this question.

No; the mode is larger than the mean

To measure attraction, a researcher records the following data for the distance (in inches) between two persons sitting in a waiting room: 46, 32, 10, 23, 18, 46, and 60. Is the mode equal to the median in this example? Yes. No; the median is larger than the mode. No; the mode is larger than the median. There is not enough information to answer this question.

No; the mode is larger than the median.

A researcher reports that "the average shopper in the sample (n = 12) purchased $65.00 worth of items ( μ = $65.00) during a busy shopping day." What mistake was made is this citation? None; this citation is written appropriately. The sample mean is written using the wrong notation. The sample size is written using the wrong notation both B and C

The sample mean is written using the wrong notation.

A researcher selects a sample of 6 professors, 6 students, and 6 administrators at a local school and has them rate the effectiveness of an innovative new teaching style. In this example, is it possible that the weighted mean ratings will equal the arithmetic mean for the entire sample of 18 participants? No, the weighted mean is never exactly equal to the arithmetic mean. Yes, because there are an even number of participants in each sample. Yes, because the sample sizes are equal in this example. It is not possible to know this without knowing the mean for each sample.

Yes, because the sample sizes are equal in this example.

A researcher records the following data for how participants rated the likability (on a scale from 1 = not liked at all to 7 = very likable) of an individual who blushed after making a mistake: 5, 4, 7, 6, 6, 4, 6, 7, 2, 5, and 6. Is the mode equal to the median in this example? Yes. No; the median is larger than the mode. No; the mode is larger than the median. There is not enough information to answer this question.

Yes.

A researcher records the following data for the number of dreams recalled during a night of sleep for 10 college students: 3, 2, 4, 4, 3, 1, 1, 0, 2, and 0. Is the mean equal to the median in this example? Yes. No; the median is larger than the mean. No; the mean is larger than the median. There is not enough information to answer this question.

Yes.

The mean is an appropriate measure of central tendency for data that are normally distributed data that are on an interval or ratio scale data in which the mean, median, and mode are equal all of the above

all of the above

The median is an appropriate measure of central tendency for data that are positively skewed data that are negatively skewed data that are on an ordinal scale all of the above

all of the above

The mode is an appropriate measure of central tendency for data that are bimodal use with other measures of central tendency data that are on a nominal scale all of the above

all of the above

Adding the same constant to each score in a distribution (or subtracting the same constant from it) will cause the mean to change by that constant not change the mean at all because the same constant was added to or subtracted from each score

cause the mean to change by that constant

Multiplying or dividing each score in a distribution by the same constant will cause the mean to change by that constant not change the mean at all because each score was multiplied or divided by the same constant

cause the mean to change by that constant

A researcher asks adult participants to rank their top five favorite songs from their childhood. Based on the scale of measurement described, which measure of central tendency is most appropriate to describe these data? mean median mode range

median

The ________ is the value that occurs most often or at the highest frequency in a distribution. mean median mode range

mode

A researcher records 52 scores. What is the median position of these scores? the 26th score in numeric order the average of the 26th and 27th scores in numeric order the 27th score in numeric order It's not possible to know this without the raw scores.

the average of the 26th and 27th scores in numeric order

Given the same set of data for a population and sample, would the mean for both data sets be equal? no, the population mean would be larger no, the sample mean would be larger yes, but only if the sample size equaled the population size yes, this would be true anytime both data sets are the same

yes, this would be true anytime both data sets are the same

A researcher records the time (in seconds) that participants arrive late for a scheduled research study. Assuming these data are normally distributed, which measure of central tendency is most appropriate to describe these data? mean median mode range

mean

If a portion of people from a population are asked to complete an assessment, then the average score among that group of people would be considered a sample mean population mean median split modal mean

sample mean

The population mean is symbolized as ________, whereas the sample mean is symbolized as ________. μ; M M; μ n; N N; n

μ; M

Which of the following is not a symbol used with samples: x M μ n

μ