Statistics Quiz 3

A researcher records 17 scores. What is the median position of these scores?

the 9th score in numeric order

Which of the following will decrease the value of the mean?

adding a score below the mean

Which type of mean is used to describe a portion of individuals in a given population?

sample mean

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

weighted mean

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

the 50th percentile of a cumulative percentage distribution

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

remain 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

Which of the following is not a symbol used with samples:

μ

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

The mode can be used with the mean to describe which of the following variables?

volume in a container

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?

3.5

Which of the following is NOT a characteristic of the mean?

Delete a score above the mean and the mean will increase

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

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

Median

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?

No; the mean is larger than the median

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?

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?

The sample mean is written using the wrong notation.

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 equal to zero.

Which of the following statements about a weighted mean is true.

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.

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]

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

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

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

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?

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

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

average, middle, and most

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

Multiplying or dividing each score in a distribution by the same constant will

cause the mean to change by that constant

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]

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

increase

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

larger

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

mean

The sum of the squared differences of scores from their mean is

minimal

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?

mode

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?

mode

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

mode

A researcher records 52 scores. What is the median position of these scores?

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

The fact that the sum of the differences of scores from their mean is zero best illustrates that

the mean is the "balance point" of a distribution

The mathematical term ∑x is the numerator for

the population mean the sample mean

When would a researcher calculate a population mean?

when data are measured for all members of a population

Given the same set of data for a population and sample, would the mean for both data sets be equal?

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

The population mean is symbolized as ________, whereas the sample mean is symbolized as ________.

μ; M

The median would be used to describe which of the following variables?

rankings

The mean would be used to describe which of the following variables?

distance traveled in miles

The size of a population is symbolized as ________, whereas the size of a sample is symbolized as ________.

N; n

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]

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

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