Question 1

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

Accepted Answer

F1F1F1S1F1F1F10 is not a commonly used symbol for samples. The other options (x, M, n) are commonly used to represent sample values.

Question 2

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?

Accepted Answer

First, we need to find the mean and median of the given data. 
Mean = (3 + 2 + 4 + 4 + 3 + 1 + 1 + 0 + 2 + 0) / 10 = 2
To find the median, we need to arrange the data in order:
0, 0, 1, 1, 2, 2, 3, 3, 4, 4
Median = (2 + 2) / 2 = 2
Since the mean and median are both 2, the answer is A.

Question 3

A researcher reports that "the average shopper in the sample (n = 12)purchased $65.00 worth of items ($\mu$ = $65.00)during a busy shopping day." What mistake was made in this citation?

Accepted Answer

The correct notation for the sample mean is $\bar{x}$, not $\mu$, which is used for the population mean. The sample size notation (n = 12) is correct.

Question 4

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?

Accepted Answer

The mean (average) is calculated by adding all the numbers together and dividing by the total count: (3+8+5+0+4+6+2+1+1+4+2+0)/12 = 36/12 = 3. The median is the middle value when the numbers are arranged in order, which, for these 12 numbers, is the average of the 6th and 7th values (2 and 2), so the median is also 2. Therefore, the mean (3) is larger than the median (2).

Question 5

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

Accepted Answer

The mean is the average of all scores, calculated by adding up all the scores and dividing by the number of scores.

Question 6

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?

Accepted Answer

The answer of A researcher records the following data for...

Question 7

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?

Accepted Answer

A) The average calculation is (1+3+8)/3=4, so the coach won an average of four games per season.

B) The median (middle value) of the three values is 3, so the coach won a median of three games per season.

C) There were a total of 10 x 3 = 30 games played over the three seasons. The coach won 1+3+8=12 games, which is 12/30 = 0.4 or 40% of his games.

Thus, all three conclusions are appropriate.

Question 8

When would it be appropriate to calculate a population mean?

Accepted Answer

When data are measured for all members of a population, it is appropriate to calculate the population mean. In this scenario, the population mean would represent the average value for the entire population.

Question 9

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

Accepted Answer

The sample mean is used to describe a portion of individuals in a given population, since it is calculated from a subset (sample) of the population. The population mean refers to the mean of the entire population, while the restricted mean typically refers to a mean calculated after excluding certain extreme values or outliers.

Question 10

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?

Accepted Answer

The use of "n = 22" indicates a sample size, and "M" is commonly used to denote the mean of a sample, suggesting that the data comes from a sample rather than the entire population of patrons.

Question 11

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

Accepted Answer

The mode is defined as the value in a distribution that appears most frequently. It is a measure of central tendency that can give insight into the typical or most common value in a set of data. The mean is the sum of all values divided by the total number of values, and the median is the middle value when data is arranged from least to greatest. The range is the difference between the highest and lowest values in a dataset. While all of these measures can be useful in different contexts, the mode is the best choice for identifying the most frequently occurring value.

Question 12

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?

Accepted Answer

To find if the mean is equal to the median, we need to first arrange the data in ascending order: 1, 2, 3, 4, 5, 6, 7. The median is the middle value, which is 4. The mean can be calculated by adding up all values and dividing by the total number of participants: (1+2+3+4+5+6+7)/7 = 4. Therefore, the mean and median are both equal to 4 in this example.

Question 13

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

Accepted Answer

The median is the value that falls exactly in the middle of a distribution when scores are listed in numeric order. It is not influenced by extreme values, like the mean can be, and is a useful measure of central tendency for skewed distributions. The mode refers to the most frequently occurring value(s), while the range is the difference between the highest and lowest values in a distribution.

Question 14

The mathematical term Σ x is the numerator for

Accepted Answer

Σ x represents the sum of all observations in a data set. It is used in both the formula for population mean (μ) and sample mean (x̄) as:

μ = Σx / N (population mean)
x̄ = Σx / n (sample mean)

Therefore, Σ x is present in the numerator for both population mean and sample mean calculations.

Question 15

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

Accepted Answer

The size of a population is usually represented by the symbol N, while the size of a sample is represented by the symbol n. Therefore, choice D, which includes these symbols, is the correct answer. Choice C is close, but the symbols listed are actually correct, just in the wrong order. Choices A and B include symbols that are not commonly used to represent population and sample sizes.

Question 16

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

Accepted Answer

The population mean is symbolized as μ, whereas the sample mean is often symbolized as M or $\bar{x}$, indicating choice A is correct despite the formatting issues.

Question 17

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

Accepted Answer

The mean is the average of a set of numbers, the median is the middle value when the numbers are arranged in order, and the mode is the value that appears most frequently.

Question 18

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

Accepted Answer

The mean for both data sets would be equal as long as the same set of data is used for both the population and sample. The sample size does not have to equal the population size for this to be true.

Question 19

Which of the following can be used to estimate the median?

Accepted Answer

The median is the value that divides a data set into two equal halves, and the 50th percentile of a cumulative percentage distribution represents the point where half of the observations fall below and half fall above that value. Therefore, B is the best choice for estimating the median. A relative percentage distribution only shows the proportion of observations in each category, whereas the mean and mode are measures of central tendency that may not accurately represent the midpoint of a skewed distribution.

Question 20

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

Accepted Answer

When a portion of a population is asked to complete an assessment, the average score among that group of people would be considered a sample mean. This is because only a portion of the total population is being examined and the results are used to generalize about the population as a whole. It is important to note that the sample mean may differ from the population mean, which is the average score across the entire population.

Quiz 3: Summarizing Data: Central Tendency

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

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?

A researcher reports that "the average shopper in the sample (n = 12) purchased $65.00 worth of items ( $\mu$ = $65.00) during a busy shopping day." What mistake was made in this citation?

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?

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

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?

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?

When would it be appropriate to calculate a population mean?

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

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

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?

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

The mathematical term Σ x is the numerator for

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

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

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

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

Which of the following can be used to estimate the median?

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

Quiz 3: Summarizing Data: Central Tendency

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

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?

A researcher reports that "the average shopper in the sample (n = 12) purchased $65.00 worth of items ( μ\muμ = $65.00) during a busy shopping day." What mistake was made in this citation?

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?

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

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?

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?

When would it be appropriate to calculate a population mean?

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

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

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?

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

The mathematical term Σ x is the numerator for

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

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

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

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

Which of the following can be used to estimate the median?

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

A researcher reports that "the average shopper in the sample (n = 12) purchased $65.00 worth of items ( $\mu$ = $65.00) during a busy shopping day." What mistake was made in this citation?

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

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