Deck 4: Measures of Central Tendency: Whats so Average About the Mean

Question 1

The exact midpoint of the data is the median.

Answer 1

True

Question 2

In a data set where you have one extreme outlier, only the mean is influenced.

Answer 2

True

Question 3

Of the three forms of central tendency, the median is most sensitive to outliers.

Answer 3

False

Question 4

A negatively skewed distribution has a longer tail to the left of the center.

Question 5

When the data is skewed positive, the mean is expected to be larger than the median and the mode

Question 6

A trimmed mean can be appropriate used when the data is heavily skewed

Question 7

A trimmed mean is most useful when the data is a normal distribution

Question 8

The mean, median, and mode of a dataset can be used to describe both qualitative and quantitative data meaningfully.

Question 9

of the three measures of central tendency, only the mode is useful for certain types of data, like those on a nominal scale.

Question 10

The mode is the most commonly observed datapoint in a dataset

Question 11

A unimodal distribution is always a normal distribution

Question 12

Outliers are defined strictly as scores that are much higher or larger than the rest of the dataset

Question 13

Skewed distributions causes outliers in datasets.

Question 14

If the mean is less than the median, and the median is less than the mode, the distribution is likely skewed negative

Question 15

50% of the data points are larger than the median, and 50% of the datapoints are less than the median

Question 16

A normal distribution is unimodal and symmetric.

Question 17

A bi-modal distribution is characterized by the median and mean being located between two modes

Question 18

If one data point changes in a dataset, the mean is most likely to change

Question 19

The mean is the sum of all data values divided by the number of observations.

Question 20

The mean is also the…

A) sum
B) arithmetic average.
C) the most frequent response.
D) the exact mid point (i.e., center) of the data set after ranking it in cardinal order.

Question 21

The median of the data set is defined as…

A) The exact midpoint of a rank ordered dataset
B) the arithmetic average.
C) the largest data point subtract the smallest data point.
D) the most frequently observed response.

Question 22

The mode of a data set is the…

A) the exact mid point (i.e., center) of a rank ordered dataset
B) The sum of the data points.
C) the largest data point subtract the smallest data point.
D) the most frequently observed response.

Question 23

Consider the data set that consists of: 10, 20, 32, 35, 44, 30, 60, 11. The value 31 is the…

A) median only.
B) median and mean.
C) median, mode, and mean.
D) mean only.

Question 24

Which of the following measure(s) are commonly used as "typical" measures of center?

A) The Mean, Median, and Mode
B) The Mean and Median
C) The Mean and Mode
D) The Mode and Median

Question 25

Given the dataset, what is x̅? 104, 102, 109, 95, 102, 98, 101, 97, 92, 94, 119, 102

A) 102.
B) 101.25
C) 101.5
D) 27

Question 26

If you have a dataset with 95 observations, and you pick one and add 5 to it, which of the following is most likely to change?

A) The mean will change
B) The median will change
C) The mode will change
D) The mean, median, and mode all have the same likelihood of changing

Question 27

If you have a dataset, and you add 5 to each datapoint, what is likely to occur?

A) The mean will be 5 units larger
B) The mean will change but not systematically
C) All three measures of central tendency will be 5 units larger
D) None of the above.

Question 28

In this dataset, one score is missing. However, it is known that the average of the dataset is 60.31. The data values are: 28, 86, 46, 80, 68, 58, 40, 99, 90, 24, 34, 98, X. Find the missing value, X.

A) 33
B) 34
C) 32
D) Insufficient information

Question 29

A research scientist lost a data point out of 100 observations, but luckily has the median. Of the dataset. He asks one of his research assistants to find the missing data point with the remainder 99 observations and the median. Which of the following is true?

A) this task is impossible, because the median does not take into account the magnitude of each observation.
B) this task is possible, but the research assistant also needs the mode.
C) This task is possible, but only after the research assistant puts the data into rank order.
D) This task is possible, but only after the research assistant is given the type of distribution that best represents the data.

Question 30

Imagine in a data set where the smallest value is not the mode. Now imagine if that smallest value decreases by 50. Everything else about the data set remains the same. Which of the following must be true?

A) The mean decreases
B) The mean increases
C) The median and mean decreases
D) The mean and median decreases, but the mode remains constant.

Question 31

In a perfectly uni-modal distribution with perfectly symmetric sides around the mode, which of the following is true?

A) The mean and median are different values from the mode
B) The mean, median, and mode share the same value.
C) The distribution has three different values for mean, median, and mode.
D) Any of the above can be true. There is insufficient information to tell.

Question 32

In a distribution where there is a long tail towards the right side of the mode, which of the following is true?

A) The distribution is considered normal because it is unimodal
B) The median is most heavily influenced out of the three central tendencies by the extreme values in the long tail
C) The mean is the least influenced by the extreme values in the long tail
D) None of the above are true

Question 33

In a positively skewed uni-modal distribution, how are the three measures of central tendency most likely arranged??

A) Median > mode > mean.
B) Mode > median > mean.
C) Mean > median > mode.
D) Mean > mode > median.

Question 34

In a unimodal distribution where the mean is much greater than the median and the mode. What which of the following is the distribution of the data more likely to resemble?

A) Negatively skewed
B) Positively skewed
C) Normally distributed
D) Uniformly distributed

Question 35

Which of the following is false of a normal distribution?

A) The mean, median, and mode very close.
B) There can be outliers, but only on one side of the center.
C) The distribution is symmetrical around the center.
D) All of the above are true statements about a normal distribution.

Question 36

For which of the following datasets would a mean not be useful?

A) The number of minutes students spend daydreaming in class
B) Individuals' favorite music artist
C) The number of words a group of toddlers know
D) None of the above

Question 37

A researcher has an experiment with three conditions that generates data on the number of calories worth of food a participant puts on their plate. Which of the following can she do with this data?

A) She can only use the mode for this type of data.
B) She can calculate means only
C) She can calculate means and modes. Medians are not informative.
D) She can calculate means, medians, and mode for each condition

Question 38

Which of the following correctly describes finding the center of a grouped frequency distribution?

A) You need to find the midpoint of each grouped interval
B) The mode is the midpoint of an interval that occurs more frequently
C) The numbers may differ slightly from using the same data from an ungrouped frequency table.
D) All of the above are correct.

Question 39

A trimmed mean is the mean without the top and bottom ______ of the data included in the calculation

A) 5%
B) 1%
C) 10%
D) 5 observations

Question 40

Adolphe Quetelet made which of the following observations about data that permeates the social sciences, even today?

A) many traits can be measured in a way to make the mean meaningful
B) the mean is a very important number for a dataset because it is influenced by every datapoint
C) many traits and characteristics that we measure tend to fall on a normal distribution
D) Many traits and characteristics that we measure tend to have a fairly uniform distribution.

Question 41

When reporting a mean in APA format, the correct way to represent the mean is with which symbol?

A) x?
B) $\Sigma$ x
C) M
D) Any of the above is acceptable according to the APA guidelines.

Question 42

The following data represent the number of children people have.
$\begin{array}{cc}\hline \text { Number of } & \\ \text {Kids } &\\\hline 2 \\1 \\4 \\3 \\3 \\2 \\4 \\1 \\1 \\1 \\2 \\3 \\1 \\4 \\2 \\3 \\2 \\1 \\5 \\1 \\2 \\3 \\1 \\1 \\\hline\end{array}$
What is the mean?

A) 2
B) 2.1
C) 1
D) 2.2

Question 43

The following data represent the number of children people have.
$\begin{array}{cc}\hline \text { Number of } & \\ \text {Kids } &\\\hline 2 \\1 \\4 \\3 \\3 \\2 \\4 \\1 \\1 \\1 \\2 \\3 \\1 \\4 \\2 \\3 \\2 \\1 \\5 \\1 \\2 \\3 \\1 \\1 \\\hline\end{array}$
What is the mode?

A) 1
B) 2
C) 3
D) 4

Question 44

The following data represent the number of children people have.
$\begin{array}{cc}\hline \text { Number of } & \\ \text {Kids } &\\\hline 2 \\1 \\4 \\3 \\3 \\2 \\4 \\1 \\1 \\1 \\2 \\3 \\1 \\4 \\2 \\3 \\2 \\1 \\5 \\1 \\2 \\3 \\1 \\1 \\\hline\end{array}$
What is the median?

A) 2.1
B) 2.2
C) 2
D) 3

Question 45

Below are income data for individuals who participated in a recent study.
This data set contains information about the number of hours safe students studied before taking a recent exam. Using this information, answer questions.
What is the mean?

Question 46

Below are income data for individuals who participated in a recent study.
This data set contains information about the number of hours safe students studied before taking a recent exam. Using this information, answer questions.
What is the median?

Question 47

Below are income data for individuals who participated in a recent study.
This data set contains information about the number of hours safe students studied before taking a recent exam. Using this information, answer questions.
What is the mode?

Question 48

How many minutes of television do children watch at home? A researcher surveyed parents and asked them to report the number of minutes per day children spend watching tv. The data are below
What is the mean?

Question 49

How many minutes of television do children watch at home? A researcher surveyed parents and asked them to report the number of minutes per day children spend watching tv. The data are below
What is the median?

Question 50

How many minutes of television do children watch at home? A researcher surveyed parents and asked them to report the number of minutes per day children spend watching tv. The data are below
What is the mode?

Question 51

How many minutes of television do children watch at home? A researcher surveyed parents and asked them to report the number of minutes per day children spend watching tv. The data are below
Based on the three measures of center, what kind of shape do you expect the distribution to have?

Question 52

A researcher who is examining stress-related hormones has data on indivdiuals' body mass index. Below are the data
What is the average body mass index in this sample?

Question 53

A researcher who is examining stress-related hormones has data on indivdiuals' body mass index. Below are the data
What is the median body mass index in this sample?

Question 54

A researcher who is examining stress-related hormones has data on indivdiuals' body mass index. Below are the data
What is the most common body mass index in this sample?

Question 55

A researcher is running an experiment with two conditions. One in which she asks participants to bite into an apple when remembering a list of words to prevent them from rehearsing the words (i.e., saying them aid memory) and another group where they do not bite into an apple. Below are the data showing the number of words participants were able to recall out of 30.
What was the mean of each group?

Question 56

A researcher is running an experiment with two conditions. One in which she asks participants to bite into an apple when remembering a list of words to prevent them from rehearsing the words (i.e., saying them aid memory) and another group where they do not bite into an apple. Below are the data showing the number of words participants were able to recall out of 30.
What was the median of each group?

Question 57

A researcher is running an experiment with two conditions. One in which she asks participants to bite into an apple when remembering a list of words to prevent them from rehearsing the words (i.e., saying them aid memory) and another group where they do not bite into an apple. Below are the data showing the number of words participants were able to recall out of 30.
What was the mode of each group?

Question 58

The three measures of central tendency are not appropriate for any type of measurement scale. Identify what measurement scale is appropriate for each measure of central tendency