### Measure of Central Tendency, Frequency Distribution, Symmetrical Distribution

The key terms in these statistic chapters include Measure Of Central Tendency, Median, Distribution, Frequency Distribution, Mean, Skewed Distribution, Sample, Normal Distribution, Population, Mode, Symmetrical Distribution, Ordinal Scale, Population Distribution, Ratio Scale.

One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?

X f

5 2

4 3

3 2

2 1

1 1

0 1

a) the mean

**b) the median**

c) the mode

d) central tendency cannot be determined for these data

Under what circumstances is the median likely to produce a better measure of central tendency than the mean?

a) with a symmetrical distribution**b) with an extremely skewed distribution**

c) when the data consist of nominal measurements

d) when the data are numerical scores from an interval or a ratio scale

What is the preferred measure of central tendency for scores measured on an ordinal scale?

a) the mean**b) the median**

c) the mode

d) central tendency cannot be determined for ordinal data

A population of scores has mean of u = 26, a median of 23, and a mode of 22. What is the most likely shape for the population distribution?

a) symmetrical**b) positively skewed**

c) negatively skewed

d) cannot be determined from the information given

What is the most likely shape for a distribution with a mean of 40 and a mode of 45?

a) symmetrical

b) positively skewed**c) negatively skewed**

d) either positively or negatively skewed

It is impossible for the value of the mode to be greater than the value of the mean.

**False**

Assuming that SS Y is constant in a research study, which of the following correlations would have the largest SS residual?

**r = – 0.10**

A normal distribution has a mean of µ = 60 with σ = 8. For this population, which is the X value that corresponds to the third quartile?

**X = 65.36**

Which proportion of a normal distribution is located between the mean and z = +1.40?

**0.4192**

For a perfectly symmetrical distribution with u = 30, what is the mode?

a) 30

b) greater than 30

c) less than 30**d) cannot be determined from the information given**

A distribution is positively skewed. Which is the most probably order, from smallest to largest, for the three measures of central tendency?

a) mean, median, mode**b) mode, median, mean**

c) mean, mode, median

d) median, mean, mode

For a perfectly symmetrical distribution with a median of 30, what is the value of the mean?

**a) 30**

b) greater than 30

c) less than 30

For a set of scores measured on an ordinal scale, the median is preferred to the mean as a measure of central tendency.

**True**

There are situations for which it is either impossible to compute a mean or the mean does not provide a central, representative value.

**True**

In order to facilitate independent random sampling, ____ must be utilized.

**Sampling with replacement**

For a severely skewed distribution, the median often provides a better measure of central tendency than the mean.

**True**

For a distribution with one or two extreme scores, the median is usually a more representative value than the mean.

**True**

One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?

X f

5 2

4 3

3 2

2 1

1 1

0 1

a) the mean**b) the median**

c) the mode

d) central tendency cannot be determined for these data

Under what circumstances is the median likely to produce a better measure of central tendency than the mean?

a) with a symmetrical distribution**b) with an extremely skewed distribution**

c) when the data consist of nominal measurements

d) when the data are numerical scores from an interval or a ratio scale

What is the preferred measure of central tendency for scores measured on an ordinal scale?

a) the mean**b) the median**

c) the mode

d) central tendency cannot be determined for ordinal data

A population of scores has mean of u = 26, a median of 23, and a mode of 22. What is the most likely shape for the population distribution?

a) symmetrical**b) positively skewed**

c) negatively skewed

What is the most likely shape for a distribution with a mean of 40 and a mode of 45?

a) symmetrical

b) positively skewed**c) negatively skewed**

d) either positively or negatively skewed

For a perfectly symmetrical distribution with u = 30, what is the mode?

a) 30

b) greater than 30

c) less than 30**d) cannot be determined from the information given**

It is impossible for the value of the mode to be greater than the value of the mean.

**False**

Assuming that SS Y is constant in a research study, which of the following correlations would have the largest SS residual?

**r = – 0.10**

A normal distribution has a mean of µ = 60 with σ = 8. For this population, which is the X value that corresponds to the third quartile?

**X = 65.36**

Which proportion of a normal distribution is located between the mean and z = +1.40?

**0.4192**

A vertical line is drawn through a normal distribution at z = -1.20. Which proportion of the distribution is on the right-hand side of the line?

**0.8849 (body)**

A class consists of 10 male and 30 female students. A random sample of n = 3 students is selected with replacement. If the first two students are both females, what is the probability that the third student is a male?

**p = 10/40**

Which of the following is a requirement for a random sample?

a. There must be sampling with replacement.

b. Every individual has an equal chance of being selected.

c. The probabilities cannot change during a series of selections.**d. All of the above are correct**

In order to facilitate independent random sampling, ____ must be utilized.

**Sampling with replacement**

Marty is a principal who needs to contact the highest performing 15% of students in his school’s current graduating class about an opportunity to join the school’s academic honor society. At his school, students’ grade point averages is a normally distributed variable. Marty should contact students who have a grade point average that correspond with a z-score greater than or equal to _____.

**z = +1.04.**

A population of scores has mean of u = 26, a median of 23, and a mode of 22. What is the most likely shape for the population distribution?

a) symmetrical**b) positively skewed**

c) negatively skewed

It is impossible for the value of the mode to be greater than the value of the mean.

**False**

What is the most likely shape for a distribution with a mean of 40 and a mode of 45?

a) symmetrical

b) positively skewed**c) negatively skewed**

d) either positively or negatively skewed

For a perfectly symmetrical distribution with a median of 30, what is the value of the mean?

**a) 30**

b) greater than 30

c) less than 30

Assuming that SS Y is constant in a research study, which of the following correlations would have the largest SS residual?

**r = – 0.10**

One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?

X f

5 2

4 3

3 2

2 1

1 1

0 1

a) the mean**b) the median**

c) the mode

A normal distribution has a mean of µ = 60 with σ = 8. For this population, which is the X value that corresponds to the third quartile?

**X = 65.36**

Which proportion of a normal distribution is located between the mean and z = +1.40?

**0.4192**

Under what circumstances is the median likely to produce a better measure of central tendency than the mean?

a) with a symmetrical distribution**b) with an extremely skewed distribution**

c) when the data consist of nominal measurements

d) when the data are numerical scores from an interval or a ratio scale