Week 2 Chapter 3

Question 1

mean

Answer 1

sum of the scores divided by the number of scores

Question 2

population mean

Answer 2

formula wherein all scores in the population are added, and then divided by N

Question 3

sample mean

Answer 3

formula with symbols to signify population subset values

Question 4

weighted mean

Answer 4

formula combining multiple sets of scores and dividing to find overall mean for combined group

Question 5

central tendency

Answer 5

All of these:

1) statistical measure to determine a single score that defines the midpoint of a distribution
2) the concept of an average or representative score

Question 6

median

Answer 6

midpoint in a list of scores listed in order from smallest to largest. More specifically, the median is the point on the measurement scale below which 50% of the scores in the distribution are located. The median as the midpoint of a distribution means that that the scores are being divided into two equal-sized groups. We are not locating the midpoint between the highest and lowest X values.

Question 7

mode

Answer 7

score or category that has the greatest frequency in a frequency distribution. Its common usage means “the customary fashion” or “a popular style.”

Question 8

bimodal

Answer 8

distribution with two scores with greatest frequency

Question 9

multimodal

Answer 9

a distribution with more than two scores with greatest frequency

Question 10

major mode

Answer 10

taller peak when two scores with greatest frequency have unequal frequencies

Question 11

minor mode

Answer 11

shorter peak when two scores with greatest frequency have unequal frequencies

Question 12

line graph

Answer 12

diagram used when values on horizontal axis are measured on an interval or ratio scale

Question 13

In addition to describing an entire distribution, measures of central tendency are also useful for making comparisons between

Answer 13

groups of individuals or between sets of data.

Question 14

number crunching

Answer 14

take a distribution consisting of many scores and crunch them down to a single value that describes them all

Question 15

Unfortunately, there is no single, standard procedure for determining central tendency. The problem is that no single measure

Answer 15

produces a central, representative value in every situation.

Question 16

If the two samples are combined, what is the mean for the total group?

Answer 16

To calculate the overall mean, we need two values:

1. the overall sum of the scores for the combined group ΣX, and
2. the total number of scores in the combined group (n).

Question 17

Note that the overall mean is not halfway between the original two sample means. Because the samples are

Answer 17

not the same size, one makes a larger contribution to the total group and therefore carries more weight in determining the overall mean. For this reason, the overall mean we have calculated is called the weighted mean.

Question 18

changing a single score in the sample has produced a new mean. You should recognize that changing any score also changes

Answer 18

the value of ΣX (the sum of the scores), and thus always changes the value of the mean.

Question 19

Adding a new score to a distribution, or removing an existing score, will usually change the mean. The exception is

Answer 19

when the new score (or the removed score) is exactly equal to the mean.

Question 20

It is easy to visualize the effect of adding or removing a score if you remember that the mean is defined as the

Answer 20

balance point for the distribution.

Question 21

Adding a score (or removing a score) has the same effect on the mean

Answer 21

whether the original set of scores is a sample or a population.

Question 22

If a constant value is added to every score in a distribution, the same constant

Answer 22

will be added to the mean. Similarly, if you subtract a constant from every score, the same constant will be subtracted from the mean.

Question 23

If every score in a distribution is multiplied by (or divided by) a constant value, the mean will

Answer 23

change in the same way.

Question 24

Multiplying (or dividing) each score by a constant value is a common method for changing the

Answer 24

unit of measurement. Although the numerical values for the individual scores and the sample mean have changed, the actual measurements are not changed.

Question 25

To change a set of measurements from minutes to seconds, for example, you multiply by 60; to change from inches to feet, you

Answer 25

divide by 12

Question 26

One common task for researchers is converting measurements into

Answer 26

metric units to conform to international standards.

Question 27

1 inch equals

Answer 27

2.54 centimeters.

Question 28

A sample has a mean of . If one person with a score of is removed from the sample, what effect will it have on the sample mean?

Answer 28

The sample mean will increase

Question 29

the definition and the computations for the median are identical for

Answer 29

a sample and for a population.

Question 30

To find the median,

Answer 30

list the scores in order from smallest to largest. Begin with the smallest score and count the scores as you move up the list. The median is the first point you reach that is greater than 50% of the scores in the distribution. The median can be equal to a score in the list or it can be a point between two scores. Notice that the median is not algebraically defined (there is no equation for computing the median), which means that there is a degree of subjectivity in determining the exact value.

Question 31

the concept of a balance point focuses on

Answer 31

distances rather than scores

Question 32

it is possible to have a distribution in which the vast majority of the scores

Answer 32

are located on one side of the mean

Question 33

the mean does not necessarily divide the scores into

Answer 33

two equal groups. In this example, 5 out of the 6 scores have values less than the mean.

Question 34

The median defines the middle of the distribution in terms of

Answer 34

scores. The median is located so that half of the scores are on one side and half are on the other side.

Question 35

the mean and the median are both methods for defining and measuring

Answer 35

central tendency. it is important to point out that although they both define the middle of the distribution, they use different definitions of the term middle.

Question 36

To find the precise median,

Answer 36

we calculate the precise median for a continuous variable as follows: 1) Determine the real limits of the interval that contains the precise midpoint 2) Count the number of scores below the identified interval. 3) Find the number of additional scores needed to reach exactly 50% 4) Calculate a fraction=number of additional scores needed/ total number of scores in the interval 5) Add the fraction to the lower real limit of the interval

Question 37

As with the median, there are no symbols or special notation used to identify the mode or

Answer 37

to differentiate between a sample mode and a population mode. In addition, the definition of the mode is the same for a population and for a sample distribution.

Question 38

The mode is a useful measure of central tendency because

Answer 38

it can be used to determine the typical or most frequent value for any scale of measurement, including a nominal scale

Question 39

The mode is a score or category,

Answer 39

not a frequency. For this example, the mode is Luigi’s, not f = 42

Question 40

The mode also can be useful because it is the only measure of central tendency that corresponds to an actual score in the data; by definition, the mode is the most

Answer 40

frequently occurring score. The mean and the median, on the other hand, are both calculated values and often produce an answer that does not equal any score in the distribution. For example, in Figure 3.5 we presented a distribution with a mean of 4 and a median of 2.5. Note that none of the scores is equal to 4 and none of the scores is equal to 2.5. However, the mode for this distribution is and there are three individuals who actually have scores of X = 2 .

Question 41

In a frequency distribution graph, the greatest frequency will appear as the tallest part of the figure. To find the mode,

Answer 41

you simply identify the score located directly beneath the highest point in the distribution.

Question 42

Although a distribution will have only one mean and only one median, it is possible to have

Answer 42

more than one mode.

Question 43

In a frequency distribution graph, the different modes will correspond to distinct, equally high peaks. A distribution with two modes is

Answer 43

said to be bimodal, and a distribution with more than two modes is called multimodal. Occasionally, a distribution with several equally high points is said to have no mode.

Question 44

Because the mean, the median, and the mode are all trying to measure the same thing, it is reasonable to

Answer 44

expect that these three values should be related. In fact, there are some consistent and predictable relationships among the three measures of central tendency. Specifically, there are situations in which all three measures will have exactly the same value. On the other hand, there are situations in which the three measures are guaranteed to be different. In part, the relationships among the mean, median, and mode are determined by the shape of the distribution.

Question 45

For a symmetrical distribution, the right-hand side of the graph is a mirror image of the left-hand side. If a distribution is perfectly symmetrical, the median

Answer 45

is exactly at the center because exactly half of the area in the graph will be on either side of the center. The mean also is exactly at the center of a perfectly symmetrical distribution because each score on the left side of the distribution is balanced by a corresponding score (the mirror image) on the right side. As a result, the mean (the balance point) is located at the center of the distribution. Thus, for a perfectly symmetrical distribution, the mean and the median are the same. If a distribution is roughly symmetrical, but not perfect, the mean and median will be close together in the center of the distribution.

Question 46

If a symmetrical distribution has only one mode, it will also be in the center of the distribution. Thus, for a perfectly symmetrical distribution with one mode, all three measures of central tendency, the mean, the median, and the mode,

Answer 46

have the same value. For a roughly symmetrical distribution, the three measures are clustered together in the center of the distribution.

Question 47

a bimodal distribution that is symmetrical

Answer 47

will have the mean and median together in the center with the modes on each side.

Question 48

A rectangular distribution

Answer 48

has no mode because all X values occur with the same frequency. Still, the mean and the median are in the center of the distribution.

Question 49

The positions of the mean, median, and mode are not

Answer 49

as consistently predictable in distributions of discrete variables

Question 50

In skewed distributions, especially distributions for continuous variables, there is a strong tendency for the mean, median, and mode to be

Answer 50

located in predictably different positions.

Question 51

a positively skewed distribution with the peak (highest frequency) on the left-hand side. This is the position of the mode. However, it should be clear that the vertical line drawn at the mode does not divide the distribution into two equal parts.

Answer 51

To have exactly 50% of the distribution on each side, the median must be located to the right of the mode. Finally, the mean is typically located to the right of the median because it is influenced most by the extreme scores in the tail and is displaced farthest to the right toward the tail of the distribution. To have exactly 50% of the distribution on each side, the median must be located to the right of the mode. Finally, the mean is typically located to the right of the median because it is influenced most by the extreme scores in the tail and is displaced farthest to the right toward the tail of the distribution.

Question 52

Negatively skewed distributions are lopsided in the opposite direction, with the scores piling up on the right-hand side and the tail tapering off to the left.

Answer 52

For a distribution with negative skew, the mode is on the right-hand side (with the peak), while the mean is displaced toward the left by the extreme scores in the tail. As before, the median is usually located between the mean and the mode. Therefore, in a negatively skewed distribution, the most probable order for the three measures of central tendency from smallest value to largest value (left to right), is the mean, the median, and the mode.

Question 53

whenever the scores are numerical values (interval or ratio scale) the mean is usually

Answer 53

the preferred measure of central tendency. Because the mean uses every score in the distribution, it typically produces a good representative value. Remember that the goal of central tendency is to find the single value that best represents the entire distribution. Besides being a good representative, the mean has the added advantage of being closely related to variance and standard deviation, the most common measures of variability. This relationship makes the mean a valuable measure for purposes of inferential statistics. For these reasons, and others, the mean generally is considered to be the best of the three measures of central tendency. But there are specific situations in which it is impossible to compute a mean or in which the mean is not particularly representative. It is in these situations that the mode and the median are used.

Question 54

extreme scores

Answer 54

scores that are very different in value from most of the others

Question 55

when a distribution is skewed or has a few extreme scores

Answer 55

then the mean may not be a good representative of the majority of the distribution. The problem comes from the fact that the extreme values can have a large influence and cause the mean to be displaced. In this situation, the fact that the mean uses all of the scores equally can be a disadvantage.

Question 56

The breaks in the X-axis are the conventional way of notifying the reader that

Answer 56

some values have been omitted.

Question 57

When to Use the Median

Answer 57

All of these: 1) Extreme Scores or Skewed Distributions 2) Undetermined Values 3) Open-Ended Distributions 4) Ordinal Scale

Question 58

The median is not easily affected by extreme scores.

Answer 58

the median commonly is used when reporting the average value for a skewed distribution. For example, the distribution of personal incomes is very skewed, with a small segment of the population earning incomes that are astronomical. These extreme values distort the mean, so that it is not very representative of the salaries that most of us earn. As in the previous example, the median is the preferred measure of central tendency when extreme scores exist.

Question 59

Many researchers believe that it is not appropriate to use the mean to describe central tendency for ordinal data. When scores are measured on an ordinal scale,

Answer 59

the median is always appropriate and is usually the preferred measure of central tendency. You should recall that ordinal measurements allow you to determine direction (greater than or less than) but do not allow you to determine distance. The median is compatible with this type of measurement because it is defined by direction: half of the stores are above the median and half are below the median. The mean, on the other hand, defines central tendency in terms of distance. Because the mean is defined in terms of distances, and because ordinal scales do not measure distance, it is not appropriate to compute a mean for scores from an ordinal scale.

Question 60

When to Use the Mode

Answer 60

All of these: 1) Nominal Scales 2) Discrete Variables 3) Describing Shape

Question 61

Because nominal scales do not measure quantity (distance or direction), it is impossible

Answer 61

to compute a mean or a median for data from a nominal scale. When the scores are numerical values from an interval or ratio scale, the mode is usually not the preferred measure of central tendency.

Question 62

Bar graphs are used to present means (or medians) when the groups or treatments shown on the horizontal axis are measured on a

Answer 62

nominal or an ordinal scale.

Question 63

When constructing graphs of any type

Answer 63

you should recall the basic rules: 1) The height of a graph should be approximately two-thirds to three-quarters of its length. 2) Normally, you start numbering both the X-axis and the Y-axis with zero at the point where the two axes intersect. However, when a value of zero is part of the data, it is common to move the zero point away from the intersection so that the graph does not overlap the axes

Question 64

Although it is possible to construct graphs that distort the results of a study

Answer 64

researchers have an ethical responsibility to present an honest and accurate report of their research results.