Chapter 2

Question 1

proportion

Answer 1

proportion = p = f/N

Question 1

Frequency distribution

Answer 1

A frequency distribution is an organized tabulation of the number of individuals located in each category on the scale of measurement.

• A frequency distribution takes a disorganized set of scores and places them in order from highest to lowest, grouping together individuals who all have the same score.
• It shows whether the scores are generally high or low, whether they are concentrated in one area or spread out across the entire scale, and generally provides an organized picture of the data.
• a frequency distribution allows you to see the location of any individual score relative to all of the other scores in the set.

the distribution presents the same two elements:
- The set of categories that make up the original measurement scale.
- A record of the frequency, or number of individuals in each category.

Question 2

percentage

Answer 2

percentage = p(100) = f/N (100)

Question 3

range

Answer 3

The distance from the upper real limit of the highest score to the lower real limit of the lowest score; the total distance from the absolute highest point to the lowest point in the distribution.

Question 4

grouped frequency distribution table

Answer 4

A frequency distribution where scores are grouped into intervals rather than listed as individual values.

Question 5

class intervals

Answer 5

A group of scores in a grouped frequency distribution.

Question 6

apparent limits

Answer 6

The score values that appear as the lowest score and the highest score in an interval.

Question 7

histograms

Answer 7

A graph showing a bar above each score or interval so that the height of the bar corresponds to the frequency and width extends to the real limits.

• The height of the bar corresponds to the frequency for that category.
• For continuous variables, the width of the bar extends to the real limits of the category. For discrete variables, each bar extends exactly half the distance to the adjacent category on each side.

Question 8

polygons

Answer 8

A graph consisting of a line that connects a series of dots. A dot is placed above each score or interval so that the height of the dot corresponds to the frequency.

• A dot is centered above each score so that the vertical position of the dot corresponds to the frequency for the category.
• A continuous line is drawn from dot to dot to connect the series of dots.
• The graph is completed by drawing a line down to the X-axis (zero frequency) at each end of the range of scores. The final lines are usually drawn so that they reach the X-axis at a point that is one category below the lowest score on the left side and one category above the highest score on the right side.

Question 9

Bar Graphs

Answer 9

A graph showing a bar above each score or interval so that the height of the bar corresponds to the frequency. A space is left between adjacent bars.

• nominal or ordinal scale

Question 10

relative frequencies

Answer 10

The proportion of the total distribution rather than the absolute frequency. Used for population distributions for which the absolute number of individuals is not known for each category.

Question 11

Smooth curves

Answer 11

When a population consists of numerical scores from an interval or a ratio scale, it is customary to draw the distribution with a smooth curve instead of the jagged, step-wise shapes that occur with histograms and polygons. The smooth curve indicates that you are not connecting a series of dots (real frequencies) but instead are showing the relative changes that occur from one score to the next.

Question 12

symmetrical distribution

Answer 12

In a symmetrical distribution, it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other

Question 13

skewed distribution

Answer 13

In a skewed distribution, the scores tend to pile up toward one end of the scale and taper off gradually at the other end

Question 14

tail of the distribution

Answer 14

A section on either side of a distribution where the frequency tapers down toward zero as the X values become more extreme.

Question 15

positively skewed

Answer 15

A skewed distribution with the tail on the right-hand side is positively skewed because the tail points toward the positive (above-zero) end of the X-axis.

Question 16

negatively skewed

Answer 16

A distribution where the scores pile up on the right side and taper off to the left.

Question 17

Rank or percentile rank

Answer 17

The rank or percentile rank of a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value.

Question 18

percentile

Answer 18

When a score is identified by its percentile rank, the score is called a percentile.

Question 19

cumulative percentages

Answer 19

The cumulative frequencies show the number of individuals located at or below each score. To find percentiles, we must convert these frequencies into percentages. The resulting values are called cumulative percentages because they show the percentage of individuals who are accumulated as you move up the scale.

Question 20

interpolation

Answer 20

Interpolation is used to estimate values within the interval by assuming that fractional portions of one scale correspond to the same fractional portions of the other scale.

• A single interval is measured on two separate scales (for example, time and dollars). The endpoints of the interval are known for each scale.
• You are given an intermediate value on one of the scales. The problem is to find the corresponding intermediate value on the other scale.
• The interpolation process requires four steps:

1. Find the width of the interval on both scales.
2. Locate the position of the intermediate value in the interval. This position corresponds to a fraction of the whole interval: fraction = distance from the top of the interval/interval width
3. Use the same fraction to determine the corresponding position on the other scale. First, use the fraction to determine the distance from the top of the interval: distance = fraction x width
4. Use the distance from the top to determine the position on the other scale.

Question 21

stem and leaf

Answer 21

requires that each score be separated into two parts: The first digit (or digits) is called the stem, and the last digit is called the leaf. For example, X=85 would be separated into a stem of 8 and a leaf of 5. Similarly, X=42 would have a stem of 4 and a leaf of 2. To construct a stem and leaf display for a set of data, the first step is to list all the stems in a column.

The next step is to go through the data, one score at a time, and write the leaf for each score beside its stem. For the data in Table 2.3, the first score is X = 83, so you would write 3 (the leaf) beside the 8 in the column of stems. This process is continued for the entire set of scores. The complete stem and leaf display is shown with the original data in