Describing Data

Question 1

Describing Data

Answer 1

Frequency Distributions

Measures of Central Tendency

Measures of Variability

Skewness

Kurtosis

Question 2

set of test scores arrayed for recording or study.

Answer 2

distribution

Question 3

straightforward, unmodified accounting of performance that is usually numerical.

reflect a simple tally, as in number of items responded to correctly on an achievement test.

Answer 3

raw score

Question 4

the number of times each score occurred might be listed in tabular or graphic form

Table 3–2

Answer 4

frequency

distribution,

Question 5

individual scores have been used and the data have not been grouped.

Answer 5

simple frequency distribution

Question 6

frequency distribution used to summarize data

Table 3–3,

Answer 6

grouped frequency distribution

Question 7

test-score intervals, also called ____ replace the actual test
scores

Answer 7

class intervals

Question 8

diagram or chart composed of lines, points, bars, or other symbols

describe and illustrate data

Answer 8

graph

Question 9

Three kinds of graphs used to illustrate frequency distributions

Answer 9

histogram,

bar graph,

frequency polygon

Question 10

graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles.

test scores along the graph’s horizontal axis (also referred to as the abscissa or X-axis)

frequency of occurrence along the graph’s vertical axis (also referred to as the ordinate or Y-axis).

Answer 10

histogram

Question 11

numbers indicative of frequency on the Y-axis

reference to some categorization (yes/no/maybe, male/female) on the X-axis.

rectangular bars typically are not contiguous.

Answer 11

bar

graph

Question 12

expressed by a continuous line connecting the points where test scores or class intervals (on the X-axis) meet frequencies (on the Y-axis).

Answer 12

frequency polygon

Question 13

Measures of Central Tendency

Answer 13

arithmetic mean
median
mode

Question 14

the statistic that indicates the average or midmost score between the extreme scores in a distribution.

Answer 14

the measure of central tendency

Question 15

most commonly used measure of central tendency

average

takes into account the actual numerical value of every score

Answer 15

arithmetic mean

Question 16

standard statistical shorthand called

Answer 16

“summation notation”

summation meaning “the sum of”

Question 17

the symbol used to signify “sum”

Answer 17

Greek uppercase letter sigma, Σ,

Question 18

X represents

Answer 18

a test score

Question 19

expression Σ X means

Answer 19

add all the test scores

Question 20

denoted by the symbol X (and pronounced “X
bar”)

equal to the sum of the observations (test scores) divided by the number of observations.

the appropriate measure of central tendency for interval or ratio data when the distributions are believed to be approximately normal.

Answer 20

arithmetic mean

Question 21

the formula for the arithmetic mean

Answer 21

X = Σ(X/n)

Question 22

computed from a

frequency distribution. The formula is..

Answer 22

X = Σ(fX)

n

Question 23

Σ( f X) means

Answer 23

multiply the frequency of each score by

its corresponding score and then sum

Question 24

calculation

of the mean from a grouped frequency distribution

Answer 24

Table 3–4

Question 25

middle score in a distribution ordering the scores in a list by magnitude, in either ascending or descending order

Answer 25

median

Question 26

If the total number of | scores ordered is an odd number.....

Answer 26

median will be the score that is exactly in the middle

Question 27

When the total number of scores ordered is an even number....

Answer 27

median can | be calculated by determining the arithmetic mean of the two middle scores

Question 28

most frequently occurring score in a distribution of scores tends not to be a very commonly used measure of central tendency the modal score is not calculated

Answer 28

mode

Question 29

there are two scores (51 and 66) that occur with the highest frequency (of two).

Answer 29

bimodal distribution

Question 30

is not calculated in a true sense, it is a nominal statistic and cannot legitimately be used in further calculations

Answer 30

mode

Question 31

the statistic that takes into account the order of scores and is itself ordinal in nature.

Answer 31

median

Question 32

interval-level statistic is generally the most stable and useful measure of central tendency.

Answer 32

mean

Question 33

Measures of Variability

Answer 33

range interquartile and semi-interquartile ranges average deviation standard deviation

Question 34

indication of how scores in a distribution are scattered or dispersed

Answer 34

Variability

Question 35

Statistics that describe the amount of variation in a distribution

Answer 35

measures | of variability

Question 36

provides a quick but gross description of the spread of scores. Figure 3–3

Answer 36

range

Question 37

distribution of test scores (or any data) can be divided into four parts

Answer 37

interquartile and semi-interquartile ranges

Question 38

e dividing points between the four quarters in the distribution Figure 3–5

Answer 38

quartiles

Question 39

quartiles are labeled as...

Answer 39

Q1, Q2, and Q3.

Question 40

refers to a specific point

Answer 40

quartile

Question 41

refers to an interval

Answer 41

quarter

Question 42

Q2 is the same as

Answer 42

median

Question 43

Q1 and Q3 are the..

Answer 43

quarter-points in a distribution of score

Question 44

measure of variability equal to the difference between Q3 and Q1. an ordinal statistic

Answer 44

interquartile range

Question 45

is equal to the interquartile range divided by 2.

Answer 45

semi-interquartile range

Question 46

perfectly | symmetrical distribution

Answer 46

Q1 and Q3 will be exactly the same distance from the median.

Question 47

If | these distances are unequal then there is a lack of symmetry

Answer 47

skewness

Question 48

AD = ∑∣x∣ | n

Answer 48

average deviation

Question 49

AD = ∑∣x∣ n lowercase italic x in the formula signifies

Answer 49

score’s deviation from the mean

Question 50

AD = ∑∣x∣ n value of x obtained by

Answer 50

subtracting the mean from the score (X − mean = x)

Question 51

AD = ∑∣x∣ n bars on each side of x indicate

Answer 51

absolute value of the deviation score (ignoring the positive or negative sign and treating all deviation scores as positive)

Question 52

a measure of variability equal to the square | root of the average squared deviations about the mean.

Answer 52

standard deviation

Question 53

is equal to the arithmetic mean of the squares of the | differences between the scores in a distribution and their mean.

Answer 53

variance

Question 54

s2 = ∑x2 | n

Answer 54

calculate the variance (s 2) using deviation scores

Question 55

s2 = ∑x2 n variance is calculated by

Answer 55

squaring and summing all the deviation scores and | then dividing by the total number of scores.

Question 56

s2 = ∑X2 n − X2 Table 3–1

Answer 56

calculate the summation of the raw scores squared, divide | by the number of scores, and then subtract the mean squared.

Question 57

(square root with n) Σ(X − M)2 n X represents a sample mean M a population mean

Answer 57

formula for the population | standard deviation

Question 58

nature and extent to which symmetry is absent. an indication of how the measurements in a distribution are distributed

Answer 58

skewness

Question 59

when relatively few of the scores fall at the | high end of the distribution.

Answer 59

positive skew

Question 60

when relatively few of the scores fall at the low end of the distribution. examination results may indicate that the test was too easy. Figure 3–3

Answer 60

negative | skew

Question 61

Q3 − Q2 will be greater than the distance of Q2 − Q1.

Answer 61

positively skewed distribution

Question 62

Q3 − Q2 will be less than the distance of Q2 − Q1

Answer 62

negatively skewed distribution,

Question 63

distances from Q1 and Q3 to the median are the same

Answer 63

symmetrical

Question 64

refer to the steepness of a distribution in its center

Answer 64

kurtosis

Question 65

describe the peakedness/flatness of three general types of curves Figure 3–6

Answer 65

platy-, lepto-, or meso-

Question 66

Distributions are relatively flat

Answer 66

platykurtic

Question 67

Distributions are relatively peaked

Answer 67

leptokurtic

Question 68

Distributions are in the | middle

Answer 68

mesokurtic

Question 69

Distributions that have high kurtosis are | characterized by

Answer 69

high peak and “fatter” tails compared to a | normal distribution.

Question 70

lower kurtosis values indicate

Answer 70

distribution with a rounded peak and thinner tails.

Question 71

normal bell-shaped curve would have a graph A from Figure 3–3

Answer 71

kurtosis value of 3

Question 72

normal distribution would have

Answer 72

kurtosis of 0