Chapter 2 EDRS 5305 Fall 2005 Descriptive Statistics

Descriptive Statistics § Organize data into some comprehensible form so that any pattern in

Frequency Distribution § An organized tabulation of the number of individual scores located in

Frequency Distritbutions (cont. ) § Organizes data § From highest to lowest § Grouping

Example 2. 1 N=20 8, 9, 8, 7, 10, 9, 6, 4, 9, 8,

Proportions and Percentages § There are other measures that describe the distribution of scores

$Proportion § Measures the fraction of the total group that is associated with each$

Proportions (cont. ) § Proportions are called relative frequencies § Because they describe the

Percentages § Distribution can also be described as percentages § Example 15% of the

p=f/N %=p(100) X f 10 2 2/20 = 0. 10 10% 9 5 5/20

Grouped Frequency Distribution Table § Can show groups of scores instead of each score

Guidelines for Grouped Frequency Distribution Tables § Should have about 10 class intervals §

Example 2. 3 82, 58, 64, 80, 75, 72, 87, 73, 88, 94, 84,

Steps § Determine range of scores § X=53 lowest § X=94 highest

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Histograms § A picture of the frequency distribution graph § A vertical bar is

Bar Graphs § When presenting the frequency distribution for data from a nominal or

Relative Frequencies and Smooth Curves § Sometimes the population is too big to construct

Shape of Frequency Distribution § Three characteristics that completely describe any distribution § Shape

Shape § Nearly all distributions can be classified as being either symmetrical or skewed

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Chapter 2 EDRS 5305 Fall 2005

Descriptive Statistics § Organize data into some comprehensible form so that any pattern in the data can be easily seen and communicated to others

Frequency Distribution § An organized tabulation of the number of individual scores located in each category on the scale of measurement.

Frequency Distritbutions (cont. ) § Organizes data § From highest to lowest § Grouping § Allows the researcher to see “at a glance” all of the data § Allows the researcher to see a score relative to all the other scores § By adding the frequencies, you can determine the number of scores or individuals

Example 2. 1 N=20 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8

X f 10 2 9 5 8 7 7 3 6 2 5 0 4 1 Ef=N Ef=20 EX=158 EX 2=1288

Proportions and Percentages § There are other measures that describe the distribution of scores that can be incorporated into the table § Proportion § Percentage

$Proportion § Measures the fraction of the total group that is associated with each$

Proportion § Measures the fraction of the total group that is associated with each score § Example 2. 1 § 2 out of the 20 individuals scored a 6 § Proportion § 2/20 = 0. 10 § Proportion = p = f/N

Proportions (cont. ) § Proportions are called relative frequencies § Because they describe the frequency (f) in relation to the total number (N)

Percentages § Distribution can also be described as percentages § Example 15% of the class earned an A § To compute: § Find the proportion (p) § Multiply by 100 § Percentage = p(100) = f (100) N

p=f/N %=p(100) X f 10 2 2/20 = 0. 10 10% 9 5 5/20 = 0. 25 25% 8 7 7/20 = 0. 35 35% 7 3 3/20 = 0. 15 15% 6 2 2/20 = 0. 10 10% 5 0 0/20 = 0 0% 4 1 1/20 = 0. 05 5%

Grouped Frequency Distribution Table § Can show groups of scores instead of each score individually § Example 90 -100 5 scores § These groups or intervals are called class intervals

Guidelines for Grouped Frequency Distribution Tables § Should have about 10 class intervals § Width of each interval should be a relatively simple number § Count by 10 s or 5 s, etc. § Each class interval should start with a score that is a multiple of the width § 10, 20, 30, etc. § All intervals should be the same width

Example 2. 3 82, 58, 64, 80, 75, 72, 87, 73, 88, 94, 84, 78, 93, 53, 84, 87, 69, 84, 61, 91, 70, 76, 89, 75, 60

Steps § Determine range of scores § X=53 lowest § X=94 highest

Histograms § A picture of the frequency distribution graph § A vertical bar is drawn above each score § The height of the bar corresponds to the frequency § The width of the bar extends to the real limits of the score § A histogram is used when the data are measured on an interval or a ratio scale

Bar Graphs § When presenting the frequency distribution for data from a nominal or an ordinal scale, the graph is constructed so that there is some space between the bars § The bars emphasize that the scale consists of separate, distinct categories.

Relative Frequencies and Smooth Curves § Sometimes the population is too big to construct a frequency distribution so researchers obtain frequencies from the entire group § Draw frequencies using relative frequencies (proportions) on the vertical axis. § Create a smooth curve

Shape of Frequency Distribution § Three characteristics that completely describe any distribution § Shape § Central Tendency § Variability

Shape § Nearly all distributions can be classified as being either symmetrical or skewed § Symmetrical § Skewed § Tail § Positively skewed § Negatively skewed