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Percentages

Graphing

•Step 1: Distribution -arrangement of scores in order of magnitude -RAW DATA of stress ratings of 30 students: 8,7,4,10,8,6,8,9,9,7,3,7,6,5,0,9,10,7,7,3,6,7,5,2,1,6,7,10,8,8 -Distributed scores: 0,1,2,3,3,4,5,5,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,9,9,9,10,10,10

•Step 2: Frequency Distribution -arrangement of scores in order of magnitude with the number of

times each score occurred

Graphing

•Step 3: Make a graph -raw scores go on the horizontal line (X-axis or abscissa) -frequency goes on the vertical line (Y-axis or ordinate)

•Step 4: Make a histogram -rectangular bar drawn above each raw score

**bar graphs are used for noncontinuous or categorical data (EX: college major) -steps between values are separate **histograms are used for continuous data (EX: SAT scores) -steps between values are not separate

•Step 5: Make a frequency polygon -single point used to show the frequency of each score & points are connected with lines -especially useful when showing two distributions simultaneously

Graphing

•Stem & Leaf Graph -just another way to graph data -first digit in stem column (EX: 9 represents scores in the 90’s) -trailing digit in leaf column (EX: 0 represents 90 & 4 represents 94)

•WOW! Graph -A deceptive graph due to not setting the base of the ordinate at 0 -Some corporations hire statisticians to create wow graphs so their annual sales report looks better!

• Normal and kurtotic distributions -Normal curve (mesokurtic): bell-shaped & symmetrical

*standard of comparison because distributions observed in nature usually take this shape

-Kurtosis: extent to which a frequency distribution deviates from the normal curve

*Leptokurtic: high & peaked

--more scores in the tails than the normal curve

*Platykurtic: low & flat

--less scores in the tails than the normal curve

Shapes of Frequency Distributions

Carl Gauss“Father of the Normal

Curve”

Mesokurtic Leptokurtic Platykurtic

Shapes of Frequency Distributions

• Non-bell shaped -Unimodal distribution: one value clearly occurs more

than any other

-Bimodal distribution: two values clearly occur more than any other

-Rectangular distribution: all values occur equally

Shapes of Frequency Distributions

• Symmetrical and Non-symmetrical distributions -usually distributions look “normal” or symmetrical

-skewed distribution: a distribution that is not symmetrical

*the side with fewer scores is considered the direction of the skew

--positively skewed: skewed to the right

--negatively skewed: skewed to the left

*usually happens when what is being measured has an upper or lower limit

--EX: how many kids do each of you have?

--Can’t have less than 0 so the distribution will probably look positively skewed

Symmetrical Non-Symmetrical/Skewed to the right(positively skewed)

Non-Symmetrical/Skewed to the left

(negatively skewed)

• Question: How can a group of scores be summarized with a single number?

• Answer: Central Tendency! -The typical or most representative value of a group of scores• Includes the mean, median & mode

Central Tendency

Central Tendency: Mean

•Sum of all the scores divided by the number of scores•Formula for the mean:

Σ (sigma) means “summation of”X stands for raw scoreN stands for entire number of observations M stands for mean

Most stable measure of central tendency because all the scores in a distribution are included in its calculation (not true to mode or median)Use with equal-interval variables: equal amount between numbers (EX: age, weight, GPA)

Central Tendency: Median• Median (Mdn): middle score when all the scores in a distribution are arranged from highest to lowest -If you have even numbers, calculate the mean between the 2 middle numbers

• Better to use than the mean when there are extreme scores (outliers) -EX: Calculate the mean and median for these scores:

.74, .86, 2.32, .79, .81

-Which represents the data better?

• Use with rank-ordered variables: numeric variable in which values are ranks (EX: 1st place)

Central Tendency:Mode• Mode (Mo): value with the greatest frequency in a distribution -aka: the highest point on a histogram or frequency polygon

• In a perfectly symmetrical bimodal distribution the mode & mean are the same -if the distribution doesn’t look this way then the mode is usually unrepresentative

• Rarely used in psychology research• Used with nominal variables: values that are categories (EX: gender)

Central Tendency: Skewness

•If the distribution has little or no skew then the median, mode & mean should be the same or close •In skewed distributions (due to extreme scores), the mean is “pulled” toward the tail of the distribution & is unrepresentative of the body of scores.

•In a negatively skewed distribution, the mean is lower than the median (a)

•In a positively skewed distribution, the mean is higher than the median (b)