Frequency Distributions Lecture Notes PDF

FREQUENCY DISTRIBUTIONS Descriptive Statistics Overview  Frequency distributions & tables  Relative & cumulative frequencies/percentages  Graphs Describing data  On a 7pt scale with anchors of 1 (very easy) and 7 (very difficult), how difficult do you think this class is?...

FREQUENCY DISTRIBUTIONS Descriptive Statistics Overview  Frequency distributions & tables  Relative & cumulative frequencies/percentages  Graphs Describing data  On a 7pt scale with anchors of 1 (very easy) and 7 (very difficult), how difficult do you think this class is? 7 2 5 3 6 6 4 5 3 6 6 5 6 2 5 5 1 3 Frequency Distribution Table Scores f Sf = N 7 1 6 5  N? 5 5  Maximum score? 4 2  Minimum score? 3 3  Range? 2 2  Scores cluster? 1 1  Spread of scores? Constructing a Frequency Table Scores f  Scores listed from high to low 7 1  Note: can do it the other way, 6 0 but it will be easier to check answers if everyone does it the 5 3 same way 4 1  List all possible scores 3 3 between highest & lowest, even if nobody obtained such 2 2 score  Notice f is in italics Example Gender f Men 24 Women 7 N = 31 Notice: This is on a nominal scale.  Simple Frequency Distribution 7 Can find ΣX using frequency distribution:  Multiply each X by f, then sum Scores f f*Scores 10 2 9 5 8 7 7 3 6 2 5 0 4 1 ΣX =  Simple Frequency Distribution 8 Finding ΣX Scores f f*Scores 10 2 20 9 5 45 8 7 56 7 3 21 6 2 12 5 0 0 4 1 4 ΣX = 158 Grouped frequency distribution  Scores grouped into intervals & listed along with the frequency of scores in each interval  Guidelines: Non-overlapping intervals, 10-20 intervals, Score fwidths rel. of f intervals cf should be simple percen tile (e.g., 40-44 5, 10) 2.08 25 100 35-39 2.08 23 92 30-34 0.00 21 84 25-29 3.12 21 84 Note: We lose 20-24 2.09 18 72 info about 15-19 4.16 16 64 specific values. 10-14 1.04 12 48 5-9 4.16 11 44 0-4 7.28 7 28 Relative & Cumulative Frequencies Relative Frequency Relative frequency (rel. f or rf) Score f rel. f f 6 1.05 rel. f = 5 0.00 N 4 3 2 3.10.15 2 10.50 1 4.20 Relative Frequency Score f rel. f 12 3.15 (15% of the class received a score of 12) 11 2.10 10 5.25 (25% of the class received a score of 10) 9 3.15 8 2.10 7 5.25 N = 20 Cumulative Frequency Frequency of all scores at or below a particular score Score f cf 17 1 20 16 2 19 15 4 17 14 6 13 13 4 7 12 0 3 11 2 3 10 1 1 Cumulative Frequency Distribution Score f cf 12 3 20 11 2 17 (17 people scored at or below 11) 10 5 15 9 3 10 (10 people scored at or below 9) 8 2 7 7 5 5 (5 people scored at or below 7) N = 20 Cumulative %  Percent of all scores in the data that are at or below the score  cf  Cumulative   100  %= N  Practice 1  Using the following data set:  Create a simple distribution table - find the relative frequency, find the cumulative frequency, and find the cumulative percent for each remaining data points  Note: Round to the 2nd decimal place 5 4 3 5 1 1 4 3 3 1 4 4 Practice 1: Answers Scores f rf cf c% 5 2.17 12 100% 4 4.33 10 83% 3 3.25 6 50% 2 0.00 3 25% 1 3.25 3 25% Practice 2  Using the following data set:  Create a simple distribution table - find the relative frequency, find the cumulative frequency, and find the cumulative percent for each remaining data points  Note: Round to the 2nd decimal place 2 5 5 2 8 8 8 6 6 4 7 8 6 Practice 2: Answers scores f rf cf c% 8 4.31 13 100% 7 1.08 9 69% 6 3.23 8 62% 5 2.15 5 38% 4 1.08 3 23% 3 0.00 2 15% 2 2.15 2 15% Graphs Graphs  X axis – horizontal (scores increase from left)  Y axis – vertical (scores increase from bottom)  Scale of measurement determines type of graph  Bar graph  Histogram  Polygon Bar Graphs  Spaces between bars  Distinct categories  Used with nominal scales or qualitative data  Sometimes also used with ordinal scales Histograms  No spaces between bars  Labels directly under each box  Used with ordinal, interval, or ratio scales  Usually used with discrete data Polygons  Used when  larger range of scores  Interval or ratio scales  Continuous data  Dot centered above each score if it is discrete data “Most misleading graph ever published” Distributions  Normal curve Variations in Distributions  Kurtosis = how peaked or flat distribution Mesokurtic = normal Leptokurtic = thin Platykurtic = broad/ fat Variations in Distributions Negatively skewed enjoy psych courses 14 (left skew) 12 10 Frequency 8 6 4 2 0 0.0 1.0 2.0 3.0 4.0 5.0 enjoy psych courses Variations in Distributions Positively skewed AGE 14 (right skew) 12 10 Frequency 8 6 4 2 0 20.0 25.0 30.0 35.0 40.0 45.0 AGE Variations in Distributions Bimodal 12 10 Frequency 8 6 4 2 F D C B A GRADE Practice 3  Using the following data set:  Create a simple distribution table, find the relative frequency, find the cumulative frequency, and find the cumulative percent for each remaining data point --- also, create a graph.  Note: Round to the 2nd decimal place (assume interval scale) 14 14 13 15 11 15 13 10 12 13 14 13 14 15 17 14 14 15  Practice 3: Histogram 7 6 5 4 Frequency 3 2 1 0 Series1 16 10 11 12 13 14 15 17 Scores Practice 3: Answers X f rf cf c% 17 1.06 18 100% 16 0.00 17 94% 15 4.22 17 94% 14 6.33 13 72% 13 4.22 7 39% 12 1.06 3 17% 11 1.06 2 11% 10 1.06 1 06%