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Sept 20 Lecture Notes.docx

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Daniela Palombo

Sept 20 Learning objectives: - Use 5 steps to calculate frequency distribution of scores sorted into intervals - Distinguish among 3 types of frequency distributions (calculation and interpretation) - Distinguish between 4 types of graphs - Interpret and calculate percentile score - Distinguish between percentile and percentile mark - Interpret and calculate mean, median, and mode - List and describe all 5 properties that make mean special - Explain how measures of central tendency change when shape of distribution changes How many students fit within 60-69% range? E. A. How do we calculate a frequency distribution using intervals? (i) Find the range of scores a. Range = Highest score-Lowest score b. 93-42 =51 (ii) Determine interval width a. Assume we want ~10 intervals b. Determine i (interval width) c. i = Range/Number of intervals d. Ex. i=51/10=5.1 e. Round i to same number of decimal places as in raw data (iii) List the limits of each class interval a. Begin with lowest interval i. Lowest interval must contain lowest score ii. Lower limit of lowest interval must be evenly divisible by i b. Ex. Lowest score is 42. What is the lowest interval? B i. A. 38-43 ii. B. 40-44 iii. C. 42-47 iv. E. 42-48 (iv) Tally up the scores in each interval and enter amount in frequency (f) column B. 3 Kinds of Frequency Distributions - Relative Frequency Distribution o Indicates proportion of total number of scores that occur in each interval o Relative f = f/N o Ex. If N=40, what is the relative frequency of 85-89 interval?  5/40=.125 (.12) - Cumulative Frequency Distribution o Number of scores that fall below the upper real limit of each interval o Starting on the bottom interval add the frequency of interval to frequencies of all intervals below it - Cumulative Percentage Distribution o % of scores that fall below upper real limit of each interval o cum % = (cum f/n)x100 - What is the relative frequency of the interval 25-29?  f=f/N; N=3+4+2+3+5=17  f=4/17=0.24 - What is the cumulative frequency of the interval 25-29? o (20-24): 3, (25-29): 4+3=7 - What is the cumulative percentage of the interval 25-29? o (7/17)x100%=41.18% o DO NOT FORGET TO MULTIPLY BY 100 TO GET PERCENT! C. General Information on Graphing - Vertical Axis o Called Y axis or ordinate o Plot frequency of scores (frequency distributions) o Plot dependent variable (Results of experiment) - Horizontal Axis o Called X axis or abscissa o Plot score values or intervals (frequency distribution) o Plot levels of independent variable (experiment) - Both axes must be labeled - Both axes should start at 0. If not, indicate with break near intersection D. 4 Types of Graphs - Bar Graphs o For nominal or ordinal scale data o Separate bar on X axis for each category or rank o Bars do NOT touch; to reflect discrete nature of data o Height of bar (Y axis) indicates frequency of category - Histograms o Created when data are on an interval or ratio scale o Separate bar drawn along X axis for each class interval  Each bar begins and ends at the real limits of the interval  The midpoint of each class interval is plotted on the X axis o Height of bars (Y axis) indicates frequency of class intervals o Bars DO touch; reflects continuous nature of data - Frequency Polygon o Similar to histogram; interval or ratio data o Point plotted over midpoint of each interval, corresponding to frequency o Points are joined, line extended to meet the x-axis at the midpoint of two intervals immediately beyond last intervals used - Cumulative Percentage Curve o Y-axis: percentage o X-axis: upper real limit of the interval o o Shapes of cumulative frequency curves o - Interp
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