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Chapter 3 Frequency Distributions

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Frequency Distributions A frequency distribution lists the number of times, or frequency (f), each raw score (X) in a set of score (distribution) appears. Xf 32 23 12 Ex: 1, 1, 2, 2, 2, 3, 3 It’s easy to spot the mode.

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Constructing a Frequency Distribution 14, 14, 10, 8, 14, 16, 8, 10, 10, 8, 10, 16, 16, 6, 20, 16, 9, 10, 17, 10, 18, 14, 14, 8 Step 1: Find the highest and lowest scores. Step 2: Construct a table including all numbers. By convention, the highest score is listed first and the lowest score is listed last.

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Constructing a Frequency Distribution Step 3: Make a tally mark for each score. Step 4: Count up the tally marks and fill in the frequency column.

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Frequency Distributions Like inferential statistics, descriptive statistics, and graphs, frequency distributions are judgment aids. They make it easier for a scientist or another person to react meaningfully to the results of an experiment or to other information (data).

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Grouped frequency distribution In a grouped frequency distribution, the total range of scores is divided into a number of mutually exclusive (nonoverlapping) and collectively exhaustive categories (class intervals) and the frequency of scores in each category is reported. – Categories typically are of the same width (e.g., 1-4, 5- 9, 10-14). – The number of categories depends on the data of interest; the textbook recommends 10-15 categories. – To determine the size of class intervals, subtract the lowest score from the highest score and divide by the number of desired class intervals.

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Six Groups

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Eleven Groups

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Sixteen Groups

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Your Turn: Activity #1 17, 3, 16, 16, 28, 5, 3, 23, 31, 19, 2, 20, 19, 17, 27, 25, 18, 15, 19, 6, 22, 9, 15, 22, 1, 18, 16 1.Make 10 categories for your frequency distribution. 1.Create a frequency distribution using the above data. 1.Put your name on your paper.

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Discrete vs. Continuous Variables Discrete variables can take only specific values (usually whole numbers). – Ex: The number of people in a family can be three, but it can’t be 3.45. Continuous variables can take an infinite number of values. – Ex: The amount of alcohol consumed can take on any value. For example, someone could consume 29.5698359167 oz. of tequila.

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Apparent vs. Real Limits Xf 8 7 6 5 Apparent Limits: When we are working with continuous variables, this table won’t do. It has gaps in it. (In fact, the probability of getting a value of exactly 6 is infinitely small.) Real Limits: We can transform this table into one that includes all possible values in the range. In this case, we will use the original value ±.5 to eliminate the gaps. Xf 7.5 – 8.5 6.5 – 7.5 5.5 – 6.5 4.5 – 5.5

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Percentage (or Relative) Distributions It is possible to express frequencies as percentages, which may make frequency distributions more useful as judgment aids. f = frequency (of a particular score) N = total number of scores

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Why is it Useful? One of the main advantages is that you can compare results from samples of different sizes.

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Activity #2 Write on a small piece of paper the number of times you think most university students have had sexual intercourse in the last 30 days. Pass the paper to the end of your row. Our categories: 0, 1, 2-5, 6-10, 11+ Change the number in each category to a percentage and construct a frequency table Put your name on the paper.

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How many times in the last 30 days have you had sexual intercourse? How many times in the last 30 days have most students had sexual intercourse? (from Wechsler & Kuo, 2000)

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Cumulative Frequency Distributions Starting with the lowest score and moving to the highest, the frequency is accumulated. For example: X 3 2 1 f 2 3 2 Cum f 7 5 2

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Why is it useful? The Cumulative Frequency Distribution allows you to see the median and the distribution of scores around the median.

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Cumulative Percentage Distributions Cumulative percentage frequencies also can easily be calculated. Use the data from the previous chart and this formula: You try. X 3 2 1 f 2 3 2 Cum f 7 5 2 Cum %age 100 71 29

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Why is it Useful? The Cumulative Percentage Distribution allows you to see the percentage of scores that fall at or below a given score.

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Students’ Estimates of Binge Drinkers in their School RESPONSE (%)%ageCum %age 0-98.2 10-1911.719.8 20-2914.434.2 30-391650.2 40-499.259.4 50-5910.369.7 60-699.779.4 70-796.786.1 80-1003.289.3 Don’t know10.7100.0

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Combine All Methods X 3 2 1 f 2 3 2 Cum f 7 5 2 Cum %age 100 71 29 %age 29 43 29

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Homework Prepare for Quiz 3 over Chapter 3 Read Chapter 4 Finish Chapter 3 Homework (check course website or WebCT) Prepare for Basic Math Re-test

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Thursday August 29, 2013 The Z Transformation. Today: Z-Scores First--Upper and lower real limits: Boundaries of intervals for scores that are represented.

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