77714_02p (1).pptx - What you will learn in Chapter 2 Measures of central tendency Computing the mean for a set of scores Computing the mode and median

77714_02p (1).pptx - What you will learn in Chapter 2...

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Unformatted text preview: What you will learn in Chapter 2 – Measures of central tendency – Computing the mean for a set of scores – Computing the mode and median for a set of scores – Selecting a measure of central tendency Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Measures of Central Tendency • The AVERAGE is a single score that best represents a set of scores • Another name for AVERAGES is Measures of Central Tendency • Examples include the mean, median, and mode Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Computing the Mean • • (X Bar) is the mean value of the group of scores • (sigma) tells you to add together whatever follows it • X is each individual score in the group • The n is the sample size Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Steps to Computing the Mean 1. List the entire set of values in one or more columns. These are all the Xs. 2. Compute the sum or total of all the values. 3. Divide the total or sum by the number of values. Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Things to remember… • N = population n = sample • Sample mean is the measure of central tendency that best represents the population mean • It is also called the arithmetic mean – Mean is the centermost point where all the values on one side of the mean are equal in weight to all the values on the other side of the mean • Mean is VERY sensitive to extreme scores that can “skew” or distort findings Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Weighted Mean • Step 1: List all values for which the mean is being calculated (list them only once) • Step 2: List the frequency (number of times) that value appears • Step 3: Multiply the value by the frequency • Step 4: Sum all Value x Frequency • Step 5: Divide by the total Frequency (total n size) Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Median • point/score at which 50% of remaining scores fall below it and 50% fall above it Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Steps to Finding the Median 1) List the values, in order, either from highest to lowest or lowest to highest. 2) Find the middle-most score. That’s the median. Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 BUT… • What if there are two middle scores? • What if the two middle scores are the same? Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 A little about Percentiles… • Percentile ranks are used to define the percent of cases equal to and below a certain point on a distribution • 75th %tile – means that the score received is at or above 75 % of all other scores in the distribution • Median is always at the 50th percentile Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Things to Remember • The mean is the middle point of a set of values, while the median is the middle point of a set of cases • Because the median cares about the number of cases, extreme scores (i.e., outliers) do not impact it • Sometimes people use Mdn or Med to stand for median Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Computing the Mode • Mode = most frequently occurring score • This is the least precise measure of central tendency • When two values occur the same number of times -- Bimodal distribution Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Steps to Finding Mode • List all values in the distribution • Tally the number of times each value occurs • The value occurring the most is the mode Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Example of Finding Mode Party Affiliation Number or Frequency Democrats 90 Republicans 70 Independents 140 Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 When to Use What… • Use Mode: when the data are qualitative, categorical, or nominal (e.g., eye color, political party)and values can only fit into one category (i.e., mutually-exclusive) • Use Median when you have extreme scores • Use Mean when the data does not include extreme scores (i.e., outliers) and are not qualitative, categorical, or nominal Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 Skewed Distribution • A distribution of scores has a high number of scores clustered at one end of the distribution with relatively few scores spread out toward the other end of the distribution, forming a tail. • Similarities between a skewed and normal distribution: • • The procedures used to calculate a mean, median, and mode are the same Differences between a skewed and normal distribution: • The position of the three measures of central tendency in the distribution Example: The Mean, Median, and Mode of a Distribution The following distribution of test scores are given: 86 90 96 96 100 105 115 121 Mean = 86+90+96+96+100+105+115+121 = 101.13 8 Calculating the mean: Add up all the scores, then divide by the number of scores. In this case, there are 8 IQ scores. Median = 96+100 = 98 2 Calculating the median: Because there is an even amount of scores, sum the two scores that are found in the middle of the distribution when it is put into numerical order, then divide by two. Mode = 96 Calculating the mode: 96 is the most frequent number that occurs in the distribution Using SPSS Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition, SAGE Inc. © 2014 ...
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