Presentation on theme: "Summarizing Scores With Measures of Central Tendency"— Presentation transcript:
1 Summarizing Scores With Measures of Central Tendency Chapter 3Summarizing Scores With Measures of Central Tendency
2 Moving Forward Your goals in this chapter are to learn: What central tendency isWhat the mean, median, and mode indicate and when each is appropriateThe uses of the meanWhat deviations around the mean areHow to interpret and graph the results of an experiment
3 New Symbols and Procedures The symbol S is the Greek letter “S” and is called sigma.This symbol means to sum (add).You will see it used with a symbol for scores such as SX. This is pronounced as the “sum of X” and means to find the sum of the X scores.
8 The ModeThe mode is the score having the highest frequency in the dataThe mode is used to describe central tendency when the scores reflect a nominal scale of measurement
9 Unimodal Distributions When a polygon has one hump (such as on the normal curve) the distribution is called unimodal.
10 Bimodal Distributions When a distribution has two scores tied for the most frequently occurring score, it is called bimodal.
11 The Median The median is the score at the 50th percentile The median is used to summarize ordinal or highly skewed interval or ratio scores
12 Determining the Median When data are normally distributed, the median is the same score as the modeThe symbol for the median is MdnUse the median for ordinal data or when you have interval or ratio scores in a very skewed distribution
13 Determining the Median When data are normally distributed, the median is the same score as the mode. When data are only approximately normally distributed:Arrange the scores from lowest to highestDetermine NIf N is an odd number, the median is the score in the middle positionIf N is an even number, the median is the average of the two scores in the middle
14 The MeanThe mean is the score located at the exact mathematical center of a distributionThe mean is used to summarize interval or ratio data in situations when the distribution is symmetrical and unimodal
15 Computing a Sample Mean The formula for the sample mean is
16 Comparing the Mean, Median, and Mode All three measures of central tendency are located at the same score on a perfectly normal distributionIn a roughly normal distribution, the mean, median, and mode will be close to the same scoreThe mean inaccurately describes a skewed distribution
19 Deviations A score’s deviation is equal to the score minus the mean In symbols, this isThe sum of the deviations around the mean is the sum of all the differences between the scores and the meanIt is symbolized by
20 Summarizing Research Scores are from the dependent variable Choose the mean, median, or mode based onThe scale of measurement used on the dependent variable andThe shape of the distribution, if you have interval or ratio scores
21 Graphing the Results of an Experiment Plot the independent variable on the X (horizontal) axis and the dependent variable on the Y (vertical) axisCreate a line graph when the independent variable is an interval or a ratio variableCreate a bar graph when the independent variable is a nominal or ordinal variable
22 A line graph uses straight lines to connect adjacent data points Line GraphsA line graph uses straight lines to connect adjacent data points
23 Bar GraphsThe bar above each condition on the X axis is placed to the height on the Y axis that corresponds to the mean score for that condition.
24 ExampleFor the following data set, find the mode, the median, and the mean.14131511101217
25 Example—Mode The mode is the most frequently occurring score In this data set, the mode is 14 with a frequency of 6
26 Example—MedianThe median is the score at the 50th percentile. To find it, we must first place the scores in order from smallest to largest.10111213141517
27 Example—MedianSince this data set has 18 observations, the median will be half-way between the 9th and 10th score in the ordered datasetThe 9th score is 14 and the 10th score also is 14. To find the midpoint, we use the formula:The median is 14
28 Example—MeanFor the mean, we need SX and NWe know N = 18