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M&Ms Statistics

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**Measures of Central Tendency**

Mode: The most frequently occurring score in a distribution. Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by the number of scores that were added together. Median: The middle score in a rank-ordered distribution. OBJECTIVE 17| Describe three measures of central tendency and tell which is most affected by extreme scores.

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**M&Ms Activity Quantify (count) the data within the bag=total M&Ms**

2) Classify candy by color and count each color-list each color total on your work paper

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**M&M Activity 3) Determine the groups quantity (total)**

4) Calculate the groups mean * Work with your own pieces now 5) Calculate the mean 6) Calculate the mode 7) Calculate the median Bi-modal=> two categories with the same mode

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**Measures of Central Tendency**

A Skewed Distribution

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Measures of Variation Range: The difference between the highest and lowest scores in a distribution. Standard Deviation: A computed measure of how much scores vary around the mean. OBJECTIVE 18| Explain two measures of variation.

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**M&M Activity Find the range of group’s bag quantity**

*Highest # of m&ms-lowest # of m&ms 8) Find the range of colors in individual bag 9) Calculate Standard Deviation-a measure of spread

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**Standard Deviation Determine the mean**

Subtract the mean from every number to get the list of deviations (negative numbers are ok) Square the resulting list of numbers Add up all the resulting squares to get their total sum Divide your result by one less than the number of items in the list To get the SD, take the square root of the resulting number

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**Practice Standard Deviation**

your list of numbers: 1, 3, 4, 6, 9, 19 1) mean: ( ) / 6 = 42 / 6 = 7 2) list of deviations: -6, -4, -3, -1, 2, 12 3) squares of deviations: 36, 16, 9, 1, 4, 144 4) sum of deviations: = 210 5) divided by one less than the number of items in the list: 210 / 5 = 42 6) square root of this number: square root (42) = about 6.48

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Standard Deviation

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Making Inferences A statistical statement of how frequently an obtained result occurred by experimental manipulation or by chance.

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**When is an Observed Difference Reliable?**

Making Inferences When is an Observed Difference Reliable? Representative samples are better than biased samples. Less variable observations are more reliable than more variable ones. More cases are better than fewer cases. OBJECTIVE 19| Identify three principles for making generalizations from samples.

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**When is a Difference Significant?**

Making Inferences When is a Difference Significant? When sample averages are reliable and the difference between them is relatively large, we say the difference has statistical significance (how likely it is that an obtained result occurred by chance) For psychologists this difference is measured through alpha level set at 5 percent (.05) OBJECTIVE 20| Explain how psychologists decide whether differences are meaningful.

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