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An explanation of the concepts of mean, median, and standard deviation, along with step-by-step calculations and examples using test scores. Mean is the average value, median is the middle value, and standard deviation measures the spread of data from the mean.
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Notes Unit 8: Mean, Median, Standard Deviation The mean is found by adding all the values in the set, then dividing the sum by the number of values.
The MEDIAN is the number that is in the middle of a set of data
**1. Arrange the numbers in the set in order from least to greatest.
63 73 84 86 88 95 97 97 100
Half the numbers are less than the median. Half the numbers are greater than the median.
**1. Add the two numbers.
The median is 91. Ex 2: Find the median.
B. Bell Curve: The bell curve, which represents a normal distribution of data, shows what standard deviation represents. One standard deviation away from the mean ( ) in either direction on the horizontal axis accounts for around 68 percent of the data. Two standard deviations away from the mean accounts for roughly 95 percent of the data with three standard deviations representing about 99 percent of the data.
C. Steps to Finding Standard Deviation
2
2
2
2 ( 24) 576
Remember:
Thus the standard deviation of the second set of test scores is 19.6.
Consider both sets of scores. Both classes have the same mean, 76. However, each class does not have the same scores. Thus we use the standard deviation to show the variation in the scores. With a standard variation of 14.53 for the first class and 19.6 for the second class, what does this tell us?