statistics assumed you have had this in previous math classes…
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StatisticsStatistics
Assumed you have had this in Assumed you have had this in previous math classes…previous math classes…
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What are measures of central tendency?
How do you tell measures of central tendency apart?
What is standard deviation? How is it calculated?
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An intro to StatisticsAn intro to Statistics
• Statistics – numerical values used to summarize & compare sets of data (such as ERA in baseball).
• Measures of Central Tendency – mean, median, & mode are the 3 we will be using. Tells you what the “center” of the data is.
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Mean – ( x ) average of n numbers (add all #s & divide by n)
Median – the middle # when the #s are written in order from least to greatest or greatest to least. If there are 2 middle numbers, the median will be the average of those 2.
Mode – the number(s) that occur most frequently. It is possible to have more than 1 mode or even no mode.
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Ex: Find the mean, median, & mode of Ex: Find the mean, median, & mode of the following set of numbers: 36, 39, 40, the following set of numbers: 36, 39, 40,
34, 48, 33, 25, 30, 37, 17, 42, 40, 24.34, 48, 33, 25, 30, 37, 17, 42, 40, 24.
• MeanMean - 445
13
MedianMedian – Put the numbers in order first!17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
ModeMode – most frequent!
40 is the mode.
2.34
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Measures of DispersionMeasures of Dispersion – tell how spread out the data are.
* Range – Difference between the largest and smallest values.
(for example: the range of the last example would be 48-17=31)
* Standard Deviation - (σ – “sigma”)
n
xxxxxx n22
22
1 )(...)()(
x1, x2, x3, …, xn are the entries in the data set.n is the number of entries in the set
x is the mean
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is the mean
Standard Deviation symbol - (σ – “sigma”)
Standard deviation describes the typical difference (deviation) between the mean and a data value.
x
“A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values.
Standard deviation is commonly used to measure confidence in statistical conclusions.” http://en.wikipedia.org/wiki/Standard_deviation
This is why you see standard deviation on test scores.
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Ex: Find the standard deviation of the data from the first example.
13
)2.3424(...)2.3440()2.3439()2.3436( 2222
13
32.856
87.65
12.8
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What are measures of central tendency?
Mean, medium and mode
How do you tell measures of central tendency apart?
Mean=average, median=middle, mode=appears most often
What is standard deviation? How is it calculated?
Standard deviation=typical difference between the mean and a data value.
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Assignment
Worksheet 7.7