StatisticsStatistics

Assumed you have had this in Assumed you have had this in previous math classes…previous math classes…

What are measures of central tendency?

How do you tell measures of central tendency apart?

What is standard deviation? How is it calculated?

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.

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.

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

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

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.

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

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.

Assignment

Worksheet 7.7