Statistics Statistical Graphs An intro to Statistics Statistics

Statistics & Statistical Graphs

An 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 the following set of numbers: 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24. • Mean - 445 13 Median – Put the numbers in order first! 17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 42, 48 Mode – most frequent! 40 is the mode.

Measures 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”) x is the mean n is the number of entries in the set x 1, x 2, x 3, …, xn are the entries in the data set.

Ex: Find the standard deviation of the data from the first example.

Box-and-whisker plots Box Whisker 0 10 20 Minimum value (17) Lower Quartile – median of all numbers in the list to the left of the median (25+30)/2 = 27. 5 30 Whisker 40 Median (36) 50 Maximum value (48) Upper Quartile – median of all numbers to the right of the median (40+40)/2 = 40

Hints for making a box-and-whiskers plot: • Make sure data is in order from least to greatest. • Find the minimum value, median, maximum value, upper & lower quartiles. • Plot the points for this info below a number line. • Draw the box and whiskers.

Frequency Distribution Assign appropriate intervals that will include all data values in the set. Interval 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 Put a tally mark for each data value in the appropriate row. Count the number of tally marks and put the total in the last column. Title Goes Here Tally Frequency 0 l 1 ll 2 llll l 6 llll 4

Another way to show the same info. is in a histogram. Frequency L A B E L H E R E TITLE HERE Bars should be touching! 6 5 4 3 2 1 0 9 0 10 9 1 - 9 20 -2 9 30 LABEL HERE -3 9 40 -4 Intervals