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Statistics & Statistical Graphs

Learn about statistics, including statistical graphs, measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and frequency distribution.

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Statistics & Statistical Graphs

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  1. Statistics & Statistical Graphs

  2. 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.

  3. 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.

  4. 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, 40, 42, 48 Mode – most frequent! 40 is the mode.

  5. 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 x1, x2, x3, …, xn are the entries in the data set. n is the number of entries in the set

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

  7. Box-and-whisker plots Box Whisker Whisker 0 10 20 30 40 50 Minimum value (17) Maximum value (48) Median (36) Lower Quartile – median of all numbers in the list to the left of the median (25+30)/2 = 27.5 Upper Quartile – median of all numbers to the right of the median (40+40)/2 = 40

  8. 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.

  9. Frequency Distribution Count the number of tally marks and put the total in the last column. Assign appropriate intervals that will include all data values in the set. Put a tally mark for each data value in the appropriate row.

  10. Another way to show the same info. is in a histogram. Frequency TITLE HERE Bars should be touching! L A B E L H E R E 6 5 4 3 2 1 0 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 Intervals LABEL HERE

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