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7.7 Statistics & Statistical Graphs p.445

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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? What are the part s of a box-and-whiskers plot? How do you find them? When is a box-and-whiskers plot useful? What are the parts of a frequency distribution? How do you draw a histogram? Why?

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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.

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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 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.

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

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

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Box-and-whisker plots 0 10 20 30 40 50 Minimum value (17) Median (36) Maximum value (48) 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 Box Whisker

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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.

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Frequency Distribution Title Goes Here IntervalTallyFrequency 0 to 9 0 10 to 19 l1 20 to 29 ll2 30 to 39 llll l6 40 to 49 llll4 Assign appropriate intervals that will include all data values in the set. 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.

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Another way to show the same info. is in a histogram. 65432106543210 TITLE HERE 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 LABEL HERE LABELLABELHEREHERELABELLABELHEREHERE Intervals Frequency Bars should be touching!

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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. Use the formula on page 446. What are the parts of a box-and-whiskers plot? How do you find them? Median, maximum and minimum values, upper and lower quartiles on a number line. Lower quartile=median of the lower half. Upper quartile=median of the upper half. When is a box-and-whiskers plot useful? Good for comparing median data. What are the parts of a frequency distribution? Intervals, tallys and frequency How do you draw a histogram? Why? Bar graph with bars touching because data values are continuous.

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Assignment Page 449, 12-30 every 3 rd problem, 33-35, 43-45

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