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Measures of Central Tendency Box and Whisker Plots

Measures of Central Tendency Box and Whisker Plots. Kim Hancock, CTE Updated 9/20/12. WHAT IS AN INTEGER?.

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Measures of Central Tendency Box and Whisker Plots

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  1. Measures of Central Tendency Box and Whisker Plots Kim Hancock, CTE Updated 9/20/12

  2. WHAT IS AN INTEGER? Integers can be thought of as discrete, equally spaced points on an infinitely long number line. (Nonnegative integers (purple) and negative integers (red)). Integers are not ever fractions or decimals in simplest form.

  3. MEAN- the number found when the sum of two or more numbers is divided by the number of addends in the sum; also called the average. PRACTICE! FIND THE MEAN OF THE FOLLOWING SET OF NUMBERS: 12, 13, 13, 17, 20 15

  4. MEDIAN - the middle number (or the average of the two central numbers) of a list of data when the numbers are arranged in order from the least to greatest. PRACTICE! FIND THE MEDIAN OF THE FOLLOWING SET OF NUMBERS: 10 8, 14, 6, 18, 3, 3, 12, 16

  5. MODE- the number that appears most often in a list of data. ???I have some questions for you! 1. Can a data set have no mode? 7, 9, 10, 11, 15 2. Can a data set have more than one mode? 3.5, 6, 6, 7.3, 8.1, 8.1 3. Is there a limit to the number of modes in a data set? 2, 2, 4, 4, 7, 7, 10, 10

  6. RANGE - the difference between the largest number and the smallest number in a list of numbers. What mathematical operation is indicated by the word "difference?" 54, 59, 64, 74, 74, 74, 79, 84, 89, 94, 94, 100, 100

  7. Data Display Think of some ways to display a set of data

  8. Is anyone familiar with a "box and whisker" plot? A box and whisker plot is a pictorial summary of central tendency, dispersion, asymmetry and extremes, free from the assumption of normal distribution.

  9. Definitions First, what is a quartile?

  10. Outlier: A data element that lies outside the normal distribution of the data. (IQR - Interquartile Range) There are two types of outliers: 1. Mild Outlier > 1.5(IQR) 2. Extreme Outlier > 3(IQR) (then subtract from lower quartile or add to upper quartile)

  11. Lower Extreme (minimum): The lowest value, not counting outliers, in a set of data.

  12. Lower Quartile (Q1) = the value of the median of the lower 50% of the data. • 25% of the values are smaller than the lower quartile. • 75% of the values are greater than the lower quartile. • In other words, the lower quartile is the median of the lower 50% of the data. • Q1 = lower quartile = cuts off lowest 25% of data = 25th percentile

  13. Median (Q2): the middle value when a set of data is placed in numerical order. • If there are an even number of data points, the median is the mean of the middle two values (add the two middle terms and divide by two). • Med = Q2 = median = cuts data set in half = 50th percentile

  14. Interquartile Range (IQR): the value of the IQR is the difference of the 3rd (Upper) and 1st (Lower) quartile. • The IQR contains approximately the middle 50% of the data points. • IQR = Q3 - Q1

  15. Upper Quartile (Q3): the value of the median of the upper 50% of the data. • 25% of the values are greater than the upper quartile • 75% are less than the upper quartile. • In other words the upper quartile is the median of the upper 50% of the data. • Q3 = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile

  16. Upper Extreme (maximum): The highest value, not counting outliers, in a set of data.

  17. Let's construct a Box and Whisker Plot together based upon Fast Plant Data. Step 1: Put the data in order from least to greatest Step 2: Find the median of all data points and plot it on a number line 14 cm 3 cm 17 cm 8 cm 17 cm 7 cm 12 cm 11 cm 10 cm 20 cm 10 cm 17 cm 20 cm 8 cm 10 cm 10 cm 7 cm 14 cm 17 cm 3 cm 11 cm 12 cm 13 6 8 10 11 3 9 14 4 5 7 15 12 16 17 18 19 20

  18. Step 3: Find the median of the lower 50% of the data and plot it on the number line. 17 cm 20 cm 8 cm 10 cm 10 cm 7 cm 14 cm 17 cm 3 cm 12 cm 11 cm 13 6 8 10 11 3 9 14 4 5 7 15 12 16 17 18 19 20 Step 4: Find the median of the upper 50% of the data and plot it on the number line.

  19. Step 5: Draw a box using those 3 points. 3 cm 7 cm 17 cm 20 cm 10 cm 11 cm 12 cm 8 cm 10 cm 14 cm 17 cm Upper Quartile Lower Quartile Median 13 6 8 10 11 3 9 14 4 5 7 15 12 16 17 18 19 20 Interquartile Range What do we have so far? Let's label some of our parts. What is the value of the interquartile range? Do we have any outliers?

  20. Step 6: Graph upper and lower extremes and draw lines to them as the "whiskers." 3 cm 7 cm 17 cm 20 cm 10 cm 11 cm 12 cm 8 cm 10 cm 14 cm 17 cm 13 6 8 10 11 3 9 14 4 5 7 15 12 16 17 18 19 20 Let's talk a little about what we can tell from a Box and Whisker plot, and why you would ever need to know this!

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