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Chapter 6
More Statistics
Section6A
• Mean -- Add the numbers and divide
• Median -- Put numbers in order and find the
one in the middle (if two “mi...
Example One
• 85 80 91 97 85 88 82
• Mean = (85+80+91+85+97+88+82) / 7 = 86.85
(Be careful using the calculator)
• Put sco...
Example Two
• 25 80 80 85 90 91 91 95
• Mean = (25+80+80+85+90+91+91+95) / 8 =
79.625 (Be careful using the calculator)
• ...
Section 6A (continued)
• Outlier – Value(s) that may be “much higher”
or “much lower” than the other values in the
group (...
Describing Variation: BoxPlots
• Sometimes called “box-and-whisker plot”
• It uses five numbers to summarize the data:
– T...
BoxPlot (“Box-and-Whisker”) Example
• The amount of marbles that 15 different
people own (one person has 18 marbles,
anoth...
BoxPlot (“Box-and-Whisker”) Example
• 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100
• Step 3: Look at the numbers to the l...
BoxPlot (“Box-and-Whisker”) Example
• 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100
• You now have the “five-number summar...
Chapter 6D (Refer to book, pp. 435 ff)
• Statistical significance
• Margin of error and Confidence Interval
• Using the on...
Margin of Error Formula
1
√ n
“n” represents the
number of people in the
sample
“Margin of Error” Example
In the online calculator, key in:
1 / 900 = 0.0333
3.3% for the margin of error (We’ll
round to ...
“Margin of Error” Example (continued)
• Take the 68% and do two more calculations:
Subtract the 3% from 68%
68% - 3% = 65%...
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Chapter 6 slide show notes math 140 summer 2011

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Chapter 6 slide show notes math 140 summer 2011

  1. 1. Chapter 6 More Statistics
  2. 2. Section6A • Mean -- Add the numbers and divide • Median -- Put numbers in order and find the one in the middle (if two “middles” add those and divide by 2) • Mode – The most commonly occurring number (could be more than one mode, or “no mode” if each number is different) • Range – Difference between the highest number and lowest number in the group
  3. 3. Example One • 85 80 91 97 85 88 82 • Mean = (85+80+91+85+97+88+82) / 7 = 86.85 (Be careful using the calculator) • Put scores in order: 80 82 85 85 88 91 97 Median = “middle one” = 85 • Mode = 85 (the most common) – 80 82 85 85 88 91 97 • Range = 97 – 80 = 17 (how far apart they are)
  4. 4. Example Two • 25 80 80 85 90 91 91 95 • Mean = (25+80+80+85+90+91+91+95) / 8 = 79.625 (Be careful using the calculator) • Scores are in order – there is no “middle one”: Median = (85+90)/2 = 87.5 • Mode = There are two modes (80 and 91) – 25 80 80 85 90 91 91 95 • Range = 95 – 25 = 70 (Why so big?) – Because “25” is an outlier value
  5. 5. Section 6A (continued) • Outlier – Value(s) that may be “much higher” or “much lower” than the other values in the group (“lies out there” away from the others) • Outliers typically will not affect the median and the mode • Outliers have a definite effect on the mean and the range • NOTE: The highest and lowest values are not necessarily outliers. Don’t assume this!
  6. 6. Describing Variation: BoxPlots • Sometimes called “box-and-whisker plot” • It uses five numbers to summarize the data: – The lowest value (the “left whisker”) – The lower quartile value (part of “the box”) – The median (part of “the box”) – The upper quartile value (part of “the box”) – The highest value (the “right whisker”)
  7. 7. BoxPlot (“Box-and-Whisker”) Example • The amount of marbles that 15 different people own (one person has 18 marbles, another person has 27 marbles, etc.): • 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100 • Step 1: BE SURE THAT NUMBERS ARE IN ORDER!! • Step 2 : Find the median
  8. 8. BoxPlot (“Box-and-Whisker”) Example • 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100 • Step 3: Look at the numbers to the left of the median (the blue numbers ) & find the median of those numbers • Step 4: Look at the numbers to the left of the median (the green numbers ) & find the median of those numbers • 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100 • Step 5: Locate the lowest and highest values • 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100
  9. 9. BoxPlot (“Box-and-Whisker”) Example • 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100 • You now have the “five-number summary” to draw the boxplot 18 52 68 87 100 The “whiskers” are the “lowest value” and “highest value” The “box numbers” are the “lower quartile” “median” and “upper quartile”
  10. 10. Chapter 6D (Refer to book, pp. 435 ff) • Statistical significance • Margin of error and Confidence Interval • Using the online calculator
  11. 11. Margin of Error Formula 1 √ n “n” represents the number of people in the sample
  12. 12. “Margin of Error” Example In the online calculator, key in: 1 / 900 = 0.0333 3.3% for the margin of error (We’ll round to 3%) √ n 1 Suppose 900 people had been polled and we found that 68% of the students preferred online teaching . The margin of error in the survey is found by replacing “n” with “900” and calculating. √900 1
  13. 13. “Margin of Error” Example (continued) • Take the 68% and do two more calculations: Subtract the 3% from 68% 68% - 3% = 65% Add the the 3% from 68% 68% + 3% = 71% Based on math theory we can be “95% confident that, in this survey, most people will prefer the online method of teaching.

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