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. 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. 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. 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. 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. 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. 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. 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. Chapter 6D (Refer to book, pp. 435 ff)
• Statistical significance
• Margin of error and Confidence Interval
• Using the online calculator
11. Margin of Error Formula
1
√ n
“n” represents the
number of people in the
sample
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. “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.
