1. 12.3 – Analyzing Data

2. Measures of Central Tendency
Mean: Add the data values and divide by the number of values
Ex: The mean of 3, 5, 6, 8, 9 = 31/5 = 6.2

3. Measures of Central Tendency
Median: The exact middle value. List the values in order from least to greatest; then find the middle value
Ex: 5, 9, 1, 4, 3 = 1, 3, 4, 4, 9
Median = 4
Ex: 5, 9, 1, 4, 3, 7 = 1, 3, 4, 5, 7, 9
Median = mean of 4 and 5
= 4.5

4. Measures of Central Tendency
Mode: The most common value in the set
Ex: Find the Mode: 2, 5, 6, 1, 2, 7, 9
Mode = 2
Ex: Find the Mode: 3, 5, 6, 1, 8, 10, 12
Mode: none
Ex: Find the Mode: 4, 8, 0, 9, 8, 3, 4
Mode: 4 and 8

5. Let’s Try One
Find the mean, median, and mode for these values: 78, 87, 84, 75, 80, 98, 78, 95, 72.
( ) 9
747
= = 83 x =
Use the symbol to designate the mean. x
72  75  78  78  80  84  87  95  98 Find the median and the
mode by ordering the values
numerically.
Mode Median
The mean is 83, the median is 80, and the mode is 78.

6. Median of the data (Q2) or Quartile 2 (72.5)
Vocabulary: Quartile
Take a set of data and arrange it from least to greatest. Find the median. Then sub-divide the lower half of the data and find the median. Repeat with the upper half of the data. The values separating the four parts are called quartiles.
Median of the lower part (Q1) or Quartile 1 (60.5)
Median of the lower part (Q3) or Quartile 3 (83)
Median of the data (Q2) or Quartile 2 (72.5)

7. Box and Whiskers Plot
A Box and Whiskers Plot is a method of displaying data that uses quartiles to form the center of the box and the minimum and maximum values to form the whiskers
2nd Quartile Q2 (median)
Sample:
1st Quartile (Q1)
3rd Quartile (Q3)
Minimum
Maximum

8. The median is a value of the data set, it is removed for
Make a box-and-whisker plot for these values: 91, 95, 88, 85, 90, 97, 94, 100, 81.
Step 1:  Find the quartile values, the minimum value, and the maximum value.
81  85  88  90  91  94  95  97  100
Q2 = median = 91
The median is a value of the data set, it is removed for
the calculation of Q1 and Q3.
81 85 88   95 97 100
Q1 = = 86.5 Q3 = = 96
( ) 2
( )
The minimum value is 81 and the maximum value is 100.

9. Step 2:  Draw a number line for the base of your box-and-whisker plot.
Above the number line, plot the three quartiles, the minimum value,
and the maximum value.
Step 3: Finish your box-and-whisker plot by drawing a box through Q1
and Q3, a vertical line through the median, and line segments
from the box outward to the minimum and maximum values.

10. Let’s Try One
Make a box-and-whisker plot for these values: 34, 36, 47, 45, 28, 31, 29, 40
Step 1:  Find the quartile values, the minimum value, and the maximum value.
Q2 = median = 35
The median is a value of the data set, it is removed for
the calculation of Q1 and Q3.
Q1 = = 30 Q3 = = 42.5
( ) 2
( )
The minimum value is 28 and the maximum value is 47.

11. Step 2:  Draw a number line for the base of your box-and-whisker plot.
Above the number line, plot the three quartiles, the minimum value,
and the maximum value. 28 30 35
42.5 47
Step 3: Finish your box-and-whisker plot by drawing a box through Q1
and Q3, a vertical line through the median, and line segments
from the box outward to the minimum and maximum values.

12. Vocabulary: Percentile
A percentile is a value that divides the range of a data set into two parts such that the part below the percentile contains a given percent of the data

13. Example: Find the 30th and 60th percentiles for the
values below.
54 98 45 87 98 64 21 61 71 82 93 65 62 98 87 24 65 97 31 47
Step 1:  Order the values.
21 24 31 45 47 54 61 62 64 65 65 71 82 87 87 93 97 98 98 98
Step 2:  Find the number of values that fall below the 30th percentile
and the number that fall below the 60th percentile.
Of the 20, 30% should fall below the 30th percentile and
60% should fall below the 60th percentile.
20  30% = 20  0.30 = 6
Since 61 is greater than
6 values, 61 is at the
30th percentile.
20  60% = 20  0.60 = 12
Since 82 is greater than
12 values, 82 is at
the 60th percentile.
The value at the 30th percentile is 61 and the value at the
60th percentile is 82.

14. Let’s Try One Example: Find the 20th and 75th percentiles for the
values below.
54 98 45 87 98 64 21 61 71 82 93 65 62 98 87 24 65 97 31 47
Step 1:  Order the values.
21 24 31 45 47 54 61 62 64 65 65 71 82 87 87 93 97 98 98 98
Step 2:  Find the number of values that fall below the 20th percentile
and the number that fall below the 75th percentile.
Of the 20, 20% should fall below the 30th percentile and
75% should fall below the 60th percentile.
20  20% = 20  0.20 = 4
Since 47 is greater than
4 values, 47 is at the
20th percentile.
20  75% = 20  0.75 = 15
Since 93 is greater than
15 values, 93 is at
the 75th percentile.
The value at the 20th percentile is 47 and the value at the
75th percentile is 93.

15. Vocabulary: Outlier
An outlier is an item of data with a value substantially different than the rest of the items in the data

16. Identify an outlier for this set of values: 15 34 28 32 30 26 34.
15   26   28   30   32   34   34
Order the data.
Find the differences between
adjacent values.
15 is substantially different, so 15 is an outlier.

17. Using a Graphing Calculator to find Measures of Central Tendency

18. Using the data in the table, find the mean, median, and mode for the water temperatures in Dauphin Island, AL.
Gulf of Mexico Eastern Coast Water Temperatures (°F)
Location J F M A M J J A S O N D
Dauphin Island,
Alabama
Step 1: Use the STAT feature to enter data as L1 in your graphing calculator.
Step 2: Use the LIST feature
to access the MATH
menu. Find the mean.
12-3

19. Analyzing Data Step 3: Return to the same menu to find the median.
ALGEBRA 2 LESSON 12-3
Analyzing Data
(continued)
Step 3: Return to the same
menu to find the median.
Step 4: Use the STAT PLOT
feature to access PLOT 1.
Choose the histogram, L1,
and Frequency 1 options.
Then enter an appropriate
viewing window.
Step 5: Graph the data. Use the
TRACE feature to move to
the highest point of the graph.
On the screen, the mode appears
as the minimum value for the
cursor. The mode is 84.
The mode occurs two
times in the data.
The mean is about 69.1°F, the median is 71°F, and the mode is 84°F.
12-3

20. ALGEBRA 2 LESSON 12-3
Analyzing Data
Use a graphing calculator to find the quartiles of the water temperature data for Dauphin, AL in Additional Example 2.
Use the STAT PLOT feature to select a box-and-whisker plot.
Enter the window values.
Graph the box-and-whisker plot.
Use the TRACE feature to find the quartile values.
They are Q1 = 58, Q2 = 71, and Q3 = 81.
12-3