1. Range and Measures of Central Tendency
Range and measures of central tendency (mean, median and mode) are values that summarize a set of data. They are useful when analyzing data.

2. Daily High Temperatures (for any given date) Over the Last Decade
Range -
the difference between the greatest and the least values in a data set
Daily High Temperatures (for any given date) Over the Last Decade
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002 59 50 49 13 40 46 53 58 47
To find the range of the daily high temperatures, subtract the least value from the greatest value.
59° - 13° = 46°

3. Daily High Temperatures (for any given date) Over the Last Decade
Mean -
(or average) the sum of a set of data divided by the number of data
Daily High Temperatures (for any given date) Over the Last Decade
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002 59 50 49 13 40 46 53 58 47
To find the mean, find the sum of the data
=465
and divide it by the number of data.
465÷10=46.5
The mean for daily high temperature over the last decade is 46.5°, or approximately 47°.

4. Daily High Temperatures (for any given date) Over the Last Decade
Median -
the middle value of a data set
Daily High Temperatures (for any given date) Over the Last Decade
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002 59 50 49 13 40 46 53 58 47
To find the median, place all the data in numerical order, then find the middle number. If there are two middle numbers, find the mean (or average) of the two middle numbers.
49+50=99
99÷2=49.5

5. Daily High Temperatures (for any given date) Over the Last Decade
Mode -
the most common value in a data set
Daily High Temperatures (for any given date) Over the Last Decade
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002 59 50 49 13 40 46 53 58 47
To find the mode, find the most common value. It helps to place data in numerical order to find the mode.
If there is not a value which appears more often than another, then there is no mode.

6. Daily High Temperatures (for any given date) Over the Last Decade
Outliers
Sometimes there are extreme values that are separated from the rest of the data. These extreme values are called outliers. Outliers affect the mean.
Daily High Temperatures (for any given date) Over the Last Decade
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002 59 50 49 13 40 46 53 58 47
The daily high temperature in 1996 is the outlier.
Mean
=494
465÷10=46.5

7. Because outliers can affect the mean, the median may be better measures of central tendency. You might consider the median to best represent the expected temperature.
Median
49+50=99
99÷2=49.5

8. Sometimes the mode is more helpful when analyzing data
Sometimes the mode is more helpful when analyzing data. If you were trying to determine what clothes to wear for a day trip, you might base your decision on the mode temperature because the mode temperature is the temperature which occurred most often.
13° 40° 46° 47° 49° 50° 50° 53° 58° 59°

9. Dropping the outlier may help when determining the mean.
=494
465÷10=46.5°
=452
452÷9=50.2°
When the 13° outlier is dropped, the average daily temperature increases by more than 4° to 50.2°, which is closer to both the median of 49.5° and the mode of 50°.

10. You Try It!
Jessica’s test scores in Algebra for the first semester are 93, 79, 88, 77, 92, 88, 80, 34, 84, 88. Calculate the range, mean, median, and mode. Then make and explain a prediction for next semester’s test scores.
Range: 59
Mean: 80.3
Median: 86
Mode: 88
Predictions will vary: Jessica will score an estimated average of 85 on her tests. I determined this by removing the outlying score of 34 and recalculated the mean.

11. Presentation developed by W. D. Martin. © 2003 www
Presentation developed by W. D. Martin © Rev