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. 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 50 53 58 47
To find the range of the daily high temperatures,
subtract the least value from the greatest value.
59 - 13 = 46

3. 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 50 53 58 47
To find the mean, find the sum of the data
59+50+50+13+40+46+50+53+58+57=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. 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 50 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.
13 40 46 47 49 50 50 53 58 59
49+50=99
99 2=49.5

5. 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 50 53 58 47
To find the mode, find the most common value.
It helps to place data in numerical order to find
the mode.
13 40 46 47 49 50 50 53 58 59
If there is not a value which appears more often
than another, then there is no mode.

6. 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 50 53 58 47
The daily high temperature in 1996 is the outlier.
Mean
59+50+49+13+40+46+50+53+58+57=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
13 40 46 47 49 50 50 53 58 59
49+50=99
99 2=49.5

8. 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.
59+50+49+13+40+46+50+53+58+57=494
465 10=46.5
40+46+47+49+50+50+53+58+59=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.
Predictions will vary: