STATISTICS
Measures of Center
Mean……
• The mean is the average of a set of numbers.
( sum of the numbers)
mean 
total number of values
Example……
• Roy compared the
prices of a cd player at
5 stores. The prices at
each store were $80,
$95, $60, $90, and
$85.
• What was the mean
price of the cd
players?
• Answer:
(80  95  60  90  85)
5
410
mean 
 82
5
mean 
Example……
• George’s scores on 3
math tests were 70,
80, and 86.
• What score does he
need to make on the
4th test to have a final
average of 84?
• Answer:
(70  80  86  x )
84 
4
(236  x)
84 
4
(84)( 4)  236  x
336  236  x
x  100
Median……
• Definition: The number in the center of the data.
a. Odd # in set – median is middle
number.
b. Even # in set – median is the
average of the 2 numbers in the
center.
c. The numbers must be in order from smallest to
largest.
Example……
• Consider the following
• Arrange in Order:
scores:
30, 95, 95, 100, 100
• 95, 30, 100, 100, and
95.
• Odd # in set – median
is the middle number.
• Find the median.
30, 95, 95, 100 100
Example……
• Use the following
numbers:
• 8, 9, 9, 10, 11, 11
• Find the median.
• Even # in set:
• Average the 2 middle
numbers:
8, 9, 9, 10, 11, 11
(9  10) 19
median 

2
2
median  9.5
Example……
• Tracey had scores of
11, 10, 12, 6, 6, and 8
on her math quizzes.
What is her median
score?
• Arrange in Order 1st:
6, 6, 8, 10, 11, 12
• Even # in set –
average the 2 in the
middle.
6, 6, 8, 10, 11, 12
(8  10) 18
median 

2
2
median  9
Mode……
• The number that appears the most often.
• There can be more than one mode.
• There can also be no mode if each item appears only
once.
Example……
• Tony had scores of 12,
11, 10, 9, 10, 11, 12,
10, 11, 11.
• What is the mode of
his scores?
• Answer:
• It helps to put them in
order to see the
grouping:
9, 10,10,10,
11,11,11,11,12,12
• The mode is 11.
Example……
• Tina had scores of 90,
96, 94, 90, 98, and 94
on her science tests.
• What is the mode?
• Put in order first:
90, 90, 94, 94, 96, 98
• 2 scores appear twice
(the most).
• The mode is 90 and
94.
Example……
• Find the mode for the
high temperatures for
the week.
• Put in order first:
88, 90, 91, 92, 94, 97,
99
• 97, 92, 88, 99, 90, 91,
and 94.
• Each number occurs
only once, therefore
there is no mode.
Range……
• Definition:
The range is the difference between the greatest and
least values of the data set.
Example……
• Joyce’s bowling scores
are 148, 195, 193,
145, 186, and 149.
• What is the range of
her scores?
• Find the highest
number and the lowest
number in the set.
148, 195, 193, 145,
186, 149
• Subtract 195 and 145.
range  195  145  50
Which is the best to use?
• Mean, median, and mode are called measures of central
tendency. They tell something about where the data
tends to cluster, or where the center of the data is located.
• When the range is small, the mean is most likely to be the
best measure of central tendency.
Example……
• Ted’s earnings for 5 weeks were $84, $76, $86, $300, and
$76.
• Which measure of central tendency best describes her
typical wage?
• Why?
$76, $76, $84, $86, $300
• Mode = 76. It is too low because it is less than 3 other
measures. NO
• Mean = 124.4. It is too high because it is greater than 4
of the 5 salaries. NO
• Range = 224. Very Big. Mean is probably not good to
use.
• Median = 84. It is the most representative of the data.
YES.
BOX PLOTS
(BOX AND WHISKERS)
Boxplot
• A graph of a set of data obtained by drawing a horizontal
line from the minimum to maximum values with quartiles
labeled in between.
• It is a graphical plot of 5 specific values called the 5-
number summary.
5-number summary…..
Minimum – lowest number in set
Q1- middle number of the lower half
Median – middle number of entire set
Q3 – middle number of upper half
Maximum – highest number in set
Steps……
• 1. Find the 5-number
summary.
• 2. Draw and label a
scale of equal
intervals.
• 4. Put a box around
Q1 and Q3.
• 5. Draw a vertical line
through the median.
• 6. Draw “whiskers”
• 3. Place dots above
the 5 numbers
from the minimum to
Q1 and maximum to
Q3.
Example……
• Draw a box plot of the following data.
33, 38, 43, 30, 29, 40, 51, 27, 42, 23, 31
Example……
• Draw a box plot of the following data.
59, 60, 65, 52, 51, 64, 71, 48, 47, 40, 50
Assignment……
• Worksheet.