Mean, Median, and
Mode
An Introduction to Data
Management:
Measures of Central
Tendencies
Why Analyze Data?
Data is collected to answer questions.
When we want to answer a question, we
collect data to provide information on
that topic. We take the collected data
and analyze it to find out if there are any
relationships.
DATA IS COLLECTED TO FIND ANSWERS TO
MANY DIFFERENT QUESTIONS.
The Mean
The sum of a list of
numbers, divided by
the total number of
numbers in that list
(average is another word for mean)
What Does SUM Mean?
The answer to an addition problem.
For example, the sum of 1 and 2 is 3.
1+2=3
How To Find The Mean
Question
A farmer wanted to know the daily mean for the number of eggs laid by his prize
hen for the last seven days. The hen laid 4 eggs on Sunday, 3 eggs on Monday, 1
egg on Tuesday, 4 eggs on Wednesday, 2 eggs on Thursday, 0 eggs on Friday, and
4 eggs on Saturday.
Sunday Monday Tuesday Wednesday Thursday Friday
4
3
1
4
2
0
1. Find the sum of the numbers
Saturday
4
4+3+1+4+2+0+4 = 18
2. Divide the sum by how many numbers you have
18÷7 = 2.6
Mean = 2.6
The hen laid an average of 2.6 eggs per day during that 7 day
period.
Your Turn…
Monday Tuesday Wednesday Thursday Friday
12
16
25
10
32
To find the mean first
you_________________, then
_________________________
Checking Your Answer
Monday
12
Tuesday
16
Wednesday
25
Thursday
10
Friday
32
1. Find the sum of the numbers
12+16+25+10+32=95
2. Divide the sum by how many numbers you have
95÷5=19
The daily average of milk cartons sold from the
vending machine during the first week of school
was 19 milk cartons per day.
Find The Mean
SHOW YOUR WORK –
GET IN THE HABIT NOW!
1. {8, 9, 12, 16, 18}
2. {1, 2, 4, 4, 5, 7, 11}
3. {25, 26, 27, 36, 42, 52}
4. {120, 134, 165, 210, 315}
Find The Mean
1. {8, 9, 12, 16, 18}
8+9+12+16+18 = 63÷5 = 12.6
2. {1, 2, 4, 4, 5, 7, 11}
1+2+4+4+5+7+11 = 34÷5 = 4.9
3. {25, 26, 27, 36, 42, 52}
25+26+27+36+42+52 = 209÷6 = 34.8
4. {120, 134, 165, 210, 315, 356}
120+134+165+210+315+356 = 1300÷5 = 216.7
The Median
The middle
value in a list
of numbers
How To Find The Median
Question
The eggs laid by a prize hen were recorded for a week. The hen laid 4 eggs
on Sunday, 3 eggs on Monday, 1 egg on Tuesday, 4 eggs on Wednesday, 2
eggs on Thursday, 0 eggs on Friday, and 4 eggs on Saturday. What is the
median?
Sunday Monday Tuesday Wednesday Thursday Friday
4
3
1
4
2
0
Saturday
4
1. Place the numbers in order, from least to greatest.
0, 1, 2, 3, 4, 4,4
2. Find the number that is in the middle of the data set
0, 1, 2, 3, 4, 4, 4
3 is the median of this data set.
Your Turn…
Question
The number of milk cartons sold from the school
vending machine were recorded for the first full
week of school. 12 were sold on Monday, 16 were
sold on Tuesday, 25 were sold on Wednesday, 10
were sold on Thursday, and 32 were sold on
Friday. What is the median?
Checking Your Answer
Monday
12
Tuesday
16
Wednesday Thursday
25
10
Friday
32
1. Place the numbers in order, from least to greatest.
10, 12, 16, 25, 32
2. Find the middle value
10, 12, 16, 25, 32
The median for this data set is 16.
Oh Oh!!!
What do you do if there are an even amount of
numbers in your data set?
< 2 middle numbers >
{10, 12, 16, 18, 20, 24}
You take the average of the two middle values.
16+18 = 34÷2 = 17
The median of this data set is 17.
Find The Median
1. {8, 9, 12, 16, 18}
2. {4, 2, 6, 4, 1, 7, 11}
3. {25, 26, 27, 36, 42, 52}
4. {120, 134, 165, 210, 315, 356}
Find The Median
1. {8, 9, 12, 16, 18}
8, 9, 12, 16, 18
2. {4, 2, 6, 4, 1, 7, 11}
1, 2, 4, 4, 6, 7, 11
3. {25, 26, 27, 36, 42, 52}
25, 26, 27, 36, 42, 52 = 27+36 = 31.5
4. {120, 134, 165, 210, 315, 356}
120, 134, 165, 210, 315, 356 = 187.5
The Mode
The most common
value or the value with
the highest frequency
in a data set.
How To Find The Mode
Question
The eggs laid by a prize hen were recorded for a week. The hen laid 4 eggs
on Sunday, 3 eggs on Monday, 1 egg on Tuesday, 4 eggs on Wednesday, 2
eggs on Thursday, 0 eggs on Friday, and 4 eggs on Saturday. What is the
mode?
Sunday Monday Tuesday Wednesday Thursday Friday
4
3
1
4
2
0
Saturday
4
1. Place the numbers in order, from least to greatest.
0, 1, 2, 3, 4, 4,4
2. Find the number that has the highest frequency in the data set.
0, 1, 2, 3, 4, 4, 4
4 is the mode of this data set.
Your Turn…
Question
The number of milk cartons sold from the school
vending machine were recorded for the first full
week of school. 12 were sold on Monday, 16 were
sold on Tuesday, 25 were sold on Wednesday, 10
were sold on Thursday, and 32 were sold on
Friday. What is the mode?
Checking Your Answer
Monday
12
Tuesday
16
Wednesday
25
Thursday
10
Friday
32
1. Place the numbers in order, from least to greatest.
10, 12, 16, 25, 32
2. Find the value that has the highest frequency in the data set.
10, 12, 16, 25, 32
There is no mode for this data set.
Find The Mode
1. {8, 9, 12, 16, 18}
2. {1, 2, 4, 4, 5, 7, 11}
2. {25, 26, 27, 36, 42, 52}
3. {120, 134, 165, 210, 315, 356}
Find The Mode
1. {8, 9, 12, 16, 18}
There is no mode in this data set.
2. {1, 2, 4, 4, 5, 7, 11}
The mode is 4.
3. {25, 26, 27, 36, 42, 52}
There is no mode in this data set.
4. {120, 134, 165, 210, 315, 356}
There is no mode in this data set.
Oh Oh!!!
What do you do if there is more than one value
that occurs at the highest frequency?
{10, 12, 12, 16, 18, 18, 20, 24}
The mode for this data set is 12 and 18.
You can have more than one mode for a data set.
Finding The Range
-
Range: The distance between the
maximum and the minimum number
Range = Max – Min
Example: 4, 6, 30, 24
Range = 30 – 4
Range = 26
Find The Range
1. {8, 9, 12, 16, 18}
18 – 8 = 10 The range is 10
2. {3, 5, 2, 4, 5, 7, 2}
7 – 2 = 5 The range is 5. Finding the
range is easier if you put the numbers in
order from least to greatest first
{120, 134, 165, 210, 315, 356}
356 – 120 = 234 The range is 234
Any Questions