Transcript Mean, Median, and Mode

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
Example
• Find the mean of 10, 12, 14, 17, 20.
• Sum = 10 + 12 + 14 + 17 + 20
• Sum = 73
• Mean = 73 ÷ 5
• Mean = 14.6
Find The Mean
SHOW YOUR WORK –
Round to 1 decimal place!
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, 356}
Find The Mean
1. {8, 9, 12, 16, 18}
Sum = 8+9+12+16+18 = 63
Mean = 63÷5 = 12.6
2. {1, 2, 4, 4, 5, 7, 11}
Mean = 34÷5 = 4.9
3. {25, 26, 27, 36, 42, 52}
Mean= 209÷6 = 34.8
4. {120, 134, 165, 210, 315, 356}
Mean = 1300÷5 = 216.7
The Median
The middle value
in an ordered list
of numbers
How To Find 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.
Example 1
• Find the median of 10, 13, 8, 7, 12.
• Order: 7, 8, 10, 12, 13
• Median = 10
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 mean of the two middle values.
16+18 = 34÷2 = 17
The median of this data set is 17.
Example 2
• Find the median of 44, 46, 39, 50, 39, 40.
• Order: 39, 39, 40, 44, 46, 50
• Median = (40 + 44) ÷ 2 = 42
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)÷2 = 31.5
4. {120, 134, 165, 210, 315, 356}
120, 134, 165, 210, 315, 356 
(165 + 210 )÷2 = 187.5
The Mode
The most common
value or the value with
the highest frequency
in a data set.
Example
• Find the mode of 14, 15, 20, 20, 14, 20, 5.
• Mode = 20 (it occurs the most)
• Find the mode of 14, 15, 20, 20, 14, 5.
• Mode = 14 and 20 (both occur twice)
• Find the mode of 14, 15, 20, 21, 12, 10, 5.
• Mode = No mode (no number occurs more than
once)
Find The Mode
1. {8, 9, 12, 16, 18}
2. {1, 2, 4, 4, 5, 7, 11}
2. {25, 26, 27, 36, 42, 52, 26, 27}
3. {120, 134, 165, 210, 315, 356, 120, 120, 210}
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, 26, 27}
The mode is 26 AND 27.
4. {120, 134, 165, 210, 315, 356, 120, 120, 210}
The mode is 120 – it occurs more than 210!
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}
2. {3, 5, 2, 4, 5, 7, 2}
3. {120, 134, 165, 210, 315, 356}
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
3. {120, 134, 165, 210, 315, 356}
356 – 120 = 234 The range is 234
Any Questions