Download Arithmetic Mean, Median and Mode2015.2

Mean, Median, and
Mode Plus Range
The 3 Central Tendencies:
Mean, Median and Mode
LEARNING GOALS:
• To use the Arithemetic Mean, Median and
Mode in a set of values.
• To collaborate and use mathematical
language during collaborative group work
and oral presentations.
• To use real-life problem-solving for the 3
central tendencies (i.e. arithmetic mean,
median and mode).
The Arithmetic Mean
The sum of a list of
numbers, divided by
the total number of
numbers in that list
M= S/N
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 Arithmetic 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}
Find The Arithmetic 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}
Sum= 1+2+4+4+5+7+11
Mean = 34÷5 = 4.9
3. {25, 26, 27, 36, 42, 52}
Mean= 209÷6 = 34.8
The Median
The middle value
in an ordered list
of numbers
Example 1
• Find the median of 10, 13, 8, 7, 12.
• Order: 7, 8, 10, 12, 13
• Median = 10
How To Find The Median
REAL LIFE PROBLEM-SOLVING:
Find the median number of part-time hours worked
during a seven day week.
Sunday Monday Tuesday Wednesday Thursday Friday
4
3
1
4
2
0
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.
Saturday
4
Example 2
• Find the median of 44, 46, 39, 50, 39, 40.
• Order: 39, 39, 40, 44, 46, 50
• Median = (40 + 44) ÷ 2 = 42
Oh Oh!!!
{10, 12, 16, 18, 20, 24}
What do you do if there are an even amount of
numbers in your data set?
< 2 middle numbers >
You take the mean 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}
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
Reflections
• Sucess Criteria: BUCK
• Self-checking Strategies
SQ-RCRC
Any Questions