12.1.2 Mode, Median and Mean
1. The mode of a set of data is the value of item which occurs most frequently.
Example:
3, 7, 6, 9, 7, 1, 5, 7, 2
Mode = 7
2. When a set of data is given in a frequency table, the value or item which has the highest frequency is the mode.
3. The median of a set of data is the value located in the middle of the set when the data is arranged in numerical order.
- If the total number of data is odd, then the median is the value in the middle of the set.
- If the total number of data is even, then the median is the average of the two middle values of the set
Example 1:
Find the medians of the following sets of data:
Find the medians of the following sets of data:
(a) 10, 9, 11, 6, 5, 8, 7
(b) 10, 9, 11, 6, 5, 8, 7,12
Solution:
(a) Number of data values = 7 ← (Odd number)
Rearranging the data in order of magnitude:
5, 6, 7, 8, 9, 10, 11
Therefore, median = 8
(b) Number of data values = 8 ← (Even number)
Rearranging the data in order of magnitude:
5, 6, 7, 8, 9, 10, 11, 12
∴Median=8+92=8.5∴Median=8+92=8.5
4. When a set of data is given in a frequency table, the value situated in the middle position of the data is the median.
5. The mean of a set of data is obtained by using formula below.
Mean =sum of all values of datatotal number of data
Example:
Find the mean of the following sets of data items:
-5, -2, -1, 7, 4, 9
Solution:
Mean=(−5)+(−2)+(−1)+7+4+96=126=2
6. When data is given in a frequency table, the mean can be found by using the formula below.
Mean =sum of(value×frequency)total frequency
Example:
The table below shows the scores obtained by a group of players in a game.
The table below shows the scores obtained by a group of players in a game.
|
Score
|
1
|
2
|
3
|
4
|
5
|
|
Frequency
|
5
|
12
|
8
|
15
|
10
|
Find the mean of the scores.
Solution:
Mean=sum of(score×frequency)total frequency=(1×5)+(2×12)+(3×8)+(4×15)+(5×10)5+12+8+15+10=16350=3.26
