In statistics, mode, median and mean are typical values to represent a pool of numerical observations. They are calculated from the pool of observations.
Mode is the most common value among the given observations. For example, a person who sells ice creams might want to know which flavour is the most popular.
Median is the middle value, dividing the number of data into 2 halves. In other words, 50% of the observations is below the median and 50% of the observations is above the median.
Mean is the average of all the values. For example, a teacher may want to know the average marks of a test in his class.
ModeThe mode of a set of observations is the value that occurs most frequently in the set. A set of observations may have no mode, one mode or more than one mode.
Example:
Find the mode of the following set of scores.
14 11 15 9 11 15 11 7 13 12
Solution:
The mode is 11 because 11 occurred more times than the other numbers
If the observations are given in the form of a frequency table, the mode is the value that has the highest frequency.
Example:
Find the mode of the following set of marks.
Marks |
1 |
2 |
3 |
4 |
5 |
Frequency |
6 |
7 |
7 |
5 |
3 |
Solution:
The marks 2 and 3 have the highest frequency. So, the modes are 2 and 3.
Note: The above example shows that a set of observations may have more than one mode.
Example:
Find the mode for each of the following frequency tables:
The frequency table below shows the weights of different bags of rice.
Weight (kg) |
45 |
50 |
55 |
60 |
65 |
70 |
75 |
80 |
Bags of rice (Frequency) |
8 |
11 |
7 |
10 |
9 |
10 |
12 |
8 |
There are 8 number cards with values 0 – 7. Each time a card is drawn at random and the card value is recorded. The frequency refers to the number of times a value is shown.
Card values |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
Frequency |
8 |
12 |
7 |
10 |
12 |
13 |
12 |
10 |
Solution:
a) Mode: 75 kg (highest frequency of 12)
b) Mode: 5 (highest frequency of 13)
Example:
The following frequency table shows the marks obtained by students in a quiz. Given that 4 is the mode, what is the least value for x?
Marks |
1 |
2 |
3 |
4 |
5 |
6 |
Number of students (Frequency) |
7 |
9 |
10 |
x |
9 |
11 |
Solution:
x is as least 12
(if x is less than 12 then 4 will not be the mode)
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