Mode
As we have said Mean is not the only measure of central tendency or the only form of representative value. For different requirements from a data, other measures of central tendencies are used.
Look at the following example.
To find out the weekly demand for different sizes of shirt, a shopkeeper kept records of sales of sizes 90 cm, 95 cm, 100 cm, 105 cm, 110 cm.
Following is the record for a week:
| Size (in cm) | Number of Shirts Sold |
|---|---|
| 90 cm | 8 |
| 95 cm | 22 |
| 100 cm | 37 |
| 105 cm | 32 |
| 110 cm | 6 |
| Total |
If he found the mean number of shirts sold, do you think that he would be able to decide which shirt sizes to keep in stock? Let's see.
Mean of total shirts sold =
Should he obtain 21 shirts of each size? If he does so, will he be able to cater to the needs of the customers?
He will not be able to cater to customers who need shirts in sizes
The shopkeeper, on looking at the record, decides to procure shirts of sizes 95 cm,100 cm, 105 cm. He decided to postpone the procurement of the shirts of other sizes because of their small number of buyers.
Look at another example
The owner of a readymade dress shop says, “The most popular size of dress I sell is the size 90 cm".
Observe that here also, the owner is concerned about the number of shirts of different sizes sold. She is however looking at the shirt size that is sold the most. This is another representative value for the data. The highest occuring event is the sale of size 90 cm. This representative value is called the mode of the data.
The mode of a set of observations is the observation that occurs most often.
Find the mode of the given set of numbers: 1, 1, 2, 4, 3, 2, 1, 2, 2, 4.
Solution : Arranging the numbers with same values together, we get.
= 1, 1, 1,
Mode of this data is 2 because it occurs more frequently than other observations.
Mode of Large Data
Putting the same observations together and counting them is not easy if the number of observations is large.
Ready for a quick game?
Click on start, enter the number which repeats the most(mode). You have to find the answer in 5 secs.
1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2
Enter your answer here: ${res}
Timer: ${timer}
It was tough, right? It's hard to quickly visualize and guess the number which comes the highest number of times. In such cases we tabulate the data. Tabulation can begin by putting tally marks and finding the frequency, as you did in your previous class.
Look at the following example:
Following are the margins of victory in the football matches of a league. Which margin of victory comes the most?
1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2.
Solution :
Let us put the data in a tabular form:
| Margins of victory | Tally Bars | Number of Matches |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
Looking at the table, we can quickly say that
Since 2 has occured the highest number of times.
Thus, most of the matches have been won with a victory margin of 2 goals.
1. Find the mode?
Example1
To find the mode of a set of numbers, we need to identify the number(s) that appear most frequently
(i) 2, 6, 5, 3, 0, 3, 4, 3, 2, 4, 5,2, 4
Solution:
1.Frequency Calculation:
| Number | 0 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Repeats | 1 | 3 | 3 | 3 | 2 | 1 |
2.Determine the Mode:
The numbers 2, 3, and 4 each appear
So, the modes are 2,3, and 4.
Example2
(ii) 2, 14, 16, 12, 14, 14, 16,14, 10, 14, 18, 14
Solution:
Data Set: 2, 14, 16, 12, 14, 14, 16,14, 10, 14, 18, 14
1.Frequency Calculation:
| Number | 2 | 10 | 12 | 14 | 16 | 18 |
|---|---|---|---|---|---|---|
| Repeats | 1 | 1 | 1 | 6 | 2 | 1 |
2.Determine the Mode:
The number 14 appears
So, the mode is 14.
Find the mode of the numbers: 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 8
Solution :
Here,
1. Find the mode of the following data:
12, 14, 12, 16, 15, 13, 14, 18, 19, 12, 14, 15, 16, 15, 16, 16, 15,17, 13, 16, 16, 15, 15, 13, 15, 17, 15, 14, 15, 13, 15, 14
2. Heights (in cm) of 25 children are given below:
168, 165, 163, 160, 163, 161, 162, 164, 163, 162, 164, 163, 160, 163, 160,165, 163, 162, 163, 164, 163, 160, 165, 163, 162 What is the mode of their heights? What do we understand by mode here?