Mode Lecture 08

 Mode 

Lecture 08

Mode

Mode is a French word that means fashion. The thing that is very common in our daily lives is called fashion. Mode is also a central measure of data. Mode is an important measure of central tendency and is used in some specific situations.

For example, 

* The educational institutions to determine the most common learning challenges that students face.

* The health care professionals use mode to identify the most common disease in a particular area or season.

* The government uses mode to identify the most common crops and livestock. 

Definition

The most frequent value or values in a dataset.

In gruoped data mode, it can be obtained by the following formula:

Where:

h = L2 - L1

L1 & L2 are the lower and upper class boundaries, respectively.

Example 3. 26: The score of a student in the last 10 tests is given below:

8, 6, 10, 9, 8, 5, 7, 8, 4, 6.

What is the model score?

Solution: Just by looking at the data, we find the frequency of 8 is 3 and more than the frequency of all others.

So, mode of the data is 8.

Example 3.27: Estimate mode for the following frequency distribution.

Classes	1 – 5	6 – 10	11 - 15	16 – 20	21- 25
Frequency	2	7	8	3	1

Solution:

Classes	Class boundaries	Frequency
1 – 5	0.50 – 5.50	2
6 – 10	5.50 – 10.50	7
11 – 15	10.50 – 15.50	8
16 – 20	15.50 – 20.50	3
21- 25	20.50 – 25.50	1

The class 10.50–15.50 has maximum frequency, so it is called a model class. The frequency of the model class is denoted by fm.

Mode can be obtained from Histogram

i. Identify the tallest bar. This represents the modal class.

ii. Join the tips of this to those of the neighboring bars on either side, with the one on the left joined to that on the right. The lines used to join these tips cross each other at some point in this bar.

iii. Drop a perpendicular line from the tip of the point where these lines meet to the base of the bar. The point where it meets the base is the mode.

Example 3.28: Construct a histogram graphically for the following frequency distribution.

Mark	10 – 19	20 – 29	30 – 39	40 – 49	50 – 59	60-69	70 – 79
No. of students	10	12	18	30	16	6	8

Solution:

Marks	Class boundaries	Frequency
10 – 19	9.50 – 19.50	10
20 – 29	19.50 – 29.50	12
30 – 39	29.50 – 39.50	18
40 – 49	39.50 – 49.50	30
50 – 59	49.50 – 59.50	16
60-69	59.50 – 69.50	6
70 – 79	69.50 – 79.50	8

Mode = 44.12 

Advantages and limitations of Mode.

Some advantages of mode are given below:

i. It is easy to calculate.

ii. It is not affected by extreme values.

iii. It can be useful for qualitative data.

iv. It can be located graphically.

Some limitations of mode are given below:

i. It is not based on all the values.

ii. It is not well defined.

iii. Its capability for further mathematical treatment is limited.

• Read: Median