MODE IN STATISTICS

About "Mode in statistics"

Mode in statistics :

Mode is one of the measures of central tendency which can be defined as follows.

For a given set of observations, mode may be defined as the value that occurs the maximum number of times.

Thus, mode is that value which has the maximum concentration of the observations around it. This can also be described as the most common value with which, even, a layman may be familiar with.

Thus, if the observations are 5, 3, 8, 9, 5 and 6, then Mode (Mo) = 5 as it occurs twice and all the other observations occur just once.

The definition for mode also leaves scope for more than one mode. Thus sometimes we may come across a distribution having more than one mode. Such a distribution is known as a multi-modal distribution. Bi-modal distribution is one having two modes.

Furthermore, it also appears from the definition that mode is not always defined. As an example,

If the marks of 5 students are 50, 60, 35, 40, 56, there is no modal mark as all the observations occur once i.e. the same number of times. 

We may consider the following formula for computing mode from a grouped frequency distribution:

Where,

l₁  =  LCB of the modal class

f₀  =  frequency of the modal class

f₋₁  =  frequency of the pre modal class

f₁  =  frequency of the post modal class

C  =  class length of the modal class

Mode in statistics- Practice problem

Compute the mode for the following distribution

Solution :

Computation of mode

For the given data, the formula to find mode is given by 

Going through the frequency column, we note that the highest frequency i.e. f₀ is 82. 

So we have, 

f₋₁  =  58

f₁  =  65

Also, the modal class i.e. the class against the highest frequency is 410 - 419

Thus, 

l₁  =  LCB  =  409.50 

C  =  429.50 - 409.50  =  20

C  =  429.50 – 409.50  =  20

Plugging these values in the above formula, we get 

Mode  =  409.50 + [ (82-58) / (2x52 - 58 - 65) ] x 20

Mode  =  409.50 + 11.71

Mode  =  421.21

Relation among mean median and mode

When it is difficult to compute mode from a grouped frequency distribution, we may consider the following empirical relationship between mean, median and mode:

Mean - Mode  =  3(Mean - Median)

or

Mode  =  3 x median - 2 x mean

The above result holds for holds for a moderately skewed distribution.

We also note that if y  = a + bx, then we have

Mode of "y"  =  a + b (Mode of "x") 

For example, if y = 2 + 1.50x and mode of x is 15, then the mode of y is given by 

Mode of "y"  =  2 + 1.50(Mode of "x") 

Mode of "y"  =  2 + 1.50x15

Mode of "y"  =  2 + 22.50

Mode of "y"  =  24.50

Properties of mode

1)  Although mode is the most popular measure of central tendency, there are cases when mode remains undefined.

2)  Unlike mean, it has no mathematical property.

3)  Mode is affected by sampling fluctuations.

After having gone through the stuff given above, we hope that the students would have understood "Mode in statistics". 

Apart from the stuff given above, if you want to know more about "Mode in statistics",please click here

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6