# MIXED QUESTIONS ON MEAN MEDIAN AND MODE FOR UNGROUPED DATA

## About "Mixed Questions on Mean Median and Mode for Ungrouped Data"

Mixed Questions on Mean Median and Mode for Ungrouped Data :

Here we are going to see some practice questions on mean, median and mode for ungrouped data.

## Mixed Questions on Mean Median and Mode for Ungrouped Data - Practice questions

Question 1 :

The monthly salary of 10 employees in a factory are given below :

₹ 5000, ₹ 7000, ₹ 5000, ₹ 7000, ₹ 8000, ₹ 7000, ₹ 7000,₹ 8000, ₹ 7000, ₹ 5000 Find the mean, median and mode

Solution :

Mean = (5000 + 7000 +  5000 + 7000 + 8000 + 7000 + 7000 + 8000 + 7000 + 5000)/10

=  66000/10

=  6600

Median :

5000, 5000, 5000, 7000, 7000, 7000, 7000, 7000,  8000, 8000

Number of observations  =  10 (Even)

Median  =  {(10/2)th observation + [(10/2) + 1]th}/2

=  (5th observation + 6th observation)/2

=  (7000 + 7000)/2

=  14000/2

=  7000

Mode :

7000 is repeating 5 times. Hence mode is 7000.

Question 2 :

Find the mode of the given data : 3.1, 3.2, 3.3, 2.1, 1.3, 3.3, 3.1

Solution :

3.1 and 3.3 are repeating twice, so mode is 3.1 and 3.3

It is a bimodal data.

Question 3 :

For the data 11, 15, 17, x+1, 19, x–2, 3 if the mean is 14 , find the value of x. Also find the mode of the data.

Solution :

Mean  =  (11 + 15 + 17 + x + 1 + 19 + x - 2 + 3)/7

14  =  (64 + 2x)/7

14(7)  =  64 + 2x

2x  =  98 - 64

2x  =  34

x  =  34/2  =  17

By applying the value of x in the given observation, we get

11, 15, 17, 18, 19, 15, 3

Mode  =  15 (Repeating twice)

Question 4 :

The demand of track suit of different sizes as obtained by a survey is given below: Solution :

Demand for the size 40 is 37.

Hence the demand of size 40 is high.

## Steps in Finding the Mode of Grouped Data

In case of a grouped frequency distribution, the exact values of the variables are not known and as such it is very difficult to locate mode accurately The class interval with maximum frequency is called the modal class.

Where l - lower limit of the modal class;

f - frequency of the modal class

f1 - frequency of the class just preceding the modal class

f2 - frequency of the class succeeding the modal class

c - width of the class interval

Question 5 :

Find the mode of the following data: Solution :

 Marks0-1010-2020-3030-4040-50 Number of students2238463420

The highest frequency is 46

modal class is 20 - 30

l = 20, f = 46, f1 = 38, f2 = 34, c = 10

=  20 + [(46-38)/2(46) - 38 - 34] x 10

=  20 + [8/(92 - 38 - 34)] x 10

=  20 + [8/20] x 10

=  20 + 4

=  24

Hence the mode is 24.

Question 6 :

Find the mode of the following distribution: Solution :

 Marks24.5 - 34.534.5 - 44.544.5 -  54.554.5 - 64.564.5 -  74.574.5 - 84.5 Number of students48101486

The highest frequency is 14

modal class is 54.5 - 64.5

l = 54.5, f = 14, f1 = 10, f2 = 8, c = 10

=  54.5 + [(14 - 10)/2(14) - 10 - 8] x 10

=  54.5 + [4/(28 - 18)] x 10

=  54.5 + [4/10] x 10

=  54.5 + 4

=  58.5

Hence the mode is 58.5. After having gone through the stuff given above, we hope that the students would have understood, "Mixed Questions on Mean Median and Mode for Ungrouped Data"

Apart from the stuff given in this section 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

Word problems on simple equations

Word problems on linear 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 