MIXED QUESTIONS ON MEAN MEDIAN AND MODE FOR UNGROUPED DATA

Question 1 :

The monthly salary (in $) 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

  =  (5^th observation + 6^th 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

Question 5 :

Find the mode of the following data:

Solution :

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 :

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.

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