Mean, Median and Mode of Ungrouped Data - Exercise 18D | Extra Documents & Tests for Class 9 PDF Download

 Page 1


        
Q u e s t i o n : 5 6
Find the mode of the following items.
0, 6, 5, 1, 6, 4, 3, 0, 2, 6, 5, 6
S o l u t i o n :
On arranging the items in ascending order, we get:
0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 6, 6
Clearly, 6 occurs maximum number of times.
? Mode = 6
Q u e s t i o n : 5 7
Determine the mode of the following values of a variable.
23, 15, 25, 40, 27, 25, 22, 25, 20
S o l u t i o n :
On arranging the values in ascending order, we get:
15, 20, 22, 23, 25, 25, 25, 27, 40
Clearly, 25 occurs maximum number of times.
? Mode = 25
Q u e s t i o n : 5 8
Calculate the mode of the following sizes of shoes sold by a shop on a particular day.
5, 9, 8, 6, 9, 4, 3, 9, 1, 6, 3, 9, 7, 1, 2, 5, 9
S o l u t i o n :
On arranging the shoe sizes in ascending order, we get:
1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 9, 9
Clearly, 9 occurs maximum number of times.
? Mode = 9
Q u e s t i o n : 5 9
A cricket player scored the following runs in 12 one-day matches:
50, 30, 9, 32, 60, 50, 28, 50, 19, 50, 27, 35.
Find his modal score.
S o l u t i o n :
On arranging the runs in ascending order, we get:
9, 19, 27, 28, 30, 32, 35, 50, 50, 50, 50, 60
Clearly, 50 occurs maximum number of times.
? Modal score = 50
Q u e s t i o n : 6 0
If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x. Using this value of x, find the mode of the data.
S o l u t i o n :
We know that,
Mean =
Sum of observations
Number of observations
The given data is 3, 21, 25, 17, (x + 3), 19, (x – 4).
Mean of the given data = 
3+21+25+17+(x+3)+19+(x-4)
7
? 18(7) = 84 +2x ? 126 -84 = 2x ? 2x = 42 ? x = 21
Hence, the value of x is 21.
Now, the given data is 3, 21, 25, 17, 24, 19, 17
Arranging this data in ascending order:
3, 17, 17, 19, 21, 24, 25
Here, 17 occurs maximum number of times.
? Mode = 17
Hence, the mode of the data is 17.
Q u e s t i o n : 6 1
The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data.
S o l u t i o n :
Arranging the given data in ascending order:
52, 53, 54, 54, (2x + 1), 55, 55, 56, 57
Number of terms = 9 odd
? Median =
n+1
2
th
 term ? 55 =
9+1
2
th
 term ? 55 = (5)
th
 term ? 55 = 2x +1 ? 2x = 55 -1 ? 2x = 54 ? x = 27
Hence, the value of x is 27.
Arranging the given data in ascending order:
52, 53, 54, 54, 55, 55, 55, 56, 57
Here, 55 occurs maximum number of times.
? Mode = 55
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Q u e s t i o n : 5 6
Find the mode of the following items.
0, 6, 5, 1, 6, 4, 3, 0, 2, 6, 5, 6
S o l u t i o n :
On arranging the items in ascending order, we get:
0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 6, 6
Clearly, 6 occurs maximum number of times.
? Mode = 6
Q u e s t i o n : 5 7
Determine the mode of the following values of a variable.
23, 15, 25, 40, 27, 25, 22, 25, 20
S o l u t i o n :
On arranging the values in ascending order, we get:
15, 20, 22, 23, 25, 25, 25, 27, 40
Clearly, 25 occurs maximum number of times.
? Mode = 25
Q u e s t i o n : 5 8
Calculate the mode of the following sizes of shoes sold by a shop on a particular day.
5, 9, 8, 6, 9, 4, 3, 9, 1, 6, 3, 9, 7, 1, 2, 5, 9
S o l u t i o n :
On arranging the shoe sizes in ascending order, we get:
1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 9, 9
Clearly, 9 occurs maximum number of times.
? Mode = 9
Q u e s t i o n : 5 9
A cricket player scored the following runs in 12 one-day matches:
50, 30, 9, 32, 60, 50, 28, 50, 19, 50, 27, 35.
Find his modal score.
S o l u t i o n :
On arranging the runs in ascending order, we get:
9, 19, 27, 28, 30, 32, 35, 50, 50, 50, 50, 60
Clearly, 50 occurs maximum number of times.
? Modal score = 50
Q u e s t i o n : 6 0
If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x. Using this value of x, find the mode of the data.
S o l u t i o n :
We know that,
Mean =
Sum of observations
Number of observations
The given data is 3, 21, 25, 17, (x + 3), 19, (x – 4).
Mean of the given data = 
3+21+25+17+(x+3)+19+(x-4)
7
? 18(7) = 84 +2x ? 126 -84 = 2x ? 2x = 42 ? x = 21
Hence, the value of x is 21.
Now, the given data is 3, 21, 25, 17, 24, 19, 17
Arranging this data in ascending order:
3, 17, 17, 19, 21, 24, 25
Here, 17 occurs maximum number of times.
? Mode = 17
Hence, the mode of the data is 17.
Q u e s t i o n : 6 1
The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data.
S o l u t i o n :
Arranging the given data in ascending order:
52, 53, 54, 54, (2x + 1), 55, 55, 56, 57
Number of terms = 9 odd
? Median =
n+1
2
th
 term ? 55 =
9+1
2
th
 term ? 55 = (5)
th
 term ? 55 = 2x +1 ? 2x = 55 -1 ? 2x = 54 ? x = 27
Hence, the value of x is 27.
Arranging the given data in ascending order:
52, 53, 54, 54, 55, 55, 55, 56, 57
Here, 55 occurs maximum number of times.
? Mode = 55
( ) ( )
Hence, the mode of the data is 55.
Q u e s t i o n : 6 2
For what value of x is the mode of the data 24, 15, 40, 23, 27, 26, 22, 25, 20, x + 3 found 25? Using this value of x, find the median.
S o l u t i o n :
Given: Mode = 25
? 25 occurs maximum number of times.
Arranging the given data in ascending order:
15, 20, 22, 23, 24, x + 3, 25, 26, 27, 40
? x + 3 = 25
? x = 25 - 3
? x = 22
Hence, the value of x is 22.
Arranging the given data in ascending order:
15, 20, 22, 23, 24, 25, 25, 26, 27, 40
Number of terms = 10 even
? Median = mean of 
n
2
th
 term and 
n
2
+1
th
 term                   = mean of 
10
2
th
 term and 
10
2
+1
th
 term                   = mean of (5)
th
 term and (6)
th
 term                   = mean of [24 and 
Hence, the median is 24.5 .
Q u e s t i o n : 6 3
The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45. Find the value of x. Hence, find the mode of the above data.
S o l u t i o n :
Arranging the given data in ascending order:
42, 43, 44, 44, (2x + 3), 45, 45, 46, 47
Number of terms = 9 odd
? Median =
n+1
2
th
 term ? 45 =
9+1
2
th
 term ? 45 = (5)
th
 term ? 45 = 2x +3 ? 2x = 45 -3 ? 2x = 42 ? x = 21
Hence, the value of x is 21.
Arranging the given data in ascending order:
42, 43, 44, 44, 45, 45, 45, 46, 47
Here, 45 occurs maximum number of times.
? Mode = 45
Hence, the mode of the data is 45.
                           
     
 
   
    
                          
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