Class 9 Maths Question Answers - Measures of Central Tendency

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Q u e s t i o n : 5 5
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
S o l u t i o n :
Given that the ratio of mode and median of a certain data is 6:5. That is,
We know that
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Q u e s t i o n : 5 5
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
S o l u t i o n :
Given that the ratio of mode and median of a certain data is 6:5. That is,
We know that
Q u e s t i o n : 5 6
If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.
S o l u t i o n :
The given data is x+2, 2x+3, 3x+4, 4x+5. They are four in numbers.
The mean is
But, it is given that the mean is x+2. Hence, we have
Q u e s t i o n : 5 7
If the median of scores 
x
2
,
x
3
,
x
4
,
x
5
and 
x
6
wherex > 0
is 6, then find the value of 
x
6
.
S o l u t i o n :
Given that the median of the scores , where is 6. The number of scores n is 5, which is an odd
number. We have to find 
Note that the scores are in descending order. Hence the median is
But, it is given that the median is 6. Hence, we have
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Q u e s t i o n : 5 5
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
S o l u t i o n :
Given that the ratio of mode and median of a certain data is 6:5. That is,
We know that
Q u e s t i o n : 5 6
If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.
S o l u t i o n :
The given data is x+2, 2x+3, 3x+4, 4x+5. They are four in numbers.
The mean is
But, it is given that the mean is x+2. Hence, we have
Q u e s t i o n : 5 7
If the median of scores 
x
2
,
x
3
,
x
4
,
x
5
and 
x
6
wherex > 0
is 6, then find the value of 
x
6
.
S o l u t i o n :
Given that the median of the scores , where is 6. The number of scores n is 5, which is an odd
number. We have to find 
Note that the scores are in descending order. Hence the median is
But, it is given that the median is 6. Hence, we have
Q u e s t i o n : 5 8
If the mean of 2, 4, 6, 8, x, y is 5, then find the value of x + y.
S o l u t i o n :
The given data is . They are 6 in numbers.
The mean is
But, it is given that the mean is 5. Hence, we have
Q u e s t i o n : 5 9
If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.
S o l u t i o n :
The given data is .
The mode is the value which occur maximum number of times, that is, the mode has maximum frequency. If the
maximum frequency occurs for more than 1 value, then the number of mode is more than 1 and is not unique.
Here it is given that the mode is 4. So, x must be 4, otherwise it contradicts that the mode is 4. Hence
Q u e s t i o n : 6 0
If the median of 33, 28, 20, 25, 34, x is 29, find the maximum possible value of x.
S o l u t i o n :
The given data is . The total number of values is , is an even number. Hence the median
depends on the observation and observation.
Since we have to find the maximum possible value of x.So we must put it in the 4
th
 position when ordering in
ascending order.
Arranging the data in ascending order, we have
Hence, the median is
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Q u e s t i o n : 5 5
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
S o l u t i o n :
Given that the ratio of mode and median of a certain data is 6:5. That is,
We know that
Q u e s t i o n : 5 6
If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.
S o l u t i o n :
The given data is x+2, 2x+3, 3x+4, 4x+5. They are four in numbers.
The mean is
But, it is given that the mean is x+2. Hence, we have
Q u e s t i o n : 5 7
If the median of scores 
x
2
,
x
3
,
x
4
,
x
5
and 
x
6
wherex > 0
is 6, then find the value of 
x
6
.
S o l u t i o n :
Given that the median of the scores , where is 6. The number of scores n is 5, which is an odd
number. We have to find 
Note that the scores are in descending order. Hence the median is
But, it is given that the median is 6. Hence, we have
Q u e s t i o n : 5 8
If the mean of 2, 4, 6, 8, x, y is 5, then find the value of x + y.
S o l u t i o n :
The given data is . They are 6 in numbers.
The mean is
But, it is given that the mean is 5. Hence, we have
Q u e s t i o n : 5 9
If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.
S o l u t i o n :
The given data is .
The mode is the value which occur maximum number of times, that is, the mode has maximum frequency. If the
maximum frequency occurs for more than 1 value, then the number of mode is more than 1 and is not unique.
Here it is given that the mode is 4. So, x must be 4, otherwise it contradicts that the mode is 4. Hence
Q u e s t i o n : 6 0
If the median of 33, 28, 20, 25, 34, x is 29, find the maximum possible value of x.
S o l u t i o n :
The given data is . The total number of values is , is an even number. Hence the median
depends on the observation and observation.
Since we have to find the maximum possible value of x.So we must put it in the 4
th
 position when ordering in
ascending order.
Arranging the data in ascending order, we have
Hence, the median is
Here it is given that the median is 29. So, we have
Q u e s t i o n : 6 1
If the median of the scores 1, 2, x, 4, 5 where1 < 2 < x < 4 < 5
is 3, then find the mean of the scores.
S o l u t i o n :
The given data is 1, 2, x, 4 and 5. Since , the given data is already in ascending order.
Here, the number of observation , which is an odd number.
Hence, the median is
Here, it is given that the median is 3. Hence, we have .
The mean is
Q u e s t i o n : 6 2
If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean
S o l u t i o n :
Given that the ratio of mean and median of a certain data is 2:3. That is,
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Q u e s t i o n : 5 5
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
S o l u t i o n :
Given that the ratio of mode and median of a certain data is 6:5. That is,
We know that
Q u e s t i o n : 5 6
If the mean of x + 2, 2x + 3, 3x + 4, 4x + 5 is x + 2, find x.
S o l u t i o n :
The given data is x+2, 2x+3, 3x+4, 4x+5. They are four in numbers.
The mean is
But, it is given that the mean is x+2. Hence, we have
Q u e s t i o n : 5 7
If the median of scores 
x
2
,
x
3
,
x
4
,
x
5
and 
x
6
wherex > 0
is 6, then find the value of 
x
6
.
S o l u t i o n :
Given that the median of the scores , where is 6. The number of scores n is 5, which is an odd
number. We have to find 
Note that the scores are in descending order. Hence the median is
But, it is given that the median is 6. Hence, we have
Q u e s t i o n : 5 8
If the mean of 2, 4, 6, 8, x, y is 5, then find the value of x + y.
S o l u t i o n :
The given data is . They are 6 in numbers.
The mean is
But, it is given that the mean is 5. Hence, we have
Q u e s t i o n : 5 9
If the mode of scores 3, 4, 3, 5, 4, 6, 6, x is 4, find the value of x.
S o l u t i o n :
The given data is .
The mode is the value which occur maximum number of times, that is, the mode has maximum frequency. If the
maximum frequency occurs for more than 1 value, then the number of mode is more than 1 and is not unique.
Here it is given that the mode is 4. So, x must be 4, otherwise it contradicts that the mode is 4. Hence
Q u e s t i o n : 6 0
If the median of 33, 28, 20, 25, 34, x is 29, find the maximum possible value of x.
S o l u t i o n :
The given data is . The total number of values is , is an even number. Hence the median
depends on the observation and observation.
Since we have to find the maximum possible value of x.So we must put it in the 4
th
 position when ordering in
ascending order.
Arranging the data in ascending order, we have
Hence, the median is
Here it is given that the median is 29. So, we have
Q u e s t i o n : 6 1
If the median of the scores 1, 2, x, 4, 5 where1 < 2 < x < 4 < 5
is 3, then find the mean of the scores.
S o l u t i o n :
The given data is 1, 2, x, 4 and 5. Since , the given data is already in ascending order.
Here, the number of observation , which is an odd number.
Hence, the median is
Here, it is given that the median is 3. Hence, we have .
The mean is
Q u e s t i o n : 6 2
If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean
S o l u t i o n :
Given that the ratio of mean and median of a certain data is 2:3. That is,
We know that
Q u e s t i o n : 6 3
The arithmetic mean and mode of a data are 24 and 12 respectively, then find the median of the data.
S o l u t i o n :
Given that the arithmetic mean and mode of a data are 24 and 12 respectively. That is,
We have to find median
We know that
Q u e s t i o n : 6 4
If the difference of mode and median of a data is 24, then find the difference of median and mean.
S o l u t i o n :
Given that the difference of mode and median of a data is 24. That is,
We have to find the difference between median and mean
We know that