Question

Which of the following has the same mean, median and mode values.


6, 2, 5, 4, 3, 4, 1

4, 2, 2, 1, 3, 2, 3

2, 3, 7, 3, 8, 3, 2

4, 3, 4, 3, 4, 6, 4
​

Answer 1

ANSWER
Option A:6,2,5,4,3,4,1
Arranging the numbers in ascending order we get,
1,2,3,4,4,5,6
⇒ Mean=
7
1+2+3+4+4+5+6
​
=
7
25
​
=3.57
⇒ The mode of a set of data values is the value that appears most often
⇒ Here, number 4 occurs 2 times, so mode is 4
⇒ We know, median is a middle number.
⇒ Here, 4th number is middle number which is 4.
∴ Median is 4.
∴ Option A does not have same mean, median and mode.

Option B:4,2,2,1,3,2,3
Arranging the numbers in ascending order we get,
1,2,2,2,3,3,4
⇒ Mean=
7
1+2+2+2+3+3+4
​
=
7
17
​
=2.42
⇒ The mode of a set of data values is the value that appears most often
⇒ Here, number 2 occurs 3 times, so mode is 2
⇒ We know, median is a middle number.
⇒ Here, 4th number is middle number which is 2.
∴ Median is 2.
∴ Option B does not have same mean, median and mode.

Option C:2,3,7,3,8,3,2
Arranging the numbers in ascending order we get,
2,2,3,3,3,7,8
⇒ Mean=
7
2+2+3+3+3+7+8
​
=
7
28
​
=4
⇒ The mode of a set of data values is the value that appears most often
⇒ Here, number 3 occurs 3 times, so mode is 3
⇒ We know, median is a middle number.
⇒ Here, 4th number is middle number which is 3.
∴ Median is 3.
∴ Option C does not have same mean, median and mode.

Option D:4,3,4,3,4,6,4
Arranging the numbers in ascending order we get,
3,3,4,4,4,4,6
⇒ Mean=
7
3+3+4+4+4+4+6
​
=
7
28
​
=4
⇒ The mode of a set of data values is the value that appears most often
⇒ Here, number 4 occurs 4 times, so mode is 4
⇒ We know, median is a middle number.
⇒ Here, 4th number is middle number which is 4.
∴ Median is 4.
∴ Option D have same mean, median and mode.
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Answer 2

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