which of the following has the same mean median and mode
(a) 6,2,5,4,3,4,1
(b) 4,2,2,1,3,2,3
(c) 2,3,7,3,8,3,2
(d) 4,3,4,3,4,6,4
Answers
Step-by-step explanation:
Correct option is
D
4,3,4,3.4.6,4
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:
Making it in sequence (decreasing or increasing order)
(d) 3,3,4,4,4,4,6
mean = 28/7 = 4
median = (n+1)/2 = 8/2 = 4th position = 4
mode = 4 (it's frequency is more)
therefore, d) 4,3,4,3,4,6,4 is correct !
Hope it will help you!