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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct  [#permalink]

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New post 25 Nov 2019, 06:23
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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

a) 1
b) 2
c) 3
d) 4
e) 5
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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct  [#permalink]

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New post 25 Nov 2019, 12:04
CaptainLevi wrote:
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

a) 1
b) 2
c) 3
d) 4
e) 5


Total of the data set is \(= 37+a\)

One of the numbers is the mean as well as the median so:

If mean is 0 as then total of Data set would be 7*0= 0 which implies \(37+a=0 \) which implies \(a= \) -37
So set looks like { -37,0, 1, 6, 9,10,11} is this NOT valid as mean \(\neq \) median , mean=0 and median =6

If mean is 1 as then total of the data set would be 7*1=7 which implies \(37+a=7 \) which implies \(a= \) -30
So set looks like { -30,0, 1, 6, 9,10,11} is this NOT valid as mean \(\neq \) median , mean=7 and median =6

If mean is 6 then total of data set is 7*6= 42 which implies \(37+a=42 \) which implies \(a= \) 5
So set looks like { 0, 1, 5, 6, 9,10,11} is this valid as mean = median = 6

If mean is 9 then total of data set is 7*9= 63 which implies \(37+a=63 \) which implies \(a= \) 26
So set looks like { 0, 1, 6, 9,10,11,26} is this also valid as mean = median = 9

If mean is 10 then total of data set is 7*10=70 which implies \(37+a=70 \) which implies \(a= \)33
So set would look like { 0, 1, 6, 9,10,11,33} this is NOT valid as mean \(\neq \)median , mean is 10 and median is 9

Hence among the elements of the data set mean cannot be 0,1, 10,11 and 13 as then mean \(\neq \)median.

Thus we can have only two values of mean 6 and 10 such that mean= median, leading to two values for \(a\) (5 and 26)

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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct   [#permalink] 25 Nov 2019, 12:04
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