If the average (arithmetic mean) of 24 consecutive odd integers is 48,

Question

If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?

A. 36
B. 47
C. 48
D. 49
E. 72

generis · Accepted Answer

I.  Rule: In ANY evenly spaced set of integers,  the median equals the mean

Median = mean = 48

ANSWER C

II.  Test a  smaller  but similar sample

Use an even number of terms. Four consecutive odd integers: {1, 3, 5, 7}

Median = "middle value." If the number of terms is even, median = 
average of the two middle terms:  \frac{(3+5)}{2}=4

Mean =  \frac{(1+3+5+7)}{4}=4

So median = mean. In prompt, mean = 48 
Median also = 48

ANSWER C

Further, in any evenly spaced set -- 
median AND mean =  \frac{FirstTerm+ LastTerm}{2}

niks18 · Answer

As the number of elements are consecutive and is an Even number 24, hence the median should be equal to mean because the distribution is symmetric

Median will be the average of 12th & 13th term, which are odd numbers, hence their average will be an Even number.

Among the options only  48  is close to mean. Hence our answer

Option  C

---------------------

Method 2: Using progression

Sum = \frac{n}{2}*  , here

Sum = 48*24 ,  n=24 ,  d=2  we need  a

=>48*24=\frac{24}{2}*(2a+23*2)

=>a=25

Now,  T_{12}=a+(n-1)d=>a+11*2=25+22=47

therefore,  T_{13}=47+2=49

Hence median  = \frac{(47+49)}{2}=48

Option  C

dave13 · Answer

i join the above solution.

everything simple is unique

targetbusiness · Answer

In an Arithmetic Progression, that is, in an evenly spaced sequence of terms, 
Mean=Median
=> Median = 48.

ScottTargetTestPrep · Answer

In any set of any number of consecutive odd integers, the average is always equal to the median. Since we are given that the average is 48, the median is also 48.

Answer: C

bumpbot · Answer

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If the average (arithmetic mean) of 24 consecutive odd integers is 48,

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If the average (arithmetic mean) of 24 consecutive odd integers is 48,

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