The above table shows a set of scores and their frequencies. If the m

Question

4.17.png The above table shows a set of scores and their frequencies. If the median score is not one of the scores displayed in the table, which of the following could be the value of x? A. 6 B. 7 C. 8 D. 9 E. 10

KarishmaB · Accepted Answer

Muammer :

Median is the middle value when all values are arranged in increasing (or decreasing order)

All values are: 
10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, ...(x number of times), 13, 13, 13 ... (8 times), 14, 14, 14 (9 times)

So in all there are 5 + 6 + x + 8 + 9 values.

Whenever we have odd number of values, the median is the middle value i.e. if we have 3 values, the median is the 2nd value, if we have 5 values, the median is the 3rd value and so on. So median will be one of the values. 
When we have even number of values, then median is the average of the middle two values. So if we have 4 values, median is average of 2nd and 3rd values. Here, since the median does not belong to the list, we must have even number of total values.

Also, the middle two values must be distinct so that their average is different from them. That is, if middle two values are both 12, their average would be 12 too. But if want that the average should not be a part of the list, the middle two values must be something like 12 and 13 so that average and hence median is 12.5.

So what should be the value of x? We already have 5 + 6 = 11 values on the left of x and 8+9 = 17 values on the right of x. So x should be 6 so that we have 17 values (of 10, 11 and 12) and 17 values of (13 and 14). Now the median will be the average of the middle two values, the 17th and the 18th values. Median will be 12 + 13 = 12.5.

balaji4799 · Answer

For the median to be not among the scores displayed, the median basically should be average of two numbers at the center.
For that to happen the total number of elements should be even. so options B and D are out. 
Since the numbers above 12 are 17, if we have the number below and equal to 12 are 17, then the median will be the 17th + 18th divided by 2. 
For that to happen the frequency of 12 should be 6. hence A is the right option. 
For other options such as C and E, the median will be a number written in the table.

MathRevolution · Answer

=>

If  x = 6 , the median is  12.5 .
If x = 7, 8, 9,  or  10 , the median is  12 .

Since  12.5  is not shown on the table, the answer is  6 .

Therefore, the answer is A.

Answer: A

kushwahasunita08 · Answer

How Median is 12.5 ,can anyone explain Iam not getting.

Posted from my mobile device

Loop123 · Answer

VeritasKarishma  can you help us with this question please?

MathRevolution · Answer

Scores: 10, 11, 12, 13, 14

Frequency: 5 + 6 + x + 8 + 9 = 28 + x

The median score shouldn't be the same as the displayed score. This is only possible when we have frequency total = even. Options B and D are eliminated.

Now median in the current situation is: first 11 number cancels last 11 numbers.

Left out numbers are 12   and 13

To find now the median we need 6   such that 4(12's) and 4(13's) cancel out each other and in the end, we are left with 12 and 13.

Then the median will be 12.5

Answer A

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The above table shows a set of scores and their frequencies. If the m

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