The table above shows the distribution of test scores for a

Hi Stne,
To find median of test-scores,we have to arrange them in an order (ascending or descending) and find the middle term.Now,the middle term is 37 th term in the order.

For the score distribution ,one can add one more column Cumulative frequency

SCORE INTERVAL---------NUMBER OF SCORES --------- Cumulative Frequency

50-59-------------------------- 2----------------------------- 2
60-69--------------------------10---------------------------- 12
70-79--------------------------16-----------------------------28
80-89--------------------------27-----------------------------55
90-99--------------------------18-----------------------------73

We can see arranging the scores in ascending, shows first 28 test scores are below 80.
Next 27 scores , i.e. 29th,30th,....,37th,......,55th score appear in SCORE INTERVAL 80-89.
So median is in interval 80-89.
Hope it helps.

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Median of 73 data points is the middle term - 37rd score. First 3 score ranges cover total of 28 scores (2+10+16), 37rd will be in fourth range (it covers scores from 80 to 89).

Answer: C.
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Since there are 73 scores so the median will be the 37th score from the starting.
Which will lie in the 80-89 interval.

So, the answer will be C

Hope it helps!

Watch the following video to Learn the Basics of Statistics


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Dear Bunnel,
As I know, the arrangement either in ascending or in descending order is a must in case of finding median. So, it would be 2+10+16+18+27. By adding 2+10+16 we get 28. Then, we need to add 18 and we get 46. So, 37 comes within 46 and the range should be 90-99 as it is the range for 18. Kindly tell me where I missed.

I think you misinterpreted the question. We have that there are:
2 scores from 50-59, say both are 55;
10 scores from 60-69, say all are 65;
16 scores from 70-79, say all are 75;
27 scores from 80-89, say all are 85;
18 scores from 90-99, say all are 95.

55, 55, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95.

Similar question to practice: the-table-above-shows-the-distribution-of-test-scores-for-a-93978.html

Hope it helps.
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Median is the "middle value" when all the data are arranged in ascending/descending order. For example, if the data is:

3,4,7,9, 87
-> Median is 7 (middle value).

Notice that there were 5 data points above, and the middle value is the 3rd value.

Here, there are 73 data points and so, the middle value will be 37th value. So, we just have to find out that 37th value will lie in which score interval.

2 values are lesser than 59
12 (2+10) values are lesser than 69
28 (2+10+16) values are lesser than 79
55 (2+10+16+27) values are lesser than 89

So, if 28 values are lesser than 79 and 55 values are lesser than 89

clearly 37th value will lie in the 80-89 bracket.

Median of a set with odd number of elements = the middle element of the set if arranged in ascending/descending order.
Median of a set with even number of elements = average of middle two numbers if arranged in ascending/descending order.

In the given case, total elements = 2 + 10 + 16 + 27 + 18 = 73 = 36 + 1 + 36
Hence the median will be the 37th term.
The 37th term will lie in the range 80 - 89

Correct Option: C

Below solution is more clear.

Median of 73 scores must be the 37th score when all the scores are arranged in increasing or decreasing order. In the score interval 50-79 there are (2 + 10 + 16) = 28 scores. Hence the 37-th score is not in this interval.

But in the score interval 50-89 there are (2 + 10 + 16 + 27) = 55 scores. Hence the 37-th score is in the score interval 80-89.

The correct answer is C.
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Since there are 73 scores, the median score will be at the (73+1)/2 = 74/2 = 37th position.

Therefore, we need to find the interval that contains the score at the 37th position. From the table, we know that the interval 50–59 contains scores of the 1st and 2nd positions, the interval 60–69 contains scores of the 3rd to 12th positions, the interval 70–79 contains scores of the 13th to 28th positions, and the interval 80–89 contains scores of the 29th to 55th positions.

Thus, the interval 80–89 must contain the median score, i.e., the score at the 37th position.

Answer: C
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Since we have an ODD number of values, the median will be the MIDDLEMOST value. In other words, if we arrange all 73 values in ASCENDING order, the median will be the 37th value (i.e., 36 values are below and 36 values are above).

The table says the first 2 scores in the 50-59 range. So, the 1st and 2nd values will be in the 50-59 range.
The table says the next 10 scores in the 60-69 range. So, 3rd to 12th values will be in the 60-69 range.
The table says the next 16 scores in the 70-79 range. So, the 13th to 28th values will be in the 70-79 range.
The table says the next 27 scores in the 80-89 range. So, the 29th to 45th values will be in the 80-89 range.

As we can see, the 37th value must be in the 80-89 range.

Answer: C

Cheers,
Brent

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