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Measurements of some variable X were made at an interval of $ \ 1 \ $ minute from $10 \ \text{ A.M. to } \ 10:20 \ \text {A.M.} $. The data, thus, obtained is as follows:

$ X : 60, 62, 65, 64, 63, 61, 66, 65, 70, 68, 63, 62, 64, 69, 65, 64, 66, 67, 66, 64 ,50.$

The value of $X$ which is exceeded $50 \%$ of the time in the duration of measurement, is

$(i) \ 69 \\ (ii) \ 68 \\ (iii) \ 67 \\ (iv) \ 66 $

Answer:

It is a multiple choice question and it is general knowledge question.

The answer is $ \ 68 $.

But I am unable to understand the question. What exactly says the question?

Help me

MAS
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  • I don't understand it either. The value $68$ is only exceeded twice (by the values $69$ and $70$,) which is $10%$ not $50%.$ Are you certain all these numbers are correct? -- Oops it's $2/21$ not $2/20$ so a bit less than $10%$. – saulspatz Sep 02 '18 at 06:49

2 Answers2

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With the given data, $$X : 60, 62, 65, 64, 63, 61, 66, 65, 70, 68, 63, 62, 64, 69, 65, 64, 66, 67, 66, 64 ,50$$

$68$ is the data collected at 10:10 which is the middle of time interval $10:00 $ to $10:20$

That is the only interpretation which makes the answer $68$ otherwise, $68$ is not the median of your data at all.

Mohammad Riazi-Kermani
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  • To add to this: The median (which the question somehow seems to try to ask for) would be 64, which is not even among the available choices. – Hagen von Eitzen Sep 02 '18 at 07:54
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Isn't the question maybe written badly? I could think the author meant:

The value of X at which 50% of the time in the duration of measurement is exceeded

Clearly if this is an exam question, I would definitely consider the question as void, as it is unclear.

b00n heT
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