This question is a moderately difficult question on Statistics. It tests your understanding of the statistical measures.
The median is the middle value (when there are an odd number of values), when all the values in the data set are arranged in ascending order/descending order. In case there are even number of values in the set, the median is the average of the two values in the middle.
The mode is that value that is seen most frequently in the data set.
Standard deviation is the root of the mean of the squared deviations, calculated with reference to the mean.
In this question, since there are 10 values, the median will be the average of the 5th and the 6th values. Since both these values are 15, the median = 15.
When one more 15 is included in the set, the number of values in the set becomes 11 and the median becomes the 6th value. But the 6th value IS 15. Therefore, the median does not change. So, statement I should not be a part of the answer. Options A, D and E can be eliminated basis this.
In the set of values given, the number 15 occurs thrice and hence is the mode. When we introduce one more 15, the mode will still remain 15. Therefore, statement II is also not a part of the answer. Option B can be eliminated.
The correct answer option should be C.
The mean of the given set of values is \(\frac{154}{10}\) = 15.4. When another 15 is added, the mean reduces to \(\frac{169}{11}\) = 15.3. Because of this, the standard deviation is bound to change. Therefore, statement III only has to be the answer.
Remember that, the Standard deviation of a set of values always depends on the mean. You change things in a way it affects the mean, the standard deviation also gets affected.
On the timing front, this is a question which can be solved in about 1 minute.
Hope this helps!
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