UPSC Prelims 2017 CSAT Paper II · Q52 of 79 Basic Numeracy easy

If for a sample data Mean < Median < Mode then the distribution is

  1. (a) symmetric
  2. (b) skewed to the right
  3. (c) neither symmetric nor skewed
  4. (d) skewed to the left ✓ UPSC's answer

Why the answer is (d)

• In a negatively skewed distribution, the long tail extends toward lower values, pulling the mean below the median.

• The median lies between the mean and mode because it is less affected by extreme low values than the mean but more than the mode.

• The mode is the highest of the three because the peak of the distribution is on the right side of the tail.

• Therefore the ordering Mean < Median < Mode identifies a left-skewed distribution.

• Hence the correct option is (d) skewed to the left.

Why the other options are wrong

(a) symmetric
A symmetric distribution has mean, median and mode equal, not Mean < Median < Mode.
(b) skewed to the right
A right-skewed distribution has a long upper tail, giving Mode < Median < Mean, the reverse of the given order.
(c) neither symmetric nor skewed
The given strict ordering is a standard indicator of skewness, so it cannot be neither symmetric nor skewed.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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