If the distribution of scores obtained by a group of examinees on a test is skewed negatively, then which of the following statements is false?

A distribution is said to be skewed when the data points cluster more toward one side of the scale than the other, creating a curve that is not symmetrical.

Important Points

• The skewness is a measure of the asymmetry of the probability distribution assuming a unimodal distribution (assuming there is only one peak in the distribution of values) .
• We can say that the skewness indicates how much our underlying distribution deviates from the normal distribution since the normal distribution has skewness 0.

Hint

• Symmetrical: When the skewness is close to 0 and the mean is almost the same as the median
• Negative skew: When the left tail of the histogram of the distribution is longer and the majority of the observations are concentrated on the right tail.
  • Distribution said to be skewed negatively or to the left when scores are massed at the high end of the scale, i.e. the right side of the curve are spread out more gradually toward the low end i.e. the left side of the curve.
  • In negatively skewed distribution the value of median will be higher than that of the value of the mean.
• In this case, we can use also the term “left-skewed” or “left-tailed”. and the median is greater than the mean.

 Additional InformationMost of the examinees crossed the passing cut‐score of the test.

• If a test shows, a left-skewed distribution, this means most of the students are high scorers who scored above average and there is a very less number of students who scored very low marks.

The average difficulty level of the test‐items was low.

•  We can conclude that the test was very easy and there are very few weak students who scored low marks and these students can be considered outliers  as they are not following the general trend.

Thus negatively skewed score the Median is always Greater than mean.