Q: Can the mean mean be less than the median?

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If the distribution is not symmetric, the mean will be different from the median. A negatively skewed distribution will have a mean hat is smaller than the median, provided it is unimodal.

It is perfectly possible.

The question is how do the mean and median affect the distribution shape. In a normal curve, the mean and median are both in the same point. ( as is the mode) If a distribution is skewed, its tail is either on the right or the left. If a distribution is skewed the median may be a better value to use than the mean since it has less effect on the shape. Also is there are large outliers, the median has less effect and is better to use. So the mean has a bigger effect on the shape many times than the median.

(1, 5, 97, 99, 100, 100) The mode is 100. The median is 98. The mean is 67.

When the distribution has outliers. They will skew the mean but will not affect the median.

Related questions

If the distribution is not symmetric, the mean will be different from the median. A negatively skewed distribution will have a mean hat is smaller than the median, provided it is unimodal.

IDN

It is perfectly possible.

When the data distribution is negatively skewed.

The question is how do the mean and median affect the distribution shape. In a normal curve, the mean and median are both in the same point. ( as is the mode) If a distribution is skewed, its tail is either on the right or the left. If a distribution is skewed the median may be a better value to use than the mean since it has less effect on the shape. Also is there are large outliers, the median has less effect and is better to use. So the mean has a bigger effect on the shape many times than the median.

The median of the 12 primes less than 40 is 15.

median

(1, 5, 97, 99, 100, 100) The mode is 100. The median is 98. The mean is 67.

One of the characteristics of mean when measuring central tendency is that when there are positively skewed distributions, the mean is always greater than the median. Another characteristic is that when there are negatively skewed distributions, the mean is always less than the median.

The median is less effected by outliers or numbers far outside of the normal range than the mean. See related link.

The mean is better than the median when there are outliers.

Yes. If the lower values tend to be farther below the median than the highest values are above the median, the mean is smaller than the median. why are write wrong