Find the first four moments about the mean from the following data. Class-interval 0-10 10-20 20-30 30-40 Frequency 1 3 4 2

Question: Find the first four moments of the mean from the following data.

Class-interval0-1010-2020-3030-40
Frequency1342

Solution:

Solution of homework

In other words, we may say that if the extreme variations in a given distribution are towards higher values they give the curve a longer tail to the right and this pulls the median and mean in that direction from the mode. If, however, extreme variations are towards lower values, the longer tail is to the left and the median and mean are pulled to the left of the mode.

It could also be shown that in a symmetrical distribution the lower and upper quartiles are equidistant from the median, so also are corresponding pairs of deciles and percentiles. This means that in a asymmetrical distribution the distance of the upper and lower quartiles from median is unequal.