Question

For dealing with qualitative data the best average is.

Answer 1

Hint: In this question we have to find out the best average when we deal with the qualitative data. Mean, mode and median are the three different types of averages out of this we have to select the best one. To solve this question we have to consider definitions and examples to find the best average.

Complete step by step answer:
Now, we have to find the best average for dealing with qualitative data.
Let us first consider following definitions of mean, mode and median:
Mean - The mean (average) of a data set is found by adding all observations in the data set and then dividing by the number of observations in the set.
Median - Median is the middle most value in case of odd number of observations. Also for even number of observations, median is the average of two middle values.
Mode - The mode is the observation that occurs most often in a data set.
Hence, from the definitions we can see that the median divides the data set into two equal halves. And hence we can say that, Median gives the more accurate and best average for qualitative data.
For example, Let us consider data set
\[\Rightarrow \left\{ 14,12,13,14,12,24,12,25,12,30 \right\}\]
Now, to find median first we have to arrange the given data in order either from lowest to highest or highest to lowest and then picking out the middle term. And if even numbers of observations are there then pick out two middle observations and find out the average.
\[\Rightarrow \text{Lowest to highest: }\left\{ 12,12,12,12,13,14,14,24,25,30 \right\}\]
Now as even numbers of observations are there we have to find the average of the middle two terms. So here we consider fifth and sixth term and their average is the median.
\[\Rightarrow \text{Median = }\dfrac{13+14}{2}=13.5\]

Hence, Median gives the best average for qualitative data.

Note: In this type of question students have to note that the value of median is not influenced by the extreme values of the data set. Also students have to note that the value of median remains unaffected in a grouping procedure.