Question

Discuss the three measures of central tendency (mode, mean, medium) in depth, to include when each is best used in statistical analysis. Explain your rationale.

Answer 1

Mean, Median and Mode are the measure of central tendency of any population set given. Based On these data set of values we can find the curve nature of the data . Now we will discuss it in details.

Mean

Mean is actually the arithmetic average of the data set , Mean is the best measure for central tendency when the data curve is bell shaped or we can say that when the distribution is normal and symmetrical and Mean , median, mode lies at the same point.

Let's say with a example

13, 18, 13, 14, 13, 16, 14, 21, 13 is the given data set

Hence (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15 is the mean calculated.

Median

Median is the Actually called as the middle number, it is the number that lies actually in the middle of the data set.Hence when the data set is skewed to the right or to the left and when the mean does not lies at the center than Median is used as the measure of central tendency.

13, 13, 13, 13, 14, 14, 16, 18, 21

In the given above data set 14 lies in the middle of the set half of the data lies to the right of the 14 and half of the data lies to the left of 14.

Mode

Mode the is data value in the set which occurs most of the time, or we can say that the frequency of that no is maximum. Lets ay with an example

13, 13, 13, 13, 14, 14, 16, 18, 21

In the above given data set 13 is the most happening number hence oure mode here will be 13.

Mode =13

On a bar chart, the mode is the highest bar. In fact, the mode is the only measure of central tendency that you can use with categorical data—such as the most preferred flavor of ice cream.