Question

Descriptive statistics is the branch of quantitative analysis that uses numerical metrics and graphs and charts to describe a data set so that we can realize the information in that data. There are a wide variety of these numerical and graphical tools measuring what is called central tendency, dispersion and shape. (See my helps aids post for the range of these tools.) Describe and discuss why there are so many of these metrics. Do you use any of these in your work?

Answer 1

The central tendency of a distribution is an estimate of the “center” of a distribution of values. There are three major types of estimates of central tendency:

• Mean
• Median
• Mode

The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values.

Dispersion in statistics is a way of describing how spread out a set of data is. When a data set has a large value, the values in the set are widely scattered; when it is small the items in the set are tightly clustered. Very basically, this set of data has a small value:
1, 2, 2, 3, 3, 4
…and this set has a wider one:
0, 1, 20, 30, 40, 100

The spread of a data set can be described by a range of descriptive statistics including variance, standard deviation, and interquartile range. Spread can also be shown in graphs: dot plots, boxplots, and stem and leaf plots have a greater distance with samples that have a larger dispersion and vice versa.

When a data set is graphed, each point is arranged to produce one of dozens of different shapes. The distribution shape can give you a visual which helps to show how the data is:

• Spread out (e.g. dispersion, variability, scatter),
• Where the mean lies,
• What the range of the data set is,

…and many other useful statistics. Shapes of distributions are defined by several different factors:

I used the mean for representation of the data . For example average run of the cricketer in a match