Chapter 4, Problem 1CR

What are descriptive statistics? How do they differ from visual displays of data?

To determine

Define descriptive statistics

Explanation of Solution

Descriptive statistics:

If a sample is taken and some statistics or sample characteristics are obtained from the sample but no inference is made about the entire population by using this information which is available from the sample, then it is termed as descriptive statistics.

The descriptive measures have three key characteristics:

• Center
• Variability
• Shape

Measures of Center:

An individual value that attempts to describe an observation by identifying the central position of the sample data is known as measures of central tendency.

Characteristics of center:

• Mean
• Median
• Mode
• Midrange
• Geometric mean
• Trimmed mean

Variability:

The measures of variability calculate the amount of spread or deviation in the observations. If the values corresponding to the variability are high, it means that the values in the data set are spread out wide.

Characteristics of the variability:

• Range
• Sample variance
• Sample standard deviation
• Coefficient of variation
• Mean absolute deviation

Measures of shape:

The shape of the data can be predicted by having the view on the shape of the graphs like histogram or boxplots or by comparing the value of the mean and median.

To determine

Explain how the descriptive measures differ from the visual displays of data.

Explanation of Solution

The statistical method helps to organize, explore and summarize the raw data in to useful information. The methods of statistics may be in visual form (Charts or graphs) or numerical form (Statistics or tables). In statistics, data visualization deals with the charts and graphs. A surveyor uses the visual form of data for clear explanation. In common, it is a practice to continue an analysis by examining graphical displays of the data set. The method of visual representation makes the people to understand the data easily.

However, the visualization has the clear logical ideas but it also needs some descriptive reports about the data. It is hard to visualize the raw data into graphical form without any descriptive measures. In order to analyze the data set, descriptive measure will give clear explanation along with graphical representation.