Answer to Question #90382 in Statistics and Probability for Sharon Tan

Question

(e) The manager wants to do a competitors’ analysis from two of their closest competitors.

Competitors’ Monthly Expenses
Statistical Measure Competitor A Competitor B
Mean 430 450
Median 450 430
Mode 420 470
Standard Deviation 200 250

Using the information in above table, compare XYZ Company with competitor A and competitor B, comment on the following:

(i) Which company has the most variation? Explain.

(ii) The manager of XYZ Company made the following statement, “Competitor A spends on the average the most amount of money in the past 5 years in the industry.” Is this an Inferential Statistics or a Descriptive Statistics?

Answer 1

(i) The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is generally expressed as a percentage. Without units, it allows for comparison between distributions of values whose scales of measurement are not comparable.

Competitor A 

$$CV_A={200 \over 430}\cdot 100\%\approx 46.51\%$$

Competitor B

$$CV_B={250 \over 450}\cdot 100\%\approx 55.56\%$$

Since $CV_B>CV_A,$ then the company $B$ has the most variation.

(ii) Descriptive statistics are functions of the sample data that are intrinsically interesting in describing some feature of the data. Classic descriptive statistics include mean, min, max, standard deviation, median, skew, kurtosis. It explains the data, which is already known, to summarize sample.

Inferential statistics are a function of the sample data that assists you to draw an inference regarding an hypothesis about a population parameter. Classic inferential statistics include $z, t, \chi^2, F-ratio,$etc.

It attempts to reach the conclusion to learn about the population, that extends beyond the data available.

The statement of the manager of XYZ Company is a Descriptive Statistics.