Question

Please answer each of the following letters:

A) Make a stemplot of the data.

B) Describe the distribution that you see

C) Find the mean growth rate. Do you think the mean gives good description of the data? Explain

D) Find the median growth rate. Do you think the median gives good description of the data? Explain

E) Find the standard deviation. Do you think the standard deviation gives good description of the data? Explain

F) Propose ways to give numerical summary for this distribution. Compute these summaries. Explain your answer.

The Suêcess of companies expanding to developing regions of the world depends in part on the prosperity of the countries in those regions. Here are World Bank data on the growth of gross domestic product (percent per year) for 2013 for 13 countries in Asia: Growth 6.1 Country Bangladesh China Hong Kong India Indonesia Japan Korea(South) Malaysia Pakistan Philippines Singapore 7.8 1.4 6.5 6.2 2.0 2.0 5.6 3.7 6.6 1.3 6.4 5.0 Thailand Vietnam

Answer 1

Sorting the data in ascending order:

Country	Growth
Singapore	1.3
Hong Kong	1.4
Japan	2.0
Korea(South)	2.0
Pakistan	3.7
Vietnam	5.0
Malaysia	5.6
Bangladesh	6.1
Indonesia	6.2
Thailand	6.4
India	6.5
Philippines	6.6
China	7.8

A) Stem plot

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Key: 1|3 = 1.3

B) We are looking at a distribution where skewness is close to -.05 ( Skewness = -0.4488)

Hence the distribution is a moderately skewed distribution.

C) Mean Growth rate = 4.66

Mean is not a good representative of this data set. Most of the countries have their growth rates around 6, whereas 4.66 average does not indicate this. Mean is getting impacted by the outliers. Let's have a look at the median.

D) Median Growth rate = 5.6

The median growth rate is a good and better representative than mean as it is near 6 growth rate that most of the countries have and also takes into account the lower growth rate countries. But median does not get impacted by the outliers.

E) Standard Deviation = 2.28

Most of the data(99.7) should be within 3 Standard deviation of the mean for a normal distribution. Our std deviation is 2.28 and the growth rates of countries are within 3 S.D of mean. Thus S.D is a good representative of the distribution.