Question

Collect some quantitative data (your data needs to be quantitative)   Find the sample mean and standard deviation. Plot it in a histogram. Does the data seem to follow the bell curve of the normal distribution? What features of the data do or do not fit in with the shape of the normal curve. How much deviation from the curve is to be expected?

Answer 1

Collect some quantitative data (your data needs to be quantitative).

Since I am very curious to analyse the statistics for the USA’s Income and improvement, I have collected the Personal Income [ in Millions of dollars] for the past year 2018. My purpose to study this data is to check which states are getting a boost on Personal Income and which states still need consideration and funds from the government to improve its economy.

What is Personal Income by State?

The income people living in each state and the District of Columbia get from wages, proprietors' income, dividends, interest, rents, and government benefits. These statistics help assess and compare the economic well-being of state residents. The data is collected from the website named Bureau of Economic Analysis which is an official website of the United States government. This data is collected by the Bureau of Economic Analysis from all the 50 States of the country.

Sample Data for the Personal Income of all 50 States of the United States is as follows:

2,66,382
2,85,704
64,566
1,00,534
4,83,653
41,277
83,293
44,236
57,648
2,06,924
33,569
10,52,550
49,760
4,81,213
57,518
1,86,685
3,80,172
2,12,223
6,02,297
1,28,286
13,41,914
1,13,469
7,08,862
4,75,927
7,25,394
2,17,276
3,12,151
3,19,401
4,75,626
4,85,098
5,63,926
73,278
2,95,073
3,13,040
1,54,091
86,328
1,46,028
1,21,886
3,16,327
14,11,021
3,23,767
75,703
50,055
1,43,324
34,719
44,015
24,75,727
77,509
1,46,333
2,09,148
4,58,017

Find the sample mean and standard deviation.

The mean Personal Income [Millions of dollars] in all 50 states of the United States for the year 2018 is 344567.2.

The Standard deviation of Personal Income [Millions of dollars] in all 50 states of the United States for the year 2018 is 432699.8.

Plot it in a histogram.

Does the data seem to follow the bell curve of the normal distribution?

No, the data doesn't seem to follow the bell curve of the normal distribution.

What features of the data do or do not fit in with the shape of the normal curve.

As the Personal Income for some states is too low and for some too high, the data is not normally distributed and do not fit in with the shape of the normal curve.

How much deviation from the curve is to be expected?

The data is not following the curve, but the deviation of the data is 432699.8.