Question

In: Statistics and Probability

Per Capita Income 23714 21375 32355 35503 51615 58227 71403 87163 38337 31659 27280 41509 24941...

Per Capita Income
23714
21375
32355
35503
51615
58227
71403
87163
38337
31659
27280
41509
24941
20355
23617
26713
26347
21257
15246
15411
20489
29026
13391
39596
15920
10951
13596
41488
12548
10697
15467
67699
60593
16942
23098
19312
9016
22056
37519
13087
39243
18928
18366
20320
23495
15393
13756
28977
17974
19007
15506
15347
16228
8535
22561
24684
16145
13138
17577
24969
12524
16938
12014
23920
15898
14405
10559
11993
17213
22078
16022
40107
19709
34221
26185
29402
33364

1.For the variable Per Capita Income for all neighborhoods create a histogram with minimum five classes.

2. Describe the Shape of the histogram that you created for the variable per Capita Income.

3. Calculate the five-number summary for the variable Per Capita Income, and represent it using a box plot.

4.In detail, summarize what the information that a five-number summary for the variable Per Capita Income provides for the City of Chicago.


Solutions

Expert Solution

### R command

Income=c(23714,21375,32355,35503,51615,58227,71403,87163,38337,31659,
27280,41509,24941,20355,23617,26713,26347,21257,15246,15411,20489,
29026,13391,39596,15920,10951,13596,41488,12548,10697,15467,67699,
60593,16942,23098,19312,9016,22056,37519,13087,39243,18928,18366,
20320,23495,15393,13756,28977,17974,19007,15506,15347,16228,8535,
22561,24684,16145,13138,17577,24969,12524,16938,12014,23920,
15898,14405,10559,11993,17213,22078,16022,40107,19709,34221,
26185,29402,33364)

## 1)
hist(Income, xlab="Per Capita Income")

## 3)
summary(Income)
boxplot(Income)

## End.

1. For the variable Per Capita Income for all neighborhoods create a histogram with a minimum five classes.

2. Describe the Shape of the histogram that you created for the variable per Capita Income.

Ans: The histogram has long tail to the right. Hence, the given variable per Capita Income has a positive skew shape.

3. Calculate the five-number summary for the variable Per Capita Income, and represent it using a box plot.

Ans:

From the above box-plot, we can observe that the given variable has extremely large observations or outliers.

4. In detail, summarize what the information that a five-number summary for the variable Per Capita Income provides for the City of Chicago.

Ans: Let Q1=first quartile

Q2=Median=second quartile

Q3=third quartile

From the five-number summary, we know that

Q1 - Median < Q3 - Median

Hence, the given das has a positive skew.

The minimum value of the variable per capita income is 8535, the 25% observation of the per capita income lies below or equal to Q1=15467, the 50% observation of the per capita income are lies below or equal to Q2=20489, the 25% observation of the per capita income are lies below or equal to Q3=29026 and the maximum value of the given data is 87163.

orchestra answered 3 years ago
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