Question

Use the data in BUSI1013 Chase Dataset.xlsx to answer these questions: (16 points)

1. What is the sample mean of the variable Income?
2. What is the sample median the variable Income?
3. Find the range of Income.
4. Find the sample standard deviation of Income.
5. Compute the first and third quartile of Income
6. What is the IQR for Income?
7. Give the five-number summary for Income.
8. Use the IQR rule to determine whether there are outliers for income

here is the link to the data set. https://courses.yorkvilleu.ca/iSpring/BBA/BUSI_1013/Resources/Exercises/BUSI1013-Chase%20Dataset.xlsx

Answer 1

following information has been generated using ms-excel

sn	Customer ID	Income(x)	x-49.86	(x-49.86)2
17	122	43.7	-6.16	37.9456
25	130	44.2	-5.66	32.0356
16	121	44.4	-5.46	29.8116
24	129	44.5	-5.36	28.7296
6	111	45.5	-4.36	19.0096
23	128	46.9	-2.96	8.7616
27	132	47.2	-2.66	7.0756
5	110	48.0	-1.86	3.4596
9	114	48.1	-1.76	3.0976
13	118	48.9	-0.96	0.9216
2	107	49.2	-0.66	0.4356
7	112	49.3	-0.56	0.3136
18	123	49.5	-0.36	0.1296
3	108	50.1	0.24	0.0576
8	113	50.6	0.74	0.5476
4	109	51.1	1.24	1.5376
12	117	51.9	2.04	4.1616
26	131	52.0	2.14	4.5796
1	106	52.1	2.24	5.0176
15	120	52.7	2.84	8.0656
21	126	52.8	2.94	8.6436
14	119	53.2	3.34	11.1556
22	127	53.5	3.64	13.2496
20	125	53.6	3.74	13.9876
11	116	54.0	4.14	17.1396
19	124	54.2	4.34	18.8356
10	115	54.9	5.04	25.4016
	n=	27	27	27
	sum=	1346.1	-0.1	304.1
	mean=sum/n=	1346.1/27=	49.86
	median=	50.1
	maximum=	54.9
	minimum=	43.7
	range=maximum-minimum=	54.9-43.7=	11.2

first quartile=Q1=	47.6
Third quartile=Q3=	52.75
IQR=Q3-Q1=	52.75-47.6=	5.15

(first) sample mean=sum/n= 1346.1/27=49.86

(second)median=50.1

middle observations after arranging in ascending or descending order. here there are 27 observations and the middle and 14th observations is 50.1 after arranging in ascending order, so median is50.1

(third)range=maximum-minimum=54.9-43.7=11.2

(fourth)sample standard deviation=sqrt(sum(x-mean)²/(n-1))=sqrt(304.1/(27-1))=3.42

(fifth) using ms-excel the Q1 and Q3 is found out as

first quartile=Q1=	47.6
Third quartile=Q3=	52.75
(sixth) IQR=Q3-Q1= 52.75-47.6= 5.15

(seventh) the five number summary is

Min. = 43.7, 1st Quartile=47.6 Median=50.1 Mean=49.86 3rd Quartile=52.75 Max=54.9

(eighth) observations below Q1-1.5*IQR=47.6-1.5*5.15=39.875 and above Q3+1.5*IQR=52.75+1.5*5.15=60.475 will be treated as outlier and no observation found below 39.875 and above 60.475. so there is no outlier