Question

A magazine discussed the capital spending of telecommunications companies in two adjacent countries. The capital​ spending, in thousands of​ dollars, for each of 27 telecommunications companies is given below. 1,046 7,639 665 417 120 1,396 1,544 2,319 11,719 3,937 2,885 5,304 5,307 3,820 438 55 8,048 785 17,395 2,036 4,097 3,149 139 7,321 780 8,798 5,088 1. Obtain the quartiles Q1=Q2=Q3= 2.Interpret the quartiles 3.Determine the IQR 4.Interpret the IQR 5. Find the 5 Number Summary 6.Interpret the 5 Number Summary 7. Identify the potential outliers if any)

Answer 1

We are given capital spending of 27 companies. Arranging in increasing order,we get 55, 120, 139, 417, 438, 665, 780, 785, 1046, 1396, 1544, 2036, 2319, 2885, 3149, 3820, 3937, 4097, 5088, 5304, 5307, 7321, 7639, 8048, 8798, 11719, 17395.

1. The first quartile is given by, item. That is,

The second quartile is given by, item. That is,

The third quartile is given by, item.

2. Based on the quartiles, we can interpret that 25% of the companies have capital spending less than 780, half of the companies have capital spending less than 2885 and 75% of companies have capital spending less than 5307.

3. The inter quartile range, IQR=

4. The difference between third and first quartile is 4527. This quantifies the scatter.