Question

A large data set on Toledo workers was collected and the first three workers are characterized by:

Worker	Age	Hourly Wage	Female	Union	High School
1	33	$20	1	0	0
2	30	$24	0	1	1
3	36	$16	0	0	0

For the entire data set the average age is 31, the standard deviation of the age is 5, the average hourly wage is $15, and the standard deviation of the hourly wage is $4.

16. What is the standardized Euclidean distance for Workers 1 and 3 based on Age and Hourly Wage?
    1. 0.371
    2. 1.166
    3. 1.923
    4. 0.942
    5. 1.543

17. What is the matching coefficient for Workers 1 and 3 based on Female, Union, and High School?
    1. 0
    2. 1
    3. 2/3
    4. 1/2
    5. 1/3

18. Refer to Exhibit 4-1. What is Jaccard’s coefficient for Workers 1 and 3 based on Female, Union, and High School?

1. 1/3
2. 1/2
3. 2/3
4. 1
5. 0     

Answer 1

solution:

1) standardized Euclidean distance for Workers 1 and 3 based on Age and Hourly Wage

standardised value = (X - average age) / standard deviation

standardised value for worker 1 based on age= (33-31) / 5 = 0.4

standardised value for worker 3 based on age = (36 - 31) / 5 = 1

standardised value for worker 1 based on hourly wagen = (20-15) / 4 = 1.25

standardised value for worker 3 based on hourly wage = (16-15)/4 = 0.25

Euclidean distance =

ans b) 1.166

2) matching coefficient for Workers 1 and 3 based on Female, Union, and High School

are 2 i,e, (there are two matching pairs of zero) in total of three

so MATCHING COEFFICIENT =(number of variables with matching for worker 1 and 3) / (total number of variables for worker 1 and 3)

MATCHING COEFFICIENT = 2/3

ans c) 2/3

3) Jaccard’s coefficient for Workers 1 and 3

= (no. of non zero matching pair) / ( total variable - no. of non zero matching pair)

no. of non zero matching pair = 0

so, Jaccard’s coefficient for Workers 1 and 3 = 0 / (3 - 2) = 0

ans e) 0