Question

. Find the z-score for Kohl’s for Profit Margin. Also, find the z-score for Kohl’s for Price/Sales. Describe, in a few sentences, the meaning of these z-scores.

Profit Margin
(cents per $1 sales)
7
2
1
11
6
3
4
-9
3
2
3
2
-2
10
2
-2
2
5
-3
2
1
6
-3
-1
5
3
4
5
4
7
3
1
4
-16
-1
-4
8
6
2
4
7
1
4

Price to Sales
(ratio)
0.8
0.4
0.2
1.1
1.2
0.4
0.4
0.1
0.3
0.6
0.3
0.2
0.1
0.2
0.7
0.2
0.2
0.7
0.1
0.3
0.7
0.6
0.1
0.1
0.3
0.5
0.5
0.5
0.4
0.8
0.6
0.2
0.5
0.1
0.1
0.1
1.2
0.6
0.2
0.5
0.9
0.5
0.5

Answer 1

Profit Margin(cents per $1 sales) (Xi)	Z = (Xi -Mean(X)) /SD(X)
		7	0.9924
2	-0.0639
1	-0.2751
11	1.8375
6	0.7812
3	0.1474
4	0.3586
-9	-2.3877
3	0.1474
2	-0.0639
3	0.1474
2	-0.0639
-2	-0.9089
10	1.6262
2	-0.0639
-2	-0.9089
2	-0.0639
5	0.5699
-3	-1.1202
2	-0.0639
1	-0.2751
6	0.7812
-3	-1.1202
-1	-0.6976
5	0.5699
3	0.1474
4	0.3586
5	0.5699
4	0.3586
7	0.9924
3	0.1474
1	-0.2751
4	0.3586
-16	-3.8665
-1	-0.6976
-4	-1.3314
8	1.2037
6	0.7812
2	-0.0639
4	0.3586
7	0.9924
1	-0.2751
4	0.3586

Price to Sales (ratio) (Xi)	Z = (Xi -Mean(X)) /SD(X)
		0.8	1.1899
0.4	-0.1391
0.2	-0.8036
1.1	2.1867
1.2	2.5189
0.4	-0.1391
0.4	-0.1391
0.1	-1.1358
0.3	-0.4713
0.6	0.5254
0.3	-0.4713
0.2	-0.8036
0.1	-1.1358
0.2	-0.8036
0.7	0.8577
0.2	-0.8036
0.2	-0.8036
0.7	0.8577
0.1	-1.1358
0.3	-0.4713
0.7	0.8577
0.6	0.5254
0.1	-1.1358
0.1	-1.1358
0.3	-0.4713
0.5	0.1932
0.5	0.1932
0.5	0.1932
0.4	-0.1391
0.8	1.1899
0.6	0.5254
0.2	-0.8036
0.5	0.1932
0.1	-1.1358
0.1	-1.1358
0.1	-1.1358
1.2	2.5189
0.6	0.5254
0.2	-0.8036
0.5	0.1932
0.9	1.5222
0.5	0.1932
0.5	0.1932

Z-scores follow Standard normal distribution with mean 0 and standard deviation 1

Z-scores are majorly used for standardizing the values so that values on different scales can be compared.