In: Statistics and Probability
Determine the proportion of the Revenue Growth data that lies within 1, 2, and 3 standard deviations of the mean. Determine, using the empirical rule, if the Revenue Growth data is approximately normally distributed.
Abercrombie & Fitch Co. | 2.7 |
American Eagle Outfitters | 2.5 |
bebe stores, inc. | 10.0 |
Birks Group Inc | 5.3 |
BJs Wholesale Club Holdings Inc | 3.4 |
Boot Barn Holdings Inc | 12.7 |
Bravada International Ltd. | -4.7 |
Buckle Inc | -14.9 |
Burlington Stores Inc | -13.5 |
Cache Inc | -9.9 |
Caleres Inc | -10.8 |
Cato Corp | 9.2 |
Chico's FAS, Inc. | 10.4 |
Childrens Place Inc | -16.0 |
Christopher & Banks Corporation | 8.9 |
Citi Trends, Inc. | -9.9 |
Companhia Brasileira de Distribuicao | 25.7 |
Costco Wholesale Corporation | 1.6 |
Designer Brands Inc | -0.2 |
Destination Maternity Corp | -15.1 |
Dillard's, Inc. | -2.4 |
Express, Inc. | -9.9 |
Foot Locker, Inc. | -0.9 |
Francesca's Holdings Corp | 24.8 |
Gap Inc | 2.4 |
Genesco Inc. | -3.3 |
Guess?, Inc. | -4.5 |
J C Penney Company Inc | -4.5 |
J.Jill Inc | -5.4 |
Kohl's Corporation | 4.4 |
L Brands Inc | 8.7 |
Macy's Inc | -8.7 |
Nordstrom, Inc. | -5.2 |
PriceSmart, Inc. | 0.4 |
Qingco Inc | -35.8 |
Ross Stores, Inc. | 2.6 |
RTW Retailwinds Inc | 0.1 |
Sears Holdings Corp | -0.5 |
Shoe Carnival, Inc. | 8.8 |
Stage Stores Inc | 52.4 |
Stein Mart, Inc. | 3.7 |
Tailored Brands Inc | -4.3 |
Tandy Leather Factory, Inc. | -9.9 |
Tilly's Inc | 7.2 |
TJX Companies Inc | 3.3 |
Urban Outfitters, Inc. | 0.8 |
Walmart Inc | -3.5 |
Zumiez Inc. | -8.1 |
Solution,
There are 48 data points
by 68-95-99.7 rule,
68% lies within 1 sd, 95% lies within 2 sd , and 99.7 % lies within 3 sd of mean
using given data
Company Name |
Revenue Growth
|
||||
(% in last year)
|
z-score | |z| < 1 | |z| < 2 | |z| < 3 | |
Abercrombie & Fitch Co. | 2.7 | 0.19 | 1 | 1 | 1 |
American Eagle Outfitters |
2.5 | 0.18 | 1 | 1 | 1 |
bebe stores, inc. | 10.0 | 0.76 | 1 | 1 | 1 |
Birks Group Inc | 5.3 | 0.39 | 1 | 1 | 1 |
BJs Wholesale Club Holdings Inc | 3.4 | 0.25 | 1 | 1 | 1 |
Boot Barn Holdings Inc | 12.7 | 0.97 | 1 | 1 | 1 |
Bravada International Ltd. | -4.7 | -0.38 | |||
Buckle Inc | -14.9 | -1.17 | 0 | 1 | 1 |
Burlington Stores Inc | -13.5 | -1.06 | 0 | 1 | 1 |
Cache Inc | -9.9 | -0.78 | 1 | 1 | 1 |
Caleres Inc | -10.8 | -0.85 | 1 | 1 | 1 |
Cato Corp | 9.2 | 0.70 | 1 | 1 | 1 |
Chico's FAS, Inc. | 10.4 | 0.79 | 1 | 1 | 1 |
Childrens Place Inc | -16.0 | -1.25 | 0 | 1 | 1 |
Christopher & Banks Corporation | 8.9 | 0.67 | 1 | 1 | 1 |
Citi Trends, Inc. | -9.9 | -0.78 | 1 | 1 | 1 |
Companhia Brasileira de Distribuicao | 25.7 | 1.97 | 0 | 1 | 1 |
Costco Wholesale Corporation | 1.6 | 0.11 | 1 | 1 | 1 |
Designer Brands Inc | -0.2 | -0.03 | 1 | 1 | 1 |
Destination Maternity Corp | -15.1 | -1.18 | 0 | 1 | 1 |
Dillard's, Inc. | -2.4 | -0.20 | 1 | 1 | 1 |
Express, Inc. | -9.9 | -0.78 | 1 | 1 | 1 |
Foot Locker, Inc. | -0.9 | -0.09 | 1 | 1 | 1 |
Francesca's Holdings Corp | 24.8 | 1.90 | 0 | 1 | 1 |
Gap Inc | 2.4 | 0.17 | 1 | 1 | 1 |
Genesco Inc. | -3.3 | -0.27 | 1 | 1 | 1 |
Guess?, Inc. | -4.5 | -0.36 | 1 | 1 | 1 |
J C Penney Company Inc | -4.5 | -0.36 | 1 | 1 | 1 |
J.Jill Inc | -5.4 | -0.43 | 1 | 1 | 1 |
Kohl's Corporation | 4.4 | 0.32 | 1 | 1 | 1 |
L Brands Inc | 8.7 | 0.66 | 1 | 1 | 1 |
Macy's Inc | -8.7 | -0.69 | 1 | 1 | 1 |
Nordstrom, Inc. | -5.2 | -0.42 | 1 | 1 | 1 |
PriceSmart, Inc. | 0.4 | 0.01 | 1 | 1 | 1 |
Qingco Inc | -35.8 | -2.79 | 0 | 0 | 1 |
Ross Stores, Inc. | 2.6 | 0.18 | 1 | 1 | 1 |
RTW Retailwinds Inc | 0.1 | -0.01 | 1 | 1 | 1 |
Sears Holdings Corp | -0.5 | -0.05 | 1 | 1 | 1 |
Shoe Carnival, Inc. | 8.8 | 0.66 | 1 | 1 | 1 |
Stage Stores Inc | 52.4 | 4.04 | 0 | 0 | 0 |
Stein Mart, Inc. | 3.7 | 0.27 | 1 | 1 | 1 |
Tailored Brands Inc | -4.3 |
-0.35 |
1 | 1 | 1 |
Tandy Leather Factory, Inc. | -9.9 | -0.78 | 1 | 1 | 1 |
Tilly's Inc | 7.2 | 0.54 | 1 | 1 | 1 |
TJX Companies Inc | 3.3 | 0.24 | 1 | 1 | 1 |
Urban Outfitters, Inc. | 0.8 | 0.05 | 1 | 1 | 1 |
Walmart Inc | -3.5 | -0.29 | 1 | 1 | 1 |
Zumiez Inc. | -8.1 | -0.64 | 1 | 1 | 1 |
0.210416667 | frequency | 40 | 46 | 47 | |
12.9299461 | proportion | 0.833 | 0.958 | 0.979 |
hence 83.3 % lies within 1 sd,
95.8 % within 2 sd
97.9 % within 3 sd
we see that there is high proportion of data within 1 sd
hence the Revenue Growth data is not approximately normally distributed.