1. Estimate the mean price of a pair of sunglasses sold at (a) an optical store (b) A sunglasses specialty store, and(c) a department store. Use 200 as the midpoint for 151+.

Answer

A. Mean Price of Optical store

C - I ∫ X ∫xMean Price of Optical store

0 – 1011 – 3031 – 5051 – 75

76 – 100101 – 150

151 +

0290

316412403654842478

520.540.56388

125.5200

05945

1251427812

32155210567195600

∑ ∫ x∑ ∫

= 7350309668

= 76.03

9668 735030

B. A sunglasses specialty store

C - I ∫ X ∫xMean Price of Sunglass

Specialty store

0 – 1011 – 3031 – 5051 – 75

76 – 100101 – 150

151 +

192708

251516971145805378

520.540.56388

125.5200

96014514

101857.5106911100760

101027.575600

∑ ∫ x∑ ∫

= 5016307440

= 67.42

7440 501630

C. Mean price of department store

C - I ∫ X ∫xMean price of department

store

0 – 1011 – 3031 – 5051 – 75

76 – 100101 – 150

151 +

12241464152748838165

520.540.56388

125.5200

612030012

61843.530744334420081000

∑ ∫ x∑ ∫

= 135071.54762

= 28.36

4762 135071.5

2. Which type of outlet had the greatest total revenue?

Answer.

x 5 20.5

40.5

63 88 125.5

200 Total Unit

Total Revenue

Optical store

0 292 3164

1240

3654 842 478 9668 735030

Specialty 192 708 2515

1697

1145 805 378 7440 501630

Department 1224

1464

1527

488 38 16 5 4762 135072

Discount 8793

5284

147 67 16 8 0 14315 164874

Showroom 153 100 65 35 29 9 0 391 11334Merchandise 614

7495 0 0 0 0 0 6642 40883

Supermarket 14108

316 0 0 0 0 0 14424 77108

Convenience 19726

2985

0 0 0 0 0 22711 159823

Chain Drug 17883

3432

50 0 0 0 0 21365 161796

Indep Drug 1352

1110

12 0 0 0 0 2474 30001

Chain apparel

3464

1804

186 112 40 17 7 5630 75945

Chain Sports 672 526 430 72 45 18 4 1767 43113Ind Sports

store875 199

7132

0528 206 85 11 5022 163033

Reasoning : Optical stores have the greatest total revenue. This is calculated by assuming uniformity and using the midpoint of the ranges. Total revenue is thus price multiplied by pairs sold

3. Which type of outlet had the greatest revenue per location? Explain your reasoning

Location Total Revenue

Revenue Per

LocationOptical store 34043 735030 21.59Specialty 2060 501630 243.51

Department 6866 135072 19.67Discount 10376 164874 15.89

Showroom 887 11334 12.78Merchandise 11868 40883 3.44Supermarket 21613 77108 3.56

Convenience 83613 159823 1.91Chain Drug 31127 161796 5.20Indep Drug 7034 30001 4.27

Chain apparel

26831 75945 2.83

Chain Sports 5760 43113 7.48Ind Sports

store14683 163033 11.10

Revenue per Location obtain by Divide the total Revenue from each store by the number of locations of stores

Reasoning : The sunglasses specialty store has the greatest Revenue per location

4. Estimate the standard deviation for a pair of sunglasses sold at (a) optical stores, (b) sunglasses specialty, (c ) Department store

Answer: a) optical stores

x X2 ∫ ∫ x ∫ x2

520.540.56383

125.5200

25420.25

1640.2539697744

15750.2540000

0290

316412403654842478

05945

12814278120

32155210567195600

0121872.551897514921560

2829657613261710.519120000

9668 735030 70911470

Standard deviation = √ ∫ x2∫ −( ∫ x∫ )2

= √ 709114709668−( 7350309668 )

2

= √7335.42−¿¿

= √7335.42−5780.12

= √1555.3

= 39.43

(b) sunglasses specialty,

x X2 ∫ ∫ x ∫ x2

520.540.56383

125.5200

25420.25

1640.2539697744

15750.2540000

192208

251516971145805378

96014514

1018575106911100760

101027.575600

4800297537

4125228.7567353938866880

12678951.2515120000

7440 501630 47828790

Standard deviation = √ ∫ x2∫ −( ∫ x∫ )2

= √ 478287907440−( 5016307440 )

2

= √6428.60−¿¿

= √6428.60−4545.91

= √1882.69

= 43.38

(c ) Department store

x X2 ∫ ∫ x ∫ x2

520.540.56383

125.5200

25420.25

1640.2539697744

15750.2540000

12241464152748838165

612030012

61843.530744334420081000

30600615246

2504661.751936872294272252004200000

4762 135071.5 5833655.75

Standard deviation = √ ∫ x2∫ −( ∫ x∫ )2

= √ 5833655.754762−( 135071.54762 )

2

= √1225.04−¿¿

= √1225.04−4545.91

= √420.501

= 20.5

4. Standard Deviation Of the 13 distributions, which has the greatest standard deviation? Explain your reasoning.

Answer: Standard Deviation Of the

13 distributions

Optical Store 39.43Specialty 43.38

Department 20.5Discount 9.1

Showroom 29.01Merchandis

e4.07

Supermarket

2.26

Convenience

5.24

Chain Drug 5.95Indep Drug 7.95

Chain apparel

15.76

Chain Sports

22.90

Ind Sports store

24.82

Sunglasses specialty, has the greatest standard deviation because it has more profit than other type of stores

6. Bell-Shaped Distribution Of the 13 distributions, which is more bell shaped? Explain

By constructing histograms to all the given 13 distributions, we can clearly observe that distribution of sunglass specialty store appeared to be more bell - shaped