Question

In: Math

The number of goods sold by “The Local” is in excess of one million per year...

The number of goods sold by “The Local” is in excess of one million per year with deliveries being about 40% of that figure. The amount of goods sold has decreased marginally in recent years. “The Local” is wholly owned but Bianca and her staff have a standard of living to maintain so there is some pressure to raise overall sales whilst keeping costs, particularly delivery costs, in check.     Bianca continues: It is your job to use the sample data from last year’s overall sales to do some statistical analyses and interpretations, investigating what the current overall sales of the business are and providing insights that will guide future business decisions.

Below is last years overall sales vs deliveries data.

1. Please identify the qualitative and quantitative discrete, continuous varibles?

2. Is it cross sectional or time series data?

3. How do you calculate z scores and which are outliers?

4. How do you calculate the covariance and correlation and what does it mean?

Product ID Fat/Sugar
Content
Item Type Overall
Sales
Deliveries
FDV28 Regular Frozen Foods 272 122
FDF34 Regular Snack Foods 397 151
FDN49 Regular Breakfast 399 192
FDP38 Low Fat/Sugar Canned 405 174
FDT36 Low Fat/Sugar Baking Goods 459 184
FDX38 Regular Dairy 575 213
DRJ59 Low Fat/Sugar Diet Drinks 579 266
FDE35 Regular Potato Crisps 586 170
FDZ02 Regular Dairy 587 317
NCK06 Regular Household 606 321
FDX48 Regular Baking Goods 618 235
FDG40 Low Fat/Sugar Frozen Foods 645 213
FDA49 Low Fat/Sugar Canned 698 181
FDV11 Regular Breads 700 224
NCI29 Regular Health and Hygiene 709 284
FDE59 Regular Potato Crisps 719 223
NCK05 Regular Health and Hygiene 735 323
DRN35 Low Fat/Sugar Diet Drinks 755 219
FDE17 Regular Frozen Foods 756 212
NCI31 Regular Others 769 400
DRI25 Regular Soft Drinks 774 333
FDU33 Regular Snack Foods 781 211
FDY40 Regular Frozen Foods 788 292
DRK35 Low Fat/Sugar Diet Drinks 797 215
FDK04 Low Fat/Sugar Frozen Foods 802 401
FDR43 Regular Fruits and Vegetables 806 258
FDY12 Regular Baking Goods 810 227
NCG43 Regular Household 833 425
FDA44 Regular Fruits and Vegetables 849 297
DRB25 Regular Soft Drinks 858 360
FDW38 Regular Dairy 863 345
FDV48 Regular Baking Goods 864 415
FDW12 Regular Baking Goods 871 226
FDW13 Low Fat/Sugar Canned 883 459
FDO60 Low Fat/Sugar Baking Goods 892 464
FDT43 Regular Fruits and Vegetables 935 234
DRL35 Low Fat/Sugar Diet Drinks 952 400
FDE22 Low Fat/Sugar Snack Foods 959 422
FDW24 Low Fat/Sugar Baking Goods 972 311
DRD25 Low Fat/Sugar Soft Drinks 1019 255
NCJ19 Regular Others 1031 454
FDX23 Low Fat/Sugar Baking Goods 1040 541
FDD10 Regular Snack Foods 1071 364
FDU26 Regular Dairy 1073 354
FDP39 Low Fat/Sugar Meat 1091 513
DRH25 Low Fat/Sugar Soft Drinks 1091 578
DRC25 Regular Soft Drinks 1117 559
FDY03 Regular Meat 1125 563
FDU46 Regular Snack Foods 1125 349
FDH27 Low Fat/Sugar Dairy 1151 633
FDB27 Low Fat/Sugar Dairy 1182 355
FDZ33 Low Fat/Sugar Snack Foods 1182 579
FDR49 Low Fat/Sugar Canned 1198 503
FDX27 Regular Dairy 1229 430
FDV04 Regular Frozen Foods 1257 679
FDH21 Regular Seafood 1268 418
FDY35 Regular Breads 1286 514
FDP24 Low Fat/Sugar Baking Goods 1333 720
FDR02 Low Fat/Sugar Dairy 1334 374
FDL38 Regular Canned 1338 455
FDC59 Regular Potato Crisps 1342 523
NCK53 Regular Health and Hygiene 1389 542
DRD37 Low Fat/Sugar Soft Drinks 1398 489
FDY60 Regular Baking Goods 1438 733
NCH54 Regular Household 1438 374
FDU32 Regular Fruits and Vegetables 1462 731
FDK15 Low Fat/Sugar Meat 1488 491
FDE53 Low Fat/Sugar Frozen Foods 1491 581
FDS48 Low Fat/Sugar Baking Goods 1505 497
FDY07 Regular Fruits and Vegetables 1516 379
FDR48 Low Fat/Sugar Baking Goods 1518 516
FDA50 Low Fat/Sugar Dairy 1545 773
FDE10 Regular Snack Foods 1574 787
FDR26 Low Fat/Sugar Dairy 1594 558
NCB06 Regular Health and Hygiene 1598 575
NCJ17 Regular Health and Hygiene 1619 550
FDJ07 Low Fat/Sugar Meat 1631 881
FDH35 Low Fat/Sugar Potato Crisps 1645 543
FDQ14 Low Fat/Sugar Dairy 1648 593
FDB34 Low Fat/Sugar Snack Foods 1657 746
FDQ56 Regular Fruits and Vegetables 1678 839
FDH14 Regular Canned 1686 506
NCJ43 Regular Household 1744 942
FDR07 Regular Fruits and Vegetables 1809 923
FDP01 Regular Breakfast 1830 769
FDH47 Low Fat/Sugar Potato Crisps 1847 720
FDS37 Low Fat/Sugar Canned 1854 686
FDD36 Low Fat/Sugar Baking Goods 1896 720
FDF16 Low Fat/Sugar Frozen Foods 1921 730
FDG53 Low Fat/Sugar Frozen Foods 1957 1037
FDM44 Regular Fruits and Vegetables 1961 1039
NCI54 Regular Household 1965 550
FDY24 Regular Baking Goods 1995 1057
NCJ30 Regular Household 2037 774
FDF33 Regular Seafood 2049 1086
FDW20 Regular Fruits and Vegetables 2094 1047
FDN15 Low Fat/Sugar Meat 2097 860
NCJ18 Regular Household 2133 619
FDB49 Regular Baking Goods 2168 542
FDE11 Regular Potato Crisps 2221 1088
DRO47 Low Fat/Sugar Diet Drinks 2264 1155
FDP59 Regular Breads 2285 686
FDX43 Regular Fruits and Vegetables 2330 1235
FDX51 Regular Meat 2349 1292
FDO24 Low Fat/Sugar Baking Goods 2377 689
FDU47 Regular Breads 2388 812
FDS12 Low Fat/Sugar Baking Goods 2391 1076
FDU35 Low Fat/Sugar Breads 2397 719
FDU57 Regular Snack Foods 2408 819
DRE49 Regular Soft Drinks 2429 1312
FDW47 Low Fat/Sugar Breads 2437 1170
DRI47 Low Fat/Sugar Diet Drinks 2445 1051
NCM43 Regular Others 2447 856
NCH18 Regular Household 2457 1302
NCH30 Regular Household 2490 921
FDB17 Low Fat/Sugar Frozen Foods 2535 1039
DRD24 Low Fat/Sugar Soft Drinks 2553 1098
DRM23 Low Fat/Sugar Diet Drinks 2587 1138
DRI01 Regular Soft Drinks 2587 802
FDZ10 Low Fat/Sugar Snack Foods 2657 1116
FDW26 Regular Dairy 2669 774
FDE04 Regular Frozen Foods 2696 755
FDX01 Low Fat/Sugar Canned 2796 1314
FDZ21 Regular Snack Foods 2800 868
DRK59 Low Fat/Sugar Diet Drinks 2812 844
FDB32 Regular Fruits and Vegetables 2816 732
FDC60 Regular Baking Goods 2834 1247
DRJ23 Low Fat/Sugar Diet Drinks 2836 936
FDP19 Regular Fruits and Vegetables 2842 1222
DRN47 Low Fat/Sugar Diet Drinks 2876 1582
FDJ41 Low Fat/Sugar Frozen Foods 2878 1266
NCF54 Regular Household 2932 1583
NCK29 Regular Health and Hygiene 2956 946
FDU58 Regular Snack Foods 2993 1377
FDZ12 Low Fat/Sugar Baking Goods 3006 1293
NCH55 Regular Household 3036 759
FDZ51 Regular Meat 3047 975
DRM47 Low Fat/Sugar Diet Drinks 3057 856
FDE05 Regular Frozen Foods 3062 1439
FDJ28 Low Fat/Sugar Frozen Foods 3079 1447
NCK19 Regular Others 3100 837
FDC35 Regular Potato Crisps 3106 1677
FDZ09 Low Fat/Sugar Snack Foods 3112 934
FDB58 Regular Snack Foods 3120 1654
NCM55 Regular Others 3147 1699
FDZ45 Low Fat/Sugar Snack Foods 3175 1111
FDK51 Low Fat/Sugar Dairy 3180 827
FDG33 Regular Seafood 3264 1697
FDF52 Low Fat/Sugar Frozen Foods 3284 1182
FDV36 Low Fat/Sugar Baking Goods 3289 1612
FDC15 Low Fat/Sugar Dairy 3300 1749
FDU23 Low Fat/Sugar Breads 3302 826
FDV60 Regular Baking Goods 3339 1469
FDM25 Regular Breakfast 3340 1102
FDZ26 Regular Dairy 3346 870
FDB28 Low Fat/Sugar Dairy 3362 1849
NCG18 Regular Household 3384 1861
FDB22 Low Fat/Sugar Snack Foods 3384 1117
FDY02 Regular Dairy 3419 1436
NCH06 Regular Household 3449 1897
FDM39 Low Fat/Sugar Dairy 3582 896
NCC54 Regular Health and Hygiene 3615 1844
FDQ39 Low Fat/Sugar Meat 3631 1852
FDS13 Low Fat/Sugar Canned 3710 1187
FDL14 Regular Canned 3739 1159
DRA12 Regular Soft Drinks 3829 1723
FDV31 Regular Fruits and Vegetables 3882 1359
NCH42 Regular Household 3905 1445
FDE28 Regular Frozen Foods 3916 1958
FDT11 Regular Breads 3943 1498
FDX12 Regular Baking Goods 4097 1967
NCH07 Regular Household 4120 1318
FDR37 Regular Breakfast 4196 1175
FDT13 Low Fat/Sugar Canned 4334 1777
FDP27 Low Fat/Sugar Meat 4364 1658
FDD47 Regular Potato Crisps 4432 1330
NCL29 Regular Health and Hygiene 4437 2041
FDZ03 Regular Dairy 4474 1253
FDY39 Regular Meat 4594 2251
FDW40 Regular Frozen Foods 4844 2277
FDB60 Low Fat/Sugar Baking Goods 4860 1215
FDA43 Regular Fruits and Vegetables 4877 1561
FDJ57 Regular Seafood 5015 2207
FDC46 Low Fat/Sugar Snack Foods 5164 2014
FDW56 Regular Fruits and Vegetables 5195 1455
DRE01 Regular Soft Drinks 5332 2506
DRF36 Low Fat/Sugar Soft Drinks 5350 2408
FDK28 Low Fat/Sugar Frozen Foods 5411 2868
FDV59 Low Fat/Sugar Breads 5661 1585
FDI38 Regular Canned 5798 2087
DRJ11 Low Fat/Sugar Diet Drinks 6051 1513
DRL01 Regular Soft Drinks 6310 2209
FDX39 Regular Meat 6332 1710
FDO11 Regular Breads 6972 2719
FDC02 Low Fat/Sugar Canned 7029 1898
DRG49 Regular Soft Drinks 7086 2551
FDB15 Low Fat/Sugar Dairy 7646 4205
FDY26 Regular Dairy 7834 3682
FDG47 Regular Potato Crisps 8132 4147
FDP15 Low Fat/Sugar Meat 9228 3599

Solutions

Expert Solution

1) Qualitative data is a data concerned with descriptions, which can be observed but cannot be computed.On the contrary, quantitative data is the one that focuses on numbers and mathematical calculations and can be calculated and computed.

Product ID , Fat/sugar Content and Item type are Qualitative variables

Where as Overall sales and deliveries are discrete quantitative variables.

2) The above data is a cross sectional because it is a part of a large population and data is collected by observing many subject like id, fat/sugar content etc.. where as time series data is data collected in regular intervals of time...

3)Almost all the data is expected to lie within 3 standard deviations from the mean(99.7%) So anything lying outside the above limits will be considered as outliers.

Z scores are calculated from mean and standard deviation of a variable..ie

you can find the standardized values(Z scores) in by importing this data to excel. give =standardize(Cell value) in excel an z score corresponds to the cell value is generated.

For eg mean of overall sales= 2507

Standard deviation of overall sales=1690

Take any value of overall sales. say 272

Now the z score for 272 is

Similarly z score for all the values are calculated

and you will find many values are lying with in the range (-3,3). According to my observation only four values in overall sales have z scores greater than 3 . They are the last four observations in the overall sales series..7646,7834,8132,9228  

Overall sales Z scores
7646 3.040809645
7834 3.152051779
8132 3.328382395
9228 3.976900367

The same procedure can be repeated for deliveries

4)Correlation matrix

Correlations Overall sales Deliveries
Overall sales 1 0.92
Deliveries 0.92 1

The value 0.92 indicates a high degree of positive correlation between the variables. ie raising the overall sales will increase the delivery cost considerably..

Covariance Matrix

Covariance is a measure of how changes in one variable are associated with changes in a second variable.

The covariance indicates that the relationship between the variables in positive or direct.

Covariances Overall sales Deliveries
Overall sales 2841843.5 1119940.984
Deliveries 1119940.984 523393.489

This matrix indicates that the variances within the data are quite high especially the variance of deliveries is double that of variance of overall sales which indicates the delivery cost increases substantially with the increase in sales. So profit will not increase by increasing the sales. There are outliers in the data so repeat the same by removing the outliers. After removing the outliers my standard deviation for sales decreased by 200 points..


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