In: Math
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 |
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..