a.
Develop a seasonal index for each month for the package sales.
Write a note on various months
a.
Answer to Problem 29CE
The seasonal index for each month for the package sales are,
Period | Month | Seasonal Index |
1 | July | 0.19792 |
2 | August | 0.25663 |
3 | September | 0.8784 |
4 | October | 2.10481 |
5 | November | 0.77747 |
6 | December | 0.18388 |
7 | January | 0.26874 |
8 | February | 0.63189 |
9 | March | 1.67943 |
10 | April | 2.73547 |
11 | May | 1.67903 |
12 | June | 0.60633 |
The two months October and April represents more than twice the average.
Explanation of Solution
Calculation:
Twelve months- moving average:
Centered Moving Average:
Specific seasonal index:
Year | Quarter | Package |
Four-quarter moving average |
Centered Moving average | Specific seasonal |
2014 | July | 18.36 | |||
August | 28.62 | ||||
September | 101.34 | ||||
October | 182.7 | ||||
November | 54.72 | ||||
December | 36.36 | ||||
2015 | January | 25.2 | 100.305 | 0.25123 | |
February | 67.5 | 100.395 | 99.9825 | 0.67512 | |
March | 179.37 | 100.215 | 99.79125 | 1.79745 | |
April | 267.66 | 99.75 | 101.5688 | 2.63526 | |
May | 179.73 | 99.8325 | 103.74 | 1.73250 | |
June | 63.18 | 103.305 | 103.5825 | 0.60995 | |
July | 16.2 | 104.175 | 103.215 | 0.15695 | |
August | 23.04 | 102.99 | 103.275 | 0.22309 | |
September | 102.33 | 103.44 | 102.6225 | 0.99715 | |
October | 224.37 | 103.11 | 103.4813 | 2.16822 | |
November | 65.16 | 102.135 | 104.5725 | 0.62311 | |
December | 22.14 | 104.8275 | 104.3925 | 0.21209 | |
2016 | January | 30.6 | 104.3175 | 104.8575 | 0.29183 |
February | 63.54 | 104.4675 | 105.585 | 0.60179 | |
March | 167.67 | 105.2475 | 105.0375 | 1.59629 | |
April | 299.97 | 105.9225 | 103.7063 | 2.89249 | |
May | 173.61 | 104.1525 | 104.5575 | 1.66042 | |
June | 64.98 | 103.26 | 105.6075 | 0.61529 | |
July | 25.56 | 105.855 | 105.1875 | 0.24299 | |
August | 31.14 | 105.36 | 105.3788 | 0.29551 | |
September | 81.09 | 105.015 | 104.2425 | 0.77789 | |
October | 213.66 | 105.7425 | 102.4688 | 2.08512 | |
November | 96.3 | 102.7425 | 101.5838 | 0.94799 | |
December | 16.2 | 102.195 | 101.5725 | 0.15949 | |
2017 | January | 26.46 | 100.9725 | ||
February | 72.27 | 102.1725 | |||
March | 131.67 | 109.1373 | |||
April | 293.4 | 116.937 | |||
May | 158.94 | 120.92 | |||
June | 79.38 | 109.3275 |
The monthly indexes are,
2014 | 2015 | 2016 | 2017 | Means | |
Jan | 0.25123 | 0.29183 | 0.27153 | ||
Feb | 0.67512 | 0.60179 | 0.63845 | ||
Mar | 1.79745 | 1.59629 | 1.69687 | ||
April | 2.63526 | 2.89249 | 2.76388 | ||
May | 1.7325 | 1.66042 | 1.69647 | ||
June | 0.60995 | 0.61529 | 0.61262 | ||
July | 0.15695 | 0.24299 | 0.19997 | ||
August | 0.22309 | 0.29551 | 0.25929 | ||
Sep | 0.99715 | 0.7778 | 0.88752 | ||
Oct | 2.16822 | 2.0851 | 2.12667 | ||
Nov | 0.6231 | 0.9479 | 0.78555 | ||
Dec | 0.21208 | 0.1594 | 0.18579 |
Seasonal index:
Here,
Therefore,
The seasonal indexes are,
2014 | 2015 | 2016 | 2017 | Means | Seasonal Index | |
Jan | - | 0.25123 | 0.29183 | - | 0.27153 | 0.268738257 |
Feb | - | 0.67512 | 0.60179 | - | 0.63845 | 0.631891717 |
Mar | - | 1.79745 | 1.59629 | - | 1.69687 | 1.679428286 |
April | - | 2.63526 | 2.89249 | - | 2.76388 | 2.735469498 |
May | - | 1.7325 | 1.66042 | - | 1.69647 | 1.679028041 |
June | - | 0.60995 | 0.61529 | - | 0.61262 | 0.606326037 |
July | - | 0.15695 | 0.24299 | - | 0.19997 | 0.19791885 |
August | - | 0.22309 | 0.29551 | - | 0.25929 | 0.256634371 |
Sep | - | 0.99715 | 0.7778 | - | 0.88752 | 0.87840128 |
Oct | - | 2.16822 | 2.0851 | - | 2.12667 | 2.104812143 |
Nov | - | 0.6231 | 0.9479 | - | 0.78555 | 0.777473047 |
Dec | - | 0.21208 | 0.1594 | - | 0.18579 | 0.183878466 |
The seasonal index for October is 2.10481 and the seasonal index for April is 2.73547. That is, the months October and April represents more than twice the average compared with other months.
b.
Develop a seasonal index for each month for the non-package sales.
Write a note on various months
b.
Answer to Problem 29CE
The seasonal index for each month for the non-package sales are,
Period | Month | Seasonal Index |
1 | July | 1.73270 |
2 | August | 1.53389 |
3 | September | 0.94145 |
4 | October | 1.29183 |
5 | November | 0.66928 |
6 | December | 0.52991 |
7 | January | 0.23673 |
8 | February | 0.69732 |
9 | March | 1.00695 |
10 | April | 1.13226 |
11 | May | 0.98282 |
12 | June | 1.24486 |
The two months December and January having the low index values.
Explanation of Solution
Calculation:
The specific seasonal indices are,
Year | Quarter | Local ($) |
Four-quarter moving average |
Centered Moving average | Specific seasonal |
2014 | July | 43.44 | |||
August | 56.76 | ||||
September | 34.44 | ||||
October | 38.4 | ||||
November | 44.88 | ||||
December | 12.24 | ||||
2015 | January | 9.36 | 36.075 | 0.259459 | |
February | 25.8 | 34.64 | 38.32 | 0.673278 | |
March | 34.44 | 37.51 | 39.485 | 0.87223 | |
April | 34.32 | 39.13 | 40.38 | 0.849926 | |
May | 40.8 | 39.84 | 40.115 | 1.017076 | |
June | 40.8 | 40.92 | 39.465 | 1.033827 | |
July | 77.88 | 39.31 | 39.625 | 1.965426 | |
August | 76.2 | 39.62 | 39.845 | 1.912411 | |
September | 42.96 | 39.63 | 40.61 | 1.057868 | |
October | 51.36 | 40.06 | 42.205 | 1.216917 | |
November | 25.56 | 41.16 | 43.24 | 0.591119 | |
December | 15.96 | 43.25 | 44.195 | 0.361127 | |
2016 | January | 9.48 | 43.23 | 44.715 | 0.212009 |
February | 30.96 | 45.16 | 43.27 | 0.715507 | |
March | 47.64 | 44.27 | 42.04 | 1.133206 | |
April | 59.4 | 42.27 | 42.275 | 1.405086 | |
May | 40.56 | 41.81 | 43.135 | 0.940304 | |
June | 63.96 | 42.74 | 44.25 | 1.445424 | |
July | 67.2 | 43.53 | 45.24 | 1.485411 | |
August | 52.2 | 44.97 | 45.69 | 1.142482 | |
September | 37.44 | 45.51 | 45.82 | 0.81711 | |
October | 62.52 | 45.87 | 46.11 | 1.355888 | |
November | 35.04 | 45.77 | 47.235 | 0.741823 | |
December | 33.24 | 46.45 | 47.88 | 0.694236 | |
2017 | January | 15.96 | 48.02 | ||
February | 35.28 | 47.74 | |||
March | 46.44 | 45.97091 | |||
April | 67.56 | 45.348 | |||
May | 59.4 | 46.22667 | |||
June | 60.6 | 44.19 |
The monthly indexes are,
2014 | 2015 | 2016 | 2017 | Means | |
Jan | 0.25123 | 0.29183 | 0.235734 | ||
Feb | 0.67512 | 0.60179 | 0.694392 | ||
Mar | 1.79745 | 1.59629 | 1.002718 | ||
April | 2.63526 | 2.89249 | 1.127506 | ||
May | 1.7325 | 1.66042 | 0.97869 | ||
June | 0.60995 | 0.61529 | 1.239626 | ||
July | 0.15695 | 0.24299 | 1.725419 | ||
August | 0.22309 | 0.29551 | 1.527446 | ||
Sep | 0.99715 | 0.7778 | 0.937489 | ||
Oct | 2.16822 | 2.0851 | 1.286403 | ||
Nov | 0.6231 | 0.9479 | 0.666471 | ||
Dec | 0.21208 | 0.1594 | 0.527681 |
The
Therefore,
The seasonal indexes are,
2014 | 2015 | 2016 | 2017 | Means | Seasonal Index | |
Jan | 0.25123 | 0.29183 | 0.235734 | 0.23673 | ||
Feb | 0.67512 | 0.60179 | 0.694392 | 0.69732 | ||
Mar | 1.79745 | 1.59629 | 1.002718 | 1.00695 | ||
April | 2.63526 | 2.89249 | 1.127506 | 1.13226 | ||
May | 1.7325 | 1.66042 | 0.97869 | 0.98282 | ||
June | 0.60995 | 0.61529 | 1.239626 | 1.24486 | ||
July | 0.15695 | 0.24299 | 1.725419 | 1.73270 | ||
August | 0.22309 | 0.29551 | 1.527446 | 1.53389 | ||
Sep | 0.99715 | 0.7778 | 0.937489 | 0.94145 | ||
Oct | 2.16822 | 2.0851 | 1.286403 | 1.29183 | ||
Nov | 0.6231 | 0.9479 | 0.666471 | 0.66928 | ||
Dec | 0.21208 | 0.1594 | 0.527681 | 0.52991 |
The seasonal index for December is 0.52991 and the seasonal index for January is 0.23673. That is, the months December and January represents having the less index values compared with other months.
c.
Develop a seasonal index for each month for the total sales.
Write a note on various months
c.
Answer to Problem 29CE
The seasonal index for each month for the total sales are,
Period | Month | Seasonal Index |
1 | July | 0.63371 |
2 | August | 0.61870 |
3 | September | 0.89655 |
4 | October | 1.86415 |
5 | November | 0.74353 |
6 | December | 0.29180 |
7 | January | 0.25908 |
8 | February | 0.65069 |
9 | March | 1.49028 |
10 | April | 2.28041 |
11 | May | 1.48235 |
12 | June | 0.78876 |
The two months December and January having the low index values.
The two months April and October having the high index values.
Explanation of Solution
Calculation:
The specific seasonal indices are,
Year | Quarter | Local ($) |
Four-quarter moving average |
Centered Moving average | Specific seasonal |
2014 | July | 61.8 | |||
August | 85.38 | ||||
September | 135.78 | ||||
October | 221.1 | ||||
November | 99.6 | ||||
December | 48.6 | ||||
2015 | January | 34.56 | 136.38 | 0.270833 | |
February | 93.3 | 135.035 | 138.3025 | 0.276527 | |
March | 213.81 | 137.725 | 139.2763 | 0.161078 | |
April | 301.98 | 138.88 | 141.9488 | 0.11365 | |
May | 220.53 | 139.6725 | 143.855 | 0.185009 | |
June | 103.98 | 144.225 | 143.0475 | 0.392383 | |
July | 94.08 | 143.485 | 142.84 | 0.827806 | |
August | 99.24 | 142.61 | 143.12 | 0.767836 | |
September | 145.29 | 143.07 | 143.2325 | 0.295684 | |
October | 275.73 | 143.17 | 145.6863 | 0.186269 | |
November | 90.72 | 143.295 | 147.8125 | 0.281746 | |
December | 38.1 | 148.0775 | 148.5875 | 0.418898 | |
2016 | January | 40.08 | 147.5475 | 149.5725 | 0.236527 |
February | 94.5 | 149.6275 | 148.855 | 0.327619 | |
March | 215.31 | 149.5175 | 147.0775 | 0.221262 | |
April | 359.37 | 148.1925 | 145.9813 | 0.165289 | |
May | 214.17 | 145.9625 | 147.6925 | 0.189382 | |
June | 128.94 | 146 | 149.8575 | 0.496045 | |
July | 92.76 | 149.385 | 150.4275 | 0.72445 | |
August | 83.34 | 150.33 | 151.0688 | 0.62635 | |
September | 118.53 | 150.525 | 150.0625 | 0.315869 | |
October | 276.18 | 151.6125 | 148.5788 | 0.226374 | |
November | 131.34 | 148.5125 | 148.8188 | 0.266788 | |
December | 49.44 | 148.645 | 149.4525 | 0.67233 | |
2017 | January | 42.42 | 148.9925 | ||
February | 107.55 | 149.9125 | |||
March | 178.11 | 155.1082 | |||
April | 360.96 | 162.285 | |||
May | 218.34 | 167.1467 | |||
June | 139.98 | 153.5175 |
The monthly indexes are,
2014 | 2015 | 2016 | 2017 | Means | |
Jan | 0.25341 | 0.267964 | 0.260687 | ||
Feb | 0.674608 | 0.634846 | 0.654727 | ||
Mar | 1.53515 | 1.463922 | 1.499536 | ||
April | 2.127388 | 2.461755 | 2.294571 | ||
May | 1.533002 | 1.450107 | 1.491555 | ||
June | 0.726891 | 0.860417 | 0.793654 | ||
July | 0.658639 | 0.616643 | 0.637641 | ||
August | 0.693404 | 0.551669 | 0.622537 | ||
Sep | 1.014365 | 0.789871 | 0.902118 | ||
Oct | 1.892629 | 1.858812 | 1.875721 | ||
Nov | 0.613751 | 0.88255 | 0.74815 | ||
Dec | 0.256415 | 0.330807 | 0.293611 |
The
Therefore,
The seasonal indexes are,
2014 | 2015 | 2016 | 2017 | Means | Seasonal Index | |
Jan | 0.25341 | 0.267964 | 0.260687 | 0.25908 | ||
Feb | 0.674608 | 0.634846 | 0.654727 | 0.65069 | ||
Mar | 1.53515 | 1.463922 | 1.499536 | 1.49028 | ||
April | 2.127388 | 2.461755 | 2.294571 | 2.28041 | ||
May | 1.533002 | 1.450107 | 1.491555 | 1.48235 | ||
June | 0.726891 | 0.860417 | 0.793654 | 0.78876 | ||
July | 0.658639 | 0.616643 | 0.637641 | 0.63371 | ||
August | 0.693404 | 0.551669 | 0.622537 | 0.61870 | ||
Sep | 1.014365 | 0.789871 | 0.902118 | 0.89655 | ||
Oct | 1.892629 | 1.858812 | 1.875721 | 1.86415 | ||
Nov | 0.613751 | 0.88255 | 0.74815 | 0.74353 | ||
Dec | 0.256415 | 0.330807 | 0.293611 | 0.29180 |
The seasonal index for January is 0.25908 and the seasonal index for December is 0.29180. That is, the months December and January representing the less index values compared with other months. The seasonal index for April is 2.28041 and the seasonal index for October is 1.86415. That is, the months April and October representing the more index values compared with other months
d.
Compare the indexes for package sales, non-package sales and total sales.
d.
Explanation of Solution
Comparison:
The seasonal index for April in Package play is large compared with remaining months. Hence, the Package play is highest play in April. The seasonal index for July in Non-package is large compared with remaining months. Hence, the Non-Package play is highest play in July. From the given information, the 70% of the total sales comes from package play. Hence, the total play is very similar to package play.
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Chapter 18 Solutions
EBK STATISTICAL TECHNIQUES IN BUSINESS
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