Question

1. Calculate the mean Days in Inventory for the cars in the sample. Also, do the following: Compare the mean to the median and the mode. Highlight the value that would be a better representation of the "typical" price of a car in inventory.

2. Calculate the standard deviation of the Days in Inventory for the cars in the sample.

3. Calculate the 5 number summary for the suggested retail prices of the cars in the sample. This consists of the 1st, 2nd, 3rd, 4th quartile, and the IQR.

Sample Car #	Color	MPG	Suggest Retail Price	Option Package	Days in Inventory
1	Grey	27.6	$    24,390.00	LX	1
2	Grey	32.4	$    21,780.00	Touring	10
3	Blue	33.2	$    21,149.00	Touring	28
4	Black	34.7	$    22,069.00	LX	21
5	Blue	27.2	$    22,532.00	Touring	16
6	Blue	26.6	$    20,345.00	Touring	22
7	Red	37.3	$    22,112.00	EX	12
8	Silver	34.9	$    21,289.00	Touring	23
9	Silver	29.6	$    24,871.00	LX	15
10	Silver	32.3	$    25,389.00	EX	8
11	Grey	31.9	$    25,998.00	EX	28
12	Red	26.4	$    19,713.00	LX	55
13	Black	34.8	$    25,213.00	EX	2
14	Silver	35.9	$    24,467.00	Touring	33
15	Black	34.6	$    21,402.00	LX	17
16	Black	33.3	$    20,351.00	LX	14
17	Grey	33.1	$    23,732.00	Touring	1
18	Red	37.5	$    24,558.00	Touring	2
19	Red	27.8	$    19,167.00	LX	18
20	Red	36.1	$    19,903.00	Touring	22
21	Blue	28.8	$    22,140.00	Touring	19
22	Red	26.2	$    22,180.00	EX	41
23	Silver	27.4	$    23,120.00	Touring	33
24	Black	34.9	$    19,837.00	Touring	21
25	Red	36.5	$    24,666.00	EX	31
26	Red	26.3	$    19,446.00	EX	35
27	Blue	31.4	$    23,954.00	Touring	11
28	Blue	30.9	$    21,201.00	LX	3
29	Red	27.4	$    21,346.00	EX	26
30	Red	36	$    19,406.00	EX	31

Answer 1

Question 1

Here, we have to find the mean days in Inventory for the cars in the given sample. The descriptive statistics for the days in Inventory by using excel are summarised as below:

It is observed that the mean number of days in Inventory is given as 19.97 days approximately.

It is observed that the median number of days in Inventory is given as 20 days.

It is observed that the mode number of days in inventory is given as 1 day.

That is, mean and median numbers of days in Inventory are approximately equal, while the mode number of days in Inventory is very different than that of mean and median.

Days in Inventory
Mean	19.96666667
Standard Error	2.347159366
Median	20
Mode	1
Standard Deviation	12.85592131
Sample Variance	165.2747126
Kurtosis	0.457174971
Skewness	0.515149156
Range	54
Minimum	1
Maximum	55
Sum	599
Count	30

Now, we have to find the descriptive statistics for the suggest retail price for the cars in the sample which is given as below:

Suggest Retail Price
Mean	22257.53333
Standard Error	373.9559681
Median	22090.5
Mode	#N/A
Standard Deviation	2048.241192
Sample Variance	4195291.982
Kurtosis	-1.18527282
Skewness	0.191610515
Range	6831
Minimum	19167
Maximum	25998
Sum	667726
Count	30

The median price would be a better representation of the typical price of a car in inventory. The median price is given as $22,090.5. The mean retail price for the cars in the sample is given as $22,257.53 approximately.

Question 2

The standard deviation for the days in Inventory for the cars in the sample is given as 12.86 days approximately.

Question 3

Here, we have to find out 5 number summary for the suggested retail prices of the cars in the sample.

The 5 number summary by using excel is given as below:

Minimum = $19,167

First Quartile = Q₁ = $20,351

Second Quartile = Q₂ = Median = $22,090.5

Third Quartile = Q₃ = $24,390

Maximum = $25,998

Inter-quartile Range = IQR = Q₃ - Q₁ = $24,390 - $20,351 = $4,039