Question

With modern UPC coding and check-out scanners, supermarkets generate large amounts of transactional data. Here we examine a data set of purchases at one supermarket in a three-day period. For our purposes a “purchase” is the buying of 1 of more units of a given item in a given market basket of purchases. Thus if a shopper buys 3 identical bottles of milk and 4 identical candy bars, this is two “purchases”. The first is of 3 units, the second is of 4 units.

Rather than list the units for all purchases, we summarize that data in the following table. The total number of units sold was:

Units Sold	Count
1	90
2	1,080
3	3,120
4	4,379
5	3,450
6	1,240
7	168
8	2

Summarizing the values of “units sold” in this way is common practice when the data set is large and the set of possible data values is limited.

1. What is the total number of purchases in this data set?

2. What is the total number of units sold?

3. What is the range of “units sold”?

4. What is the median of “units sold”?

5. What is the mode of “units sold”?

6. What is the sample mean?

Answer 1

Unit	Count	Units Sold
1	90	90
2	1,080	2160
3	3,120	9360
4	4,379	17516
5	3,450	17250
6	1,240	7440
7	168	1176
8	2	16
	13529	55008

What is the total number of purchases in this data set?

= 13529

What is the total number of units sold?

= 55008

What is the range of “units sold”?

range=max-min =    17516   -   16   =   17500

What is the median of “units sold”?

Median=0.5(n+1)th value =    4.5th
=   4800.000

What is the mode of “units sold”

= 17516 (As 4379 was highest )

What is the sample mean?

= 55008 / 13529 = 4.066 mean unit in each purchase

Please revert in case of any doubt.

Please upvote. Thanks in advance