2.2c Histograms and Frequency Tables for Grouped Data

Over a given month, he realizes that he can sell up to 25 boxes of any given item. But any item with 26 or more boxes will cause difficulties in the storage area. For each item with 26 boxes or over, he expects to lose $80 (per item, not per box) because he could have stocked other items. Based on the current information, how much money will he expect to lose because of having too much extra stock?

240 In order to determine the total expected loss, we will need to determine the number of items that have at least 26 boxes in storage. Looking at the histogram, this corresponds to the fourth and fifth bars. The fourth bar shows that 2 items have between 26 and 31 boxes in storage. The fifth bar show that 1 item has at least 32 boxes in storage. Thus, there are 2+1=3 items with at least 26 boxes in storage. Each of these items is expected to result in an $80 loss, so the total expected loss due to this overstock is 3×$80=$240.

An airport measures the check-in waiting time for people on a certain flight. The times (in minutes) for 14 passengers are given below. 13,18,21,21,24,25,26,28,30,30,30,34,35,38 Studies have shown that passenger who wait longer than 26 minutes typically report complaints to client services. Use the following grouped frequency table with 4 classes to determine how many complaints are likely to be reported for this set of passenger?

7 To determine the number of passengers that are likely to complain, we must determine how many passengers waited longer than 26 minutes. From the third row of the grouped frequency table, we see there were 4 passengers that waited between 27 and 33 minutes; and from the last row we see that 3 passengers waited between 34 and 40 minutes. So, a total of 4+3=7 passengers waited longer than 26 minutes and are thus likely to complain.

An airport measures the check-in waiting time for people on a certain flight. The times (in minutes) for 14 passengers are given below. Determine the class width for a grouped data frequency table using 4 classes. 13,18,21,21,24,25,26,28,30,30,30,34,35,38

7 Minutes

A company is measuring the effectiveness of a new drug that is designed to help people lose weight. So, they perform an experiment by giving several people the drug and track their weight loss over a 6-month period. Their overall weight loss amounts (in kilograms) are given below. Construct a frequency table for these values using 4 classes. In order to reward the participants, they decide to give the following gifts: $20 for each person losing less than 5 kg, $50 for each person losing at least 5 but less than 9 kg, and $100 for each person losing at least 9 kg. How much total will they give out to the participants?

In order to compute the total payment, we must determine the total number of people receiving each amount. Row 1 of the table shows that 2 people lost under 5 kg, and will thus receive $20 each. Row 2 of the table shows that 5 people lost at lest 5 but less than 9 kg, and will thus receive $50 each. Rows 3 and 4 of the table show that 3+1=4 people lost at least 9 kg, and will thus receive $100 each. Therefore, the total payment will be 2×$20+5×$50+4×$100=$690.