e. Draw a frequency polygon
Frequency polygon (curve, since I smoothed it) follows:
Homework solutions for chapter 2 exercises 14, 18, and 22. Solutions to odd-numbered problems are in your text.
14. (page 31) Aloha Banking Company is studying the number of times their automatic teller, located in a Loblaws Supermarket, is used daily. Following is a list of the number of times the teller was used during the last 30 days. Develop a stem-and-leaf chart...
83, 64, 84, 76, 84, 54, 75, 59, 70, 61, 63, 80, 84, 73, 68, 52, 65, 90, 52, 77, 95, 36, 78, 61, 59, 84, 95, 47, 87, 60
The leaf unit is 1 (ATM customer)
| Stem | Leaves |
| 3 | 6 |
| 4 | 7 |
| 5 | 22499 |
| 6 | 0113458 |
| 7 | 035678 |
| 8 | 0344447 |
| 9 | 055 |
On half of the days, their ATM was used 70 times or fewer. The median was 71.5 ATM customers per day. The lowest day drew 36 ATM customers, while the highest day saw 95 ATM customers. Days with fewer than 50 or more than 90 customers were unusual.
18. (pages 36 & 37) A large retailer is studying the lead time (elapsed time between when an order is placed and when it is filled) for a sample of recent orders. The lead times are reported in days.
|
Lead Time (days) |
Frequency, f |
| 0 and under 5 | 6 |
| 5 and under 10 | 7 |
| 10 and under 15 | 12 |
| 15 and under 20 | 8 |
| 20 and under 25 | 7 |
| Total | 40 |
a. How many orders were studied?
40 orders
b. What is the midpoint of the first class?
2.5 is first class mark
c. What are the coordinates of the first class in a frequency polygon?
2.5, 6 are the (x,y) coordinates of the point representing the first class in the
frequency polygon.
d. Draw a histogram.
Histogram follows:
e. Draw a frequency polygon
Frequency polygon (curve, since I smoothed it) follows:
f. Interpret the lead times using the two charts.
Lead time ranges from 0 to almost 25 days. The most common lead time is 10 to 15 days.
22. Refer to the frequency distribution of lead time from exercise 18.
a. How many orders were filled in less than 10 days? How many were filled in
less than 15 days?
13 were filled in less than 10 days, 25 orders were filled in less than 15 days
b. Convert the frequency distribution to a less-than cumulative frequency distribution.
Less-than cumulative frequency distribution follows
Lead Time |
f |
CF |
| 0 up to 5 | 6 | 6 |
| 5 up to 10 | 7 | 13 |
| 10 up to 15 | 12 | 25 |
| 15 up to 20 | 8 | 33 |
| 20 up to 25 | 7 | 40 |
| Total | 40 |
c. Develop a less-than cumulative frequency polygon (ogive).
Less-than cumulative frequency polygon (curve) follows:
d. About sixty percent of the orders were filled in less than how many days?
Sixty percent of the orders were filled in less than 14 or 15 days.