A chain of sport shops catering to beginning skiers, headquartered in Aspen, Colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. Based on these figures, it wants to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. A sample of cash register receipts revealed these initial purchases:
$140 
$82 
$265 
$168 
$90 
$114 
$172 
$230 
$142 
86 
125 
235 
212 
171 
149 
156 
162 
118 
139 
149 
132 
105 
162 
126 
216 
195 
127 
161 
135 
172 
220 
229 
129 
87 
128 
126 
175 
127 
149 
126 
121 
118 
172 
126 

a. Arrive at a suggested class interval. Use six classes, and let the lower limit of the first class be $70.
b. What would be a better class interval?
c. Organize the data into a frequency distribution using a lower limit of $80.
d. Interpret your findings.
Solution:
Step1 of 5:
Given a 44 samples of cash register receipts revealed these initial purchases.
$140 
$82 
$265 
$168 
$90 
$114 
$172 
$230 
$142 
86 
125 
235 
212 
171 
149 
156 
162 
118 
139 
149 
132 
105 
162 
126 
216 
195 
127 
161 
135 
172 
220 
229 
129 
87 
128 
126 
175 
127 
149 
126 
121 
118 
172 
126 

Step 2 of 5:
a). To arrive at a suggested class interval.
Here we use 6 classes and the lower limit of the first class be 70.
Then the class interval is
70 to 105
105 to 140
140 to 175
175 to 210
210 to 245
245 to 280.
Step 3 of 5:
b). We have to find the best class interval.
Here we have 44 observations. Then we using rule.
The 25 = 32, which is less than 44, so 5 classes are not enough.
26 = 64, which is greater than 44.
Hence, I will recommend 6 classes.
Therefore the class interval is
70 to 10
105 to 140
140 to 175
175 to 210
210 to 245
245 to 280.
So this is the better class interval.