Question

data is gathered on the number of pairs of shoes that a person owns from a sample group of 65 people. the data values range from 6 pairs to 104 pairs.
a. choose the type of grouping that would be best in setting up a relative frequency table for this data.
a. single-value grouping
b. limit grouping
c. cutpoint grouping
b. choose the choice with classes/categories that is appropriate to be used in forming a relative frequency table.
a. 0-10, 11-20, 21-30, 31-40, ... , 91-100, 101-110
b. 0-9, 10-20, 21-30, 31-40, ... , 91-100, 101-110
c. 0-10, 10-19, 20-29, 30-39, ... , 90-99, 100-109
d. 0-9, 10-19, 20-29, 30-39, ... , 90-99, 100-109

Explanation:

Part (a)

• Single - value grouping is used when data values are discrete and there are relatively few distinct values. Here, the data ranges from 6 to 104, so there are many distinct values, so single - value grouping is not suitable.
• Limit grouping is used for discrete data with a small range and when we want to group by class limits. But our data has a large range (from 6 to 104) and is about the number of pairs of shoes (a discrete variable, but with a wide range). Cut - point grouping is more appropriate for data where we can have non - integer cut - points (even though our data is discrete, the range is large and cut - point grouping helps in creating continuous - like intervals for better grouping). Also, limit grouping can have issues with overlapping or non - consistent boundaries when the data range is large. Cut - point grouping is used when we have data that can be thought of as having cut - points (e.g., for continuous data or discrete data with a large range). So the best grouping is cut - point grouping.

• The data ranges from 6 to 104 pairs of shoes. We need to create classes that cover this range without gaps or overlaps.
• Option A: The first class is 0 - 10, which includes 6. The class width is 10 (10 - 0=10, 20 - 11 = 9? No, wait, 11 - 20 has a width of 9? No, 20 - 11+1 = 10? Wait, no, for limit grouping, the class width should be consistent. Wait, 0 - 10 (width 10), 11 - 20 (width 9), which is inconsistent.
• Option B: 0 - 9 (width 9), 10 - 20 (width 10), inconsistent width.
• Option C: 0 - 10 (width 10), 10 - 19 (width 9), inconsistent width and also overlapping (10 is in two classes).
• Option D: The classes are 0 - 9, 10 - 19, 20 - 29, ..., 90 - 99, 100 - 109. The width of each class is 10 (9 - 0+1 = 10? Wait, no, for cut - point grouping, the cut - points are at 9.5, 19.5, etc. But in terms of covering the data: the minimum is 6 (in 0 - 9), the maximum is 104 (in 100 - 109). The class width is consistent (each class has a range of 10: 9 - 0 = 9? Wait, no, 0 - 9 has 10 values (0 - 9 inclusive), 10 - 19 has 10 values (10 - 19 inclusive), etc. And there are no gaps or overlaps. Also, the data from 6 to 104 is covered: 6 is in 0 - 9, 104 is in 100 - 109.

Answer:

C. Cutpoint grouping

Part (b)