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A quantitative data set has been grouped by using limit grouping with equal-width classes. The lower and upper limits of the first class are 3and 8, respectively, and the class width is 6.

a. What is the class mark of the second class?

b. What are the lower and upper limits of the third class?

c. Which class would contain an observation of 23?

Short Answer

Expert verified

(a) The class mark of the second class is 11.5.

(b) The upper and the lower limits of the third class are 20and15.

(c) The fourth class contains the observation of 23.

Step by step solution

01

Part (a) Step 1: Given information

A quantitative data set has been grouped by using limit grouping with equal-width classes.

The lower and upper limits of the first class are 3and 8.

The class width is6.

02

Part (a) Step 2: Explanation

The average of the lower and upper bounds is the class mark.

Calculation: The lower limit for second class is 9and the top limit is 14.

The second class will have a class size of

=9+142

=11.5

03

Part (b) Step 1: Given Information

A quantitative data set has been grouped by using limit grouping with equal-width classes.

The lower and upper limits of the first class are 3and 8.

The class width is 6.

04

Part (b) Step 2: Explanation

A class's lower class limit is the smallest data value that can be stored in the class.

The lower limit is one higher than the second class's upper limit, and the upper limit is the preceding class's upper limit multiplied by the class width.

05

Part (c) Step 1: Given Information 

A quantitative data set has been grouped by using limit grouping with equal-width classes.

The lower and upper limits of the first class are 3and 8respectively.

The class width is 6.

06

Part (c) Step 2: Explanation

A class's lower class limit is the smallest data value that can be stored in the class.

Because the observation of 23does not fall within the third class's bottom and higher bounds, it is placed in the fourth class.

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Most popular questions from this chapter

For data that are grouped in classes based on more than a single value, lower-class limits (or cut points) are used on the horizontal axis of a histogram for depicting the classes. Classmarks (or midpoints) can also be used, in which case each bar is centered over the mark (or midpoint) of the class it represents. Explain the advantages and disadvantages of each method.

Days to Maturity for Short-Term Investments. Refer to the days-to-maturity data in Table 2.6 on page 53 . Note that there are 40observations, the smallest and largest of which are 36and 99, respectively. Apply the preceding procedure to choose classes for limit grouping. Use approximately seven classes. Note: If in Step 2 you decide on 10 for the class width and in Step 3 you choose 30 for the lower limit of the first class, then you will get the same classes as used in Example 2.13; otherwise, you will get different classes (which is fine).

San Francisco Giants. From the Baseball Almanac website, we found the heights, in inches, of the players on the 2012 World Series-winning San Francisco Giants baseball team.

a. Construct a stem-and-leaf diagram of these data with five lines per stem.

b. Why is it better to use five lines per stem here instead of one or two lines per stem?

Weights of 18- to 24-Year-Old Males. Refer to the weight data in Table 2.8on page 54 . Note that there are 37 observations, the smallest and largest of which are 129.2and278.8, respectively. Apply the preceding procedure to choose classes for cut point grouping. Use approximately eight classes. Note: If in Step 2 you decide on 20 for the class width and in Step 3 you choose 120 for the lower cut point of the first class, then you will get the same classes as used in Example 2.14; otherwise, you will get different classes (which is fine).

When is the use of single-value grouping particularly appropriate?

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