**Class Intervals**

The limits written to describe classes are called stated class limits. However a frequency distribution may have real class limits which differ slightly from the stated limits. The difference is due to rounding. Suppose. milk I cartons state that the cartons certainty 2 qua (32 fluid ounces). Suppose Next ‘that the contents of a carton are measured to the nearest.tenth’of ari ounce. The convention usually followed in making free I quench distributions is to “round 5 or more up. That is, for example contents of 31.20, 31.21, 31.22, 31.23, and 31.24 ounces, rounded to the nearest tenth, are 31.2. But 31.25 through 31.29 are rounded to 31. 3. Consequently, fl class with stated limits of, for example, 31.5-31.7 includes the numbers 31.45,31.46, 31.47, : .. ,31.73, 31.74 and thus has the real limits

31. 45 up to, but not including, 31. 75

Sometimes, the words “up to, but not including” are replaced under.” Then the class would be described as “31.45 and under 31–75 class limit are arbitrary because they depend upon fie rounding procedure followed. You will know what the real limits are if you prepared the data set from which a frequency distribution was made. For frequency distributions prepared by others, we use the “5 in the next place” rule to determine real limits from stated limits. For example, the stated limits

**EXERCISE** The stated class limits for average hourly wage rates are $3.75-$3.99. What are the real limits?

**ANSWER** $3.745 and $3.995.

When classes describe counts, so that rounding is not involved, real c limits are the same as the stated class limits. For example, suppose quench distribution classes describe numbers of defective pa terminate day. Then a class such as 3- 5 means exactly 3 or 4 or 5 defec :. e’parts. The real limits are 3 and 5, the same as the stated limits. Class Interval A class interval is the difference between the €OJ class limits. For example, the stated limits 31.5-31.7 correspond tc he real limits 31.45 and 31.75; so the 31.5-31.7 class has a class interval of

**EXERCISE** What is the class interval forth class $3.75-$3.99 of the last exercise?

**ANSWER** $0.25.

For classes describing counts, the class interval is the difference between the stated limits, because the stated and real limits are the same. Also, when the “and under” method of describing classes is used, the class interval is taken as the difference between the stated limits. For example, the class $10.00 and under $15.00 means $10.00 and values up to, but not including, SI5.oo. The class interval is $5.00. We use the between-class width (the difference between successive lower stated class limits) in setting up the classes of a frequency distribution. The class interval, which may differ from the width, is a term used in describing classes after they have been set up.What is the class interval forthe class $3.75-$3.99 of the last exercise? ANSWER $0.25. For classes describing counts, the class interval is the difference between the stated limits, because the stated and real limits are the same. Also, when the “and under” method of describing classes is used, the class interval is taken as the difference between the stated limits. For example, the class $10.00 and under $15.00 means $10.00 and values up to, but not including, SI5.oo. The class interval is $5.00. We use the between-class width (the difference between successive lower stated class limits) in setting up the classes of a frequency distribution. The class interval, which may differ from the width, is a term used in describing classes after they have been set up.