When a class interval is expressed as: 100 up to 200,
A. observations with values of 100 are excluded from the class frequency.
B. observations with values of 200 are included in the class frequency.
C. observation with values of 200 are excluded from the class frequency.
D. the class interval is 99.
101
The correct answer is C. observation with values of 200 are excluded from the class frequency.
When a class interval is expressed as "100 up to 200," it means that observations with a value of 200 are not included in this particular class interval. However, observations with a value of 100 would be included in this class interval as it starts from 100. So, option A is incorrect. Option B is incorrect because the upper limit of the class interval is not included, only the lower limit is. Option D is incorrect because the class interval is actually 100 (as it ranges from 100 to 199).
To answer this question and understand class intervals, we need to understand the concept of inclusive and exclusive intervals.
Inclusive Interval: An inclusive interval includes the lower and upper bounds of the interval. This means that values equal to the lower and upper bounds are included in the interval. In notation, this is represented as "[a, b]".
Exclusive Interval: An exclusive interval excludes the lower and upper bounds of the interval. This means that values equal to the lower and upper bounds are not included in the interval. In notation, this is represented as "(a, b)".
In the given class interval, "100 up to 200," it is written in an exclusive interval format with the use of the word "up to" instead of using square brackets. This means that the lower bound (100) is excluded and the upper bound (200) is included in the interval.
Now, let's evaluate the given options:
A. Observations with values of 100 are excluded from the class frequency.
Since the interval is exclusive, observations with a value of exactly 100 are indeed excluded. This option is correct.
B. Observations with values of 200 are included in the class frequency.
As stated before, the upper bound (200) is included in the interval. Therefore, observations with a value of exactly 200 are included. This option is correct.
C. Observation with values of 200 are excluded from the class frequency.
This option is the opposite of what was established in option B above. Observations with a value of 200, being the upper bound of the interval, are included. Thus, this option is incorrect.
D. The class interval is 99.
This option assumes that the class interval is one less than the upper bound. However, this is not necessarily the case. The class interval is the numerical difference between the upper and lower bounds, which is 100 in this given case. Thus, this option is incorrect.
Therefore, the correct answers are options A and B.