Question

Which of the following is NOT a rule for constructing a simple frequency distribution?

Question 1 options:

The number of class intervals should equal the number of observations measured.

Each interval is equidistant.

No overlapping class intervals are allowed.

Values are rounded to the same degree of accuracy measured in the original data.

Answer 1

In the above question,

• The number of class intervals means that the number of observation that occurred in the particular predefined interval.

Hence, this is a rule for constructing a frequency distribution.

• Each interval must be of equal sizes so that we can divide our data into equal size of groups (grouped data).

Thus, this is a rule for constructing a frequency distribution.

• No overlapping class intervals are allowed.

This is obviously a rule for constructing a frequency distribution because if the overlapping is allowed then it would provide us wrong output result about the data as the same observation may be counted multiple times.

• Values are rounded to the same degree of accuracy measured in the original data

It does not affect our data that is rounding the values to the same degree of accuracy is not needed in the construction of frequency distribution because, in a frequency distribution, it reflects the information about the nature of the distribution and frequency of observations.

Hence, this is not a rule for the construction of the frequency distribution.

Answer 2

The following statement is NOT a rule for constructing a simple frequency distribution:

"The number of class intervals should equal the number of observations measured."

This statement is incorrect because the number of class intervals does not have to be equal to the number of observations measured. In a frequency distribution, the data is grouped into intervals or classes, and the number of intervals is usually determined based on the range of the data and the desired level of granularity or detail in the distribution.

The correct way to determine the number of class intervals is to use a suitable method, such as the Sturges formula or the square root rule, which consider the number of observations to determine an appropriate number of intervals that best represent the data.

The other three statements are common rules for constructing a simple frequency distribution:

1. Each interval is equidistant: Intervals in a frequency distribution should have equal width to maintain uniformity and make comparisons easier.

2. No overlapping class intervals are allowed: In a simple frequency distribution, the intervals should not overlap to avoid ambiguity and ensure each data point falls into exactly one interval.

3. Values are rounded to the same degree of accuracy measured in the original data: When constructing a frequency distribution, the values in each interval should be rounded to the same degree of accuracy as the original data to maintain consistency and avoid introducing bias.