Relative Frequency Distribution After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?
The Correct Answer and Explanation is:
The correct answer is:
A relative frequency distribution is a statistical tool used to show how often each value or range of values occurs in a dataset relative to the total number of observations. In simpler terms, it expresses the frequency of each class as a fraction or percentage of the total.
When you construct a relative frequency distribution for IQ scores (or any data set), each class or group (e.g., 90–99, 100–109, etc.) will have a relative frequency, which is calculated using the formula: Relative Frequency=Class FrequencyTotal Frequency (or sample size)\text{Relative Frequency} = \frac{\text{Class Frequency}}{\text{Total Frequency (or sample size)}}
Each relative frequency represents the proportion of the total observations that fall within a particular class. If you add up the relative frequencies of all the classes, you’re effectively counting the entire data set — just not in raw counts, but in proportions.
Therefore, the sum of all relative frequencies must equal 1 (or 100%), because all data points must be accounted for in the distribution. This rule ensures that your distribution is complete and correctly reflects the entire dataset.
For example, if you have 100 students and you calculate the relative frequencies of IQ scores in different intervals, you might get the following:
- 80–89: 0.10
- 90–99: 0.25
- 100–109: 0.40
- 110–119: 0.15
- 120–129: 0.10
Adding these together:
0.10 + 0.25 + 0.40 + 0.15 + 0.10 = 1.00
This confirms that the entire sample has been represented, and no data is missing or double-counted.
In conclusion, when constructing a relative frequency distribution of IQ scores, the sum of the relative frequencies should always be 1 (or 100%), ensuring that the entire population or sample is accurately represented.
