Question

After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?

Answer 1

In statistics, relative frequencies provide a comparison between the frequency of a specific event and the total number of possible outcomes. When constructing a relative frequency distribution, the idea is to understand the proportion of the total for each category.

Given that we've constructed a relative frequency distribution summarizing IQ scores of college students, the sum of all outcomes in this distribution represents the complete picture, i.e., 100% of the observed events.

To find the sum of the relative frequencies:

1. First, we'll note how many times each IQ score occurs, which gives us the 'frequency' of each score.

2. Next, we'll calculate the 'relative frequency' of each score. This is done by dividing the frequency of each score by the total number of scores.

3. After this step, we will have a relative frequency for each IQ score in the distribution. It's these numbers we're interested in.

4. Now we shall add up all these relative frequencies. Given that the relative frequencies represent parts of a whole (the whole being all IQ scores from our sample of college students), the sum of these frequencies should total to 1, or 100% when expressed as a percentage.

So, the sum of the relative frequencies in our frequency distribution summarizing IQ scores of college students should be 1 or 100% when converted to a percentage. This is because we've accounted for all possible outcomes in our sample of IQ scores.

Answer 2

The sum should be 100% if percentages are used and 1 if proportion is used.

Explanation:

A relative frequency distribution is a type of frequency distribution. This can be explained using the frequency table given below:

Student IQ-Score

Jake 12

Blake 10

Toby 18

Harry 20

Total 60

To calculate Relative Frequency Distribution using percentage:

We add the total IQ score 12+10+18+20 = 60

Then divide each individual IQ Score by the Total IQ Score multiply by 100

Jake will have 12/60 * 100 = 20

Blake will have 10/60 * 100 = 16.67

Toby will have 18/60 * 100 = 30

Harry will have 20/60 * 100 = 33.33.

To calculate Relative Frequency Distribution using 1:

We add the total IQ score 12+10+18+20 = 60

Then divide each individual IQ Score by the Total IQ Score.

Jake will have 12/60 = 0.2

Blake will have 10/60 = 0.17

Toby will have 18/60 = 0.3

Harry will have 20/60 = 0.33

The Relative Frequency Distribution Table becomes:

Student IQ-Score

Jake 12 20 0.2

Blake 10 16.67 0.17

Toby 18 30 0.3

Harry 20 33.33 0.33

Total 60 100 1