Question

A frequency distribution is an organized tabulation of the number of individuals located in each category on the scale of measurement.

Frequency Tables:

1. Imagine you are a teacher and your students got the following scores on a quiz you gave them: 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8. Place the scores in the table below where the 1^st column indicated the raw score and the 2^nd column indicated how many students got that score. This value indicated how frequent that particular score is. This is important to know, as it shows how well your students understood the material. So, please, organize the following quiz scores into a frequency table: 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8.

X	f

Calculate ∑f =

Calculate ∑X =

Calculate ∑X² =

Calculation of Proportions (p), or Relative Frequencies, and Percentages (%):

Now, imagine you are asked by the principle to report the proportion and percentage of the scores your students got. This will show which scores constitute the larger proportion of all scores obtained and is also reflective of how well your instructions worked. For that, you simply need to devide the frequency of each score by the total number of scores. And to get the percentage, you simply multiply it by 100! Fill out the table below and reflect on your results. Which scores constitute the largest proportion of all scores obtained? Are you satisfied with the finding?

Proportion measures the fraction of the total group that is associated with each score.

Because proportions describe the frequency (f) in relation to the total number (N), they are often called relative frequencies.

2. Using data from #2, populate the table:

X	f	p= f/N	% = p*100%

Calculation of Percentile and Percentile Ranks:

3. Now, imagine a parent approaches you and asks you how well their child is doing compared to the rest of the class….For that you have to tell them how many students did as well or worse than their child who got a 7 on the quiz. So, you calculate how many individuals did as well or worse and it is called cumulative frequency (cf). Please, find the number of individuals who are located at or below each point in the distribution and show the calulations in column cf.

X	f	cf

Now you can tell the parent how many students did as well or worse, and then the parent asks you about their child`s percentile rank. The percentile rank of a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value.

When a score is identified by its percentile rank, the score is called a percentile. Calculate in the percentile rank (c% stand for cumulative percentile) for each score in the table below. What percentile rank is score 7?

X	f	cf	c% = (cf/N)(100%)

4. Build a frequency distribution histogram and the polygon for the quiz scores in your class. Place f on the Y axis and scores on the X axis. Don’t forget about the real limits of each score.
   1. Is the distribution skewed? Positively or negatively?
   2. What score best identifies the center?
   3. Are the scores clustered together, or are they spread across the scale?

Answer 1