Question

frequency table
real limit score f rel. f cf % c% percentile rank
5.5~6.5 6 1 0.05 20 5% 100%
4.5~5.5 5 0 0.00 19 0% 95%
3.5~4.5 4 2 0.10 19 10% 95%
2.5~3.5 3 3 0.15 17 15% 85%
1.5~2.5 2 10 0.50 14 50% 70%
0.5~1. 1 4 0.20 4 20% 20%
n = 20
fill in the blanks in the table.

Explanation:

Step1: Recall relative - frequency formula

$Rel. f=\frac{f}{N}$, where $N = 20$. For example, when $f = 1$, $Rel. f=\frac{1}{20}=0.05$. When $f = 2$, $Rel. f=\frac{2}{20}=0.10$, when $f = 3$, $Rel. f=\frac{3}{20}=0.15$, when $f = 10$, $Rel. f=\frac{10}{20}=0.50$, when $f = 4$, $Rel. f=\frac{4}{20}=0.20$.

Step2: Recall cumulative - frequency formula

$Cf$ (cumulative frequency) is the sum of frequencies from the lowest score to the current score. For the score of 6, since it's the highest score and $f = 1$, $Cf = 20$. For the score of 5, $f = 0$, so $Cf$ is the same as the $Cf$ of the next - lower non - zero frequency score, which is 19. For the score of 4, $f = 2$, and $Cf$ is the sum of the frequencies of scores 4, 3, 2, 1, so $Cf=2 + 3+10 + 4=19$. For the score of 3, $f = 3$, and $Cf=3 + 10+4 = 17$. For the score of 2, $f = 10$, and $Cf=10 + 4=14$. For the score of 1, $f = 4$, and $Cf = 4$.

Step3: Recall percentage formula

$\%=\frac{f}{N}\times100\%$. For example, when $f = 1$, $\%=\frac{1}{20}\times100\% = 5\%$, when $f = 0$, $\% = 0\%$, when $f = 2$, $\%=\frac{2}{20}\times100\%=10\%$, when $f = 3$, $\%=\frac{3}{20}\times100\% = 15\%$, when $f = 10$, $\%=\frac{10}{20}\times100\%=50\%$, when $f = 4$, $\%=\frac{4}{20}\times100\%=20\%$.

Step4: Recall cumulative - percentage formula

$C\%$ (cumulative percentage) is calculated as $\frac{Cf}{N}\times100\%$. For the score of 6, $C\%=\frac{20}{20}\times100\% = 100\%$. For the score of 5, $C\%=\frac{19}{20}\times100\%=95\%$. For the score of 4, $C\%=\frac{19}{20}\times100\% = 95\%$. For the score of 3, $C\%=\frac{17}{20}\times100\%=85\%$. For the score of 2, $C\%=\frac{14}{20}\times100\% = 70\%$. For the score of 1, $C\%=\frac{4}{20}\times100\%=20\%$.

Step5: Calculate percentile rank

The percentile rank of a score $X$ is the percentage of scores in the distribution that are less than or equal to $X$. For the score of 6, since all scores are less than or equal to it, the percentile rank is 100. For the score of 5, since 95% of the scores are less than or equal to it, the percentile rank is 95. For the score of 4, since 95% of the scores are less than or equal to it, the percentile rank is 95. For the score of 3, since 85% of the scores are less than or equal to it, the percentile rank is 85. For the score of 2, since 70% of the scores are less than or equal to it, the percentile rank is 70. For the score of 1, since 20% of the scores are less than or equal to it, the percentile rank is 20.

Answer:

The completed table is as follows:

Real Limit	Score	$f$	$Rel. f$	$Cf$	$\%$	$C\%$	Percentile Rank
4.5 - 5.5	5	0	0.00	19	0%	95%	95
3.5 - 4.5	4	2	0.10	19	10%	95%	95
2.5 - 3.5	3	3	0.15	17	15%	85%	85
1.5 - 2.5	2	10	0.50	14	50%	70%	70
0.5 - 1.5	1	4	0.20	4	20%	20%	20