Question

scores on algebra ii test
scores: 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
frequency: 1, 2, 1, 9, 13, 8
a frequency distribution is shown. which table shows the correct relative frequency distribution for the data?
options:
a
scores: 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
frequency: 1, 2, 1, 9, 13, 8
relative frequency: 0.03, 0.06, 0.03, 0.26, 0.38, 0.24
b
scores: 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
frequency: 1, 2, 1, 9, 13, 8
relative frequency: 0.10, 0.20, 0.10, 0.90, 0.13, 0.80
c
scores: 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
frequency: 1, 2, 1, 9, 13, 8
relative frequency: 0.11, 0.22, 0.11, 0.90, 1.44, 0.88
d
scores: 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
frequency: 1, 2, 1, 9, 13, 8
relative frequency: 0.04, 0.07, 0.04, 0.32, 0.46, 0.29

Explanation:

Step1: Calculate total frequency

First, we find the total number of data points by summing up all the frequencies. The frequencies are 1, 2, 1, 9, 13, and 8. So, total frequency \( n = 1 + 2 + 1 + 9 + 13 + 8 \).
Calculating that: \( 1+2 = 3 \), \( 3+1 = 4 \), \( 4+9 = 13 \), \( 13+13 = 26 \), \( 26+8 = 34 \)? Wait, no, wait: 1 + 2 is 3, plus 1 is 4, plus 9 is 13, plus 13 is 26, plus 8 is 34? Wait, no, 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34? Wait, no, let's add again: 1 (41-50) + 2 (51-60) + 1 (61-70) + 9 (71-80) + 13 (81-90) + 8 (91-100). So 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34? Wait, no, 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34? Wait, maybe I made a mistake. Wait 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34? Wait, no, 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34. Wait, but let's check the options. Wait, maybe I miscalculated. Wait 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34? Wait, no, 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34. Wait, but let's check option A: relative frequencies are 0.03, 0.06, 0.03, 0.26, 0.38, 0.24. Let's sum them: 0.03+0.06=0.09, +0.03=0.12, +0.26=0.38, +0.38=0.76, +0.24=1.0. Oh, so total frequency is 1/0.03 ≈ 33.33? Wait, no, relative frequency is frequency / total. So let's calculate total frequency correctly. Let's add the frequencies: 1 + 2 + 1 + 9 + 13 + 8. 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34? Wait, no, 1+2=3, 3+1=4, 4+9=13, 13+13=26, 26+8=34. Wait, but 1/34 ≈ 0.029, which is ~0.03. 2/34 ≈ 0.058, ~0.06. 1/34 ≈ 0.029, ~0.03. 9/34 ≈ 0.264, ~0.26. 13/34 ≈ 0.382, ~0.38. 8/34 ≈ 0.235, ~0.24. So that's option A. Let's check other options. Option B: 1/10=0.1, but total frequency would be 10, but our total is 34, so no. Option C: 1/0.11≈9, but total frequency is 34, so no. Option D: 1/0.04=25, but total is 34, so no. So the correct one is A.

Step2: Verify each relative frequency

For each score range, calculate relative frequency as (frequency) / (total frequency). Total frequency is 1+2+1+9+13+8 = 34.

• 41-50: \( \frac{1}{34} \approx 0.03 \)
• 51-60: \( \frac{2}{34} \approx 0.06 \)
• 61-70: \( \frac{1}{34} \approx 0.03 \)
• 71-80: \( \frac{9}{34} \approx 0.26 \)
• 81-90: \( \frac{13}{34} \approx 0.38 \)
• 91-100: \( \frac{8}{34} \approx 0.24 \)

These match the relative frequencies in option A.

Answer:

A. Scores: 41-50, 51-60, 61-70, 71-80, 81-90, 91-100; Frequency: 1, 2, 1, 9, 13, 8; Relative Frequency: 0.03, 0.06, 0.03, 0.26, 0.38, 0.24