Question

middle school students were asked, \do you enjoy playing sports?\ the frequency table shows some of the results of the survey. complete the frequency table. then complete a relative frequency table to show the distribution of the data with respect to all 150 students.
complete the frequency table.
frequency table
enjoy playing sports?
grade
6th
7th
8th
total
yes
26
28
30
84
no
22
21
23
66
total
48
49
53
150
complete the relative frequency table.
total relative frequency table
enjoy playing sports?
grade
6th
7th
8th
total
yes
□%
□%
□%
□%
no
□%
□%
□%
□%
total
□%
□%
□%
100%
(round to the nearest tenth as needed.)

Answer:

Part 1: Complete the Frequency Table

To complete the frequency table, we need to find the missing values (6th grade "Yes", 7th grade "Total", 8th grade "Yes", and 8th grade "Total" was already given as 53, but let's verify):

Step 1: 6th Grade - Yes

Total "Yes" is 84. We know 7th grade "Yes" is 28 and 8th grade "Yes" is 30 (from the partially filled table? Wait, no, original frequency table:

Wait, original frequency table (top):

• Yes total: 84
• 7th grade Yes: 28
• 8th grade Yes:?
• 6th grade Yes:?

Wait, the middle frequency table (partially filled) shows 6th Yes:26, 7th Yes:28, 8th Yes:30 (26+28+30=84, correct).

• No total: 66
• 7th grade No:21
• 8th grade No:23
• 6th grade No:?

21 + 23 + 6th No = 66 → 6th No = 66 - 21 -23 = 22 (matches the middle table: 6th No:22).

• Total per grade:
• 6th grade total: Yes (26) + No (22) = 48 (given, correct).
• 7th grade total: Yes (28) + No (21) = 49 (matches middle table: 7th total:49).
• 8th grade total: Yes (30) + No (23) = 53 (given, correct).

Part 2: Complete the Relative Frequency Table

Relative frequency = (Frequency / Total Students) × 100, where Total Students = 150.

Step 1: 6th Grade - Yes

Frequency = 26.
Relative Frequency = (26 / 150) × 100 ≈ 17.3% (rounded to nearest tenth).

Step 2: 6th Grade - No

Frequency = 22.
Relative Frequency = (22 / 150) × 100 ≈ 14.7% (rounded to nearest tenth).

Step 3: 6th Grade - Total

Total frequency for 6th grade = 48.
Relative Frequency = (48 / 150) × 100 = 32.0% (exact, since 48/150 = 0.32).

Step 4: 7th Grade - Yes

Frequency = 28.
Relative Frequency = (28 / 150) × 100 ≈ 18.7% (rounded to nearest tenth).

Step 5: 7th Grade - No

Frequency = 21.
Relative Frequency = (21 / 150) × 100 = 14.0% (exact).

Step 6: 7th Grade - Total

Total frequency for 7th grade = 49.
Relative Frequency = (49 / 150) × 100 ≈ 32.7% (rounded to nearest tenth: 49/150 ≈ 0.32666… → 32.7%).

Step 7: 8th Grade - Yes

Frequency = 30.
Relative Frequency = (30 / 150) × 100 = 20.0% (exact).

Step 8: 8th Grade - No

Frequency = 23.
Relative Frequency = (23 / 150) × 100 ≈ 15.3% (rounded to nearest tenth: 23/150 ≈ 0.15333… → 15.3%).

Step 9: 8th Grade - Total

Total frequency for 8th grade = 53.
Relative Frequency = (53 / 150) × 100 ≈ 35.3% (rounded to nearest tenth: 53/150 ≈ 0.35333… → 35.3%).

Step 10: Total - Yes

Total Yes frequency = 84.
Relative Frequency = (84 / 150) × 100 = 56.0% (exact).

Step 11: Total - No

Total No frequency = 66.
Relative Frequency = (66 / 150) × 100 = 44.0% (exact).

Final Relative Frequency Table (filled):

Grade	Enjoy Playing Sports?	Relative Frequency (%)
6th	No	14.7
6th	Total	32.0
7th	Yes	18.7
7th	No	14.0
7th	Total	32.7
8th	Yes	20.0
8th	No	15.3
8th	Total	35.3
Total	Yes	56.0
Total	No	44.0
Total	Total	100.0

(Note: If the question only asks for specific cells, adjust accordingly. For example, the blue box in the image is 6th grade "Yes", which is 17.3%.)