Let's analyze Cody's sample data and draw conclusions based on it, addressing each statement systematically.
Step 1: Calculate the average number of books taken out per day for each grade.
For the 7th graders:
[tex]\[ (6 + 6 + 7 + 11 + 5) / 5 = 35 / 5 = 7 \text{ books} \, \text{per day on average} \][/tex]
For the 8th graders:
[tex]\[ (4 + 5 + 10 + 10 + 16) / 5 = 45 / 5 = 9 \text{ books} \, \text{per day on average} \][/tex]
Thus, the average number of books taken out per day by 8th graders is 9, and by 7th graders is 7.
Step 2: Compare the average number of books taken out per day:
8th graders, on average, take out [tex]\( 9 - 7 = 2 \)[/tex] more books per day than 7th graders.
Therefore, the statement:
- "On average, 8th graders take out 2 more books a day than 7th graders." is likely to be true.
Step 3: Compare the total number of books taken out:
Next, let's see if the 8th graders take out fewer books overall. Summing the total books taken out:
7th graders: [tex]\( 6 + 6 + 7 + 11 + 5 = 35 \text{ books} \)[/tex]
8th graders: [tex]\( 4 + 5 + 10 + 10 + 16 = 45 \text{ books} \)[/tex]
Since 45 (8th graders) is more than 35 (7th graders), the statement:
- "8th graders take out fewer books than 7th graders." is false.
Step 4: Calculate the median number of books taken out by 7th graders:
To find the median, we need the sorted list of books taken out by 7th graders: [tex]\([5, 6, 6, 7, 11]\)[/tex].
The median is the middle value, which in this case is 6.
Therefore, the statement:
- "The median number of books in the sample for 7th grade is 7." is false (the correct median is 6).
Step 5: Calculate the range of books taken out:
For 7th graders:
[tex]\[ \text{Range} = \text{Max} - \text{Min} = 11 - 5 = 6 \][/tex]
For 8th graders:
[tex]\[ \text{Range} = \text{Max} - \text{Min} = 16 - 4 = 12 \][/tex]
Comparing the ranges, the range for 7th graders is 6, and for 8th graders, it is 12. The statement:
- "The range of books in the sample is twice as great for 7th graders as compared to 8th graders." is false.
Summary:
1. "On average, 8th graders take out 2 more books a day than 7th graders." is true.
2. "8th graders take out fewer books than 7th graders." is false.
3. "The median number of books in the sample for 7th grade is 7." is false (correct median is 6).
4. "The range of books in the sample is twice as great for 7th graders as compared to 8th graders." is false.
So, only the first statement is likely to be true based on Cody's sample.
