Quiz Comparison 7C2D6F
1. Statement of the problem: Two classes have dot plots showing nine quiz scores each, and we need to analyze and compare their distributions.
2. Data given: Class B scores are 8, 9, 10, 11, 12, 13, 14, 15, 16.
3. Formulas used and important rules: Mean formula: $\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i$.
Median rule for odd $n$: the median is the middle value after sorting the data.
Mode rule: the mode is the most frequent score; if all scores are unique there is no mode.
Range formula: $\text{range}=\max(x)-\min(x)$.
Always sort data when finding the median and check frequencies when finding the mode.
4. Intermediate work for Class B (showing all arithmetic): Sum the scores: $8+9+10+11+12+13+14+15+16=108$.
Compute the mean using $\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i$ with $n=9$: $\bar{x}=\frac{108}{9}=12$.
Find the median: with 9 ordered values the median is the 5th value, which is $12$.
Find the mode: every value appears once, so there is no mode.
Find the range using $\text{range}=\max(x)-\min(x)$: $16-8=8$.
5. Missing information for Class A: The first dot plot in the prompt is not giving a clear list of the nine individual scores for Class A, so I cannot compute its mean, median, mode, or range yet.
Please provide the nine scores for Class A exactly (for example: 10, 10, 11, 12, 12, 13, 14, 15, 16) and I will compute the statistics showing all intermediate steps.
6. Final answer for the data that is fully given: Class B mean = 12.
Class B median = 12.
Class B mode = none.
Class B range = 8.
I can compute and compare Class A statistics once you supply its nine scores.