What is/are the mode(s) of the following set of scores? 2, 4, 3, 5, 2, 5, 3, 2, 4, 2, 3, 4, 4

The scores are: 2, 4, 3, 5, 2, 5, 3, 2, 4, 2, 3, 4, 4.

• Count of 2: 4 times
• Count of 3: 3 times
• Count of 4: 4 times
• Count of 5: 2 times

The highest frequency is 4, which occurs for both score 2 and score 4.
12. What is/are the mode(s) of the following set of scores?
Answer: $\boxed{\text{2, 4}}$

For Questions 13 - 15:

Assumption: The table provided has a typo. Given that the problem refers to "50 students" and the sum of the frequencies $8+12+7+10+13 = 50$, it is assumed that the second entry for 'Grade 97' (with 7 students) should be 'Grade 94' to make the grades distinct and complete the distribution for 50 students. The corrected table used for calculations is:

Grade (x)	Number of Students (f)
98	8
97	12
96	10
95	13
94	7
Total	N = 50

To find the mean of grouped data, we use the formula $\text{Mean} = \frac{\sum fx}{N}$, where $f$ is the frequency (number of students) and $x$ is the grade.

• $98 \times 8 = 784$
• $97 \times 12 = 1164$
• $96 \times 10 = 960$
• $95 \times 13 = 1235$
• $94 \times 7 = 658$

$$\sum fx = 784 + 1164 + 960 + 1235 + 658 = 4801$$ $$N = 50$$ $$\text{Mean} = \frac{4801}{50} = 96.02$$

13. What is the mean score of the 50 students? Answer: $\boxed{\text{96.02}}$

First, find the position of the median. Since there are $N=50$ students (an even number), the median is the average of the $\frac{N}{2}$-th and $(\frac{N}{2} + 1)$-th values.

$$\frac{50}{2} = 25\text{-th value}$$ $$\frac{50}{2} + 1 = 26\text{-th value}$$

Next, create a cumulative frequency (cf) column for the corrected table:

• Grade 98: cf = 8
• Grade 97: cf = $8 + 12 = 20$
• Grade 96: cf = $20 + 10 = 30$ The 25th and 26th scores both fall within the 'Grade 96' category (since the cumulative frequency reaches 20 at Grade 97, and 30 at Grade 96, meaning scores from 21st to 30th are 96). Therefore, both the 25th and 26th scores are 96.

$$\text{Median} = \frac{96 + 96}{2} = 96$$

14. What is the median score of the set of scores? Answer: $\boxed{\text{96}}$

The mode is the grade with the highest frequency (number of students).
From the corrected table:

• Grade 98: 8 students
• Grade 97: 12 students
• Grade 96: 10 students
• Grade 95: 13 students
• Grade 94: 7 students The highest frequency is 13, which corresponds to Grade 95. 15. What is the mode of the set of scores? Answer: $\boxed{\text{95}}$