(43, 54, 55, 55, 55, 34, 34, 34) In the given numbers, 55 is considered to be thea.Raw scoreb.Modec.Meand.Median

Break Down the Problem

1. Identify the definitions of raw score, mode, mean, and median.
2. Analyze the provided set of numbers: (43, 54, 55, 55, 55, 34, 34, 34).
3. Determine which of these statistical measures is represented by the number 55.

Relevant Concepts

1. Raw Score: The original score before any transformations or calculations.
2. Mode: The number that appears most frequently in a data set.
3. Mean: The average of the numbers, calculated by summing all values and dividing by the count of values.
4. Median: The middle number when the data set is ordered from least to greatest.

Analysis and Detail

1. Raw Score: 55 is a raw score in this context, but it does not define it specifically.

2. Mode Calculation: In the dataset (43, 54, 55, 55, 55, 34, 34, 34), the numbers and their frequencies are:

   • 43: 1 time
   • 54: 1 time
   • 55: 3 times
   • 34: 3 times The mode is 55 because it appears more frequently than any other number.

3. Mean Calculation: $\text{Mean} = \frac{43 + 54 + 55 + 55 + 55 + 34 + 34 + 34}{8} = \frac{ 43 + 54 + 55 + 55 + 55 + 34 + 34 + 34 = 364 }{8} = 45.5$

4. Median Calculation: To find the median, we first need to sort the numbers: (34, 34, 34, 43, 54, 55, 55, 55). The median of this even data set is the average of the 4th and 5th numbers: $\text{Median} = \frac{43 + 54}{2} = \frac{97}{2} = 48.5$

Verify and Summarize

• The most frequent number (mode) in the data set is clearly identified as 55, which appears three times.
• The mean is calculated to be 45.5, and the median is 48.5. Both are different from the mode.
• Thus, the 55 is not just a raw score but specifically the mode of the data set.

Final Answer

b. Mode