A list of 10 data values is shown. 6, 8, 16, 4, 17, 28, 8, 5, 5, 5 What is...

1. TRANSLATE the problem information

• Given information:
  • A list of 10 data values: 6, 8, 16, 4, 17, 28, 8, 5, 5, 5
  • Need to find the "mean of these data"

• What this tells us: We need to calculate the arithmetic average of all 10 numbers

2. INFER the approach

• To find the mean, we need to use the mean formula
• Strategy: Add all values together, then divide by the total count
• What to do first: Sum all 10 data values

3. SIMPLIFY by calculating the sum

• Add all values: \(6 + 8 + 16 + 4 + 17 + 28 + 8 + 5 + 5 + 5\)
• (use calculator) \(\mathrm{Sum} = 100\)
• Count the number of values: 10 data points

4. SIMPLIFY by applying the mean formula

• \(\mathrm{Mean} = \frac{\mathrm{Sum}}{\mathrm{Number\ of\ values}}\)
• \(\mathrm{Mean} = \frac{100}{10} = 10\)

Answer: 10

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Arithmetic errors when adding the 10 data values

Students often rush through the addition step and make computational mistakes, especially when adding numbers with different magnitudes (like 28 and 5). They might get sums like 98 or 102 instead of 100, leading to means like 9.8 or 10.2. This leads to confusion since their calculated answer doesn't match any obvious pattern or expected result.

Second Most Common Error:

Missing conceptual knowledge: Confusing mean with other measures of central tendency

Some students might calculate the mode (5, since it appears three times) or attempt to find the median by ordering the values. This conceptual confusion about what "mean" actually measures causes them to use the wrong approach entirely, leading to answers like 5 or other values from ordering the data.

The Bottom Line:

This problem tests both computational accuracy and conceptual understanding. While the formula for mean is straightforward, the execution requires careful arithmetic with 10 different numbers, making calculation errors the primary obstacle to success.