Question

the table below shows information about the thickness of each of the books on a shelf.

work out an estimate for the mean thickness.

\

$$\begin{tabular}{|c|c|} \\hline thickness, \\(x\\) (mm) & frequency \\\\ \\hline \\(0 < x \\le 2\\) & 3 \\\\ \\hline \\(2 < x \\le 4\\) & 8 \\\\ \\hline \\(4 < x \\le 6\\) & 9 \\\\ \\hline \\end{tabular}$$

Explanation:

Find the midpoints of each interval

Using the Interval Midpoint knowledge point

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Calculate the total frequency

Using the Total Frequency Calculation knowledge point

$$ \sum f = 3 + 8 + 9 = 20 $$

Calculate the sum of products of midpoints and frequencies

Using the Estimated Mean knowledge point

$$ \sum (f \times m) = (3 \times 1) + (8 \times 3) + (9 \times 5) = 3 + 24 + 45 = 72 $$

Calculate the estimated mean

Using the Estimated Mean knowledge point

$$ \text{Estimated Mean} = \frac{\sum (f \times m)}{\sum f} = \frac{72}{20} = 3.6 $$

Answer:

\(3.6\text{ mm}\)