Question

the table shows information about the lengths of some insects.

calculate an estimate of the mean length of the insects.

\

$$\begin{array}{|c|c|} \\hline \\text{length, } x \\text{ (mm)} & \\text{frequency} \\\\ \\hline 0 < x \\le 10 & 9 \\\\ \\hline 10 < x \\le 20 & 6 \\\\ \\hline 20 < x \\le 30 & 5 \\\\ \\hline \\end{array}$$

Explanation:

Find the midpoint of each interval

Using the Interval Midpoint knowledge point

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Calculate the total frequency

Using the Total Frequency Calculation knowledge point

$$ \sum f = 9 + 6 + 5 = 20 $$

Calculate the sum of products of midpoints and frequencies

Using the Estimated Mean knowledge point

$$ \sum (f \times m) = (9 \times 5) + (6 \times 15) + (5 \times 25) = 45 + 90 + 125 = 260 $$

Calculate the estimated mean

Using the Estimated Mean knowledge point

$$ \text{Estimated Mean} = \frac{\sum (f \times m)}{\sum f} = \frac{260}{20} = 13 $$

Answer:

\(13\text{ mm}\)