Find the mean deviation about the mean of the distribution:
$\text{Size}$$20$$21$$22$$23$$24$
$\text{Frequency}$$6$$4$$5$$1$$4$

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First,calculate the mean $\bar{x}$:
$\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{(20 \times 6) + (21 \times 4) + (22 \times 5) + (23 \times 1) + (24 \times 4)}{6 + 4 + 5 + 1 + 4} = \frac{120 + 84 + 110 + 23 + 96}{20} = \frac{433}{20} = 21.65$
Next,calculate the mean deviation about the mean:
$\text{Size } (x_i)$$\text{Freq } (f_i)$$|x_i - \bar{x}|$$f_i |x_i - \bar{x}|$
$20$$6$$1.65$$9.90$
$21$$4$$0.65$$2.60$
$22$$5$$0.35$$1.75$
$23$$1$$1.35$$1.35$
$24$$4$$2.35$$9.40$
$\text{Total}$$20$-$25.00$

$\text{Mean Deviation} = \frac{\Sigma f_i |x_i - \bar{x}|}{\Sigma f_i} = \frac{25}{20} = 1.25$

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