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Question

# Calculate the mean deviation from the mean for the following data: (i) 4, 7, 8, 9, 10, 12, 13, 17 (ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 (iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 (iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

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Solution

## Formula used for finding the mean deviation about the mean is given below: $MD=\frac{1}{n}\sum _{i=1}^{n}\left|{d}_{i}\right|,where\left|{d}_{i}\right|=\left|{x}_{i}-\overline{)x}\right|$ i) Let $\overline{)x}$ be the mean of the given data. $\overline{)x}=\frac{4+7+8+9+10+12+13+17}{8}=10$ ${x}_{i}$ $\left|{d}_{i}\right|=\left|{x}_{i}-\overline{x}\right|$ 4 6 7 3 8 2 9 1 10 0 12 2 13 3 17 7 Total 24 $MD=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{d}}_{\mathrm{i}}\right|$ $MD=\frac{1}{8}×24=3$ ii) Let $\overline{)x}$ be the mean of the given data. $\overline{)x}=\frac{13+17+16+14+11+13+10+16+11+18+12+17}{12}=14$ ${x}_{i}$ $\left|{d}_{i}\right|=\left|{x}_{i}-\overline{x}\right|$ 13 1 17 3 16 2 14 0 11 3 13 1 10 4 16 2 11 3 18 4 12 2 17 3 Total 28 $MD=\frac{1}{12}×28=2.33$ iii) Let $\overline{)x}$ be the mean of the given data. $\overline{)x}=\frac{38+70+48+40+42+55+63+46+54+44}{10}=50$ ${x}_{i}$ $\left|{d}_{i}\right|=\left|{x}_{i}-\overline{x}\right|$ 38 12 70 20 48 2 40 10 42 8 55 5 63 13 46 4 54 4 44 6 Total 84 $MD=\frac{1}{10}×84=8.4$ iv) Let $\overline{)x}$ be the mean of the given data. $\overline{)x}=\frac{36+746+42+60+45+53+46+51+59}{10}=50$ ${x}_{i}$ $\left|{d}_{i}\right|=\left|{x}_{i}-\overline{x}\right|$ 36 14 72 22 46 4 42 8 60 10 45 5 53 3 46 4 51 1 49 1 Total 72 $MD=\frac{1}{10}×72=7.2$

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