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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 6 of 34
Marks: +1, -0
xix_i 10 30 50 70 90
fif_i 4 24 28 16 8
Solution:  
xix_i 10 30 50 70 90
fif_i 4 24 28 16 8 80
fixif_i x_i 40 720 1400 1120 720 4000
∣xi−50∣\left|x_i - 50\right| 40 20 0 20 40
fi∣xi−50∣f_i\left|x_i - 50\right| 160 480 0 320 320 1280
Mean (x−)\left(\overset{-}{x}\right) = 1N∑ni=1fixi\frac{1}{N}\sum^{\underset{i=1}{n}} f_i x_i = 180×4000\frac{1}{80} \times 4000 = 50
∴ Mean deviation about mean = 1N∑ni=1fi∣xi−x−∣\frac{1}{N}\sum^{\underset{i=1}{n}} f_i\left|x_i - \overset{-}{x}\right| = 180\frac{1}{80} × 1280 = 16
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