Dear Student, The mean of the given items = 5+10+15+20+25+X6 = 75+X6(5-75+X6)2 = (-45+X6)2 = X2 + 90X +202536(10-75+X6)2 = (-15+X6)2 = X2 + 30X +22536(15-75+X6)2 = (15-X6)2 = X2 +-30X +22536(20-75+X6)2 = (45-X6)2 = X2 - 90X +202536(25-75+X6)2 = (75-X6)2 = X2 - 150X +562536(X-75+X6)2 = (5X-756)2 = 25X2 - 750X +562536Adding all of the above and dividing by 6 we get,30X2-600X+15750216for Standard deviation to be minimum,d30X2-600X+15750216dX = 060X -600 = 0X =10 Hope this information will clear your doubts about topic If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible Regards

Question number 19

Dear Student,

T h e m e a n o f t h e g i v e n i t e m s = \frac{5 + 10 + 15 + 20 + 25 + X}{6} = \frac{75 + X}{6} (5 - \frac{75 + X}{6})^{2} = (- \frac{45 + X}{6})^{2} = \frac{X^{2} + 90 X + 2025}{36} (10 - \frac{75 + X}{6})^{2} = (- \frac{15 + X}{6})^{2} = \frac{X^{2} + 30 X + 225}{36} (15 - \frac{75 + X}{6})^{2} = (\frac{15 - X}{6})^{2} = \frac{X^{2} + - 30 X + 225}{36} (20 - \frac{75 + X}{6})^{2} = (\frac{45 - X}{6})^{2} = \frac{X^{2} - 90 X + 2025}{36} (25 - \frac{75 + X}{6})^{2} = (\frac{75 - X}{6})^{2} = \frac{X^{2} - 150 X + 5625}{36} (X - \frac{75 + X}{6})^{2} = (\frac{5 X - 75}{6})^{2} = \frac{25 X^{2} - 750 X + 5625}{36} A d d i n g a l l o f t h e a b o v e a n d d i v i d i n g b y 6 w e g e t, \frac{30 X^{2} - 600 X + 15750}{216} f o r S \tan d a r d d e v i a t i o n t o b e m i n i m u m, \frac{d \frac{30 X^{2} - 600 X + 15750}{216}}{d X} = 0 60 X - 600 = 0 X = 10

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