First, let's calculate the mean and the mean absolute deviation of the first bowler.
FIRST BOWLER: <span>8,5,5,6,8,7,4,7,6 Mean = (Sum of all data)/(Number of data points) = (8+5+5+6+8+7+4+7+6)/9 <em>Mean = 6.222</em> Mean absolute deviation or MAD = [</span>∑(|Data Point - Mean|]/Number of Data Points MAD = [|8 - 6.222| + |5 - 6.222| + |5 - 6.222| + |6 - 6.222| + |8 - 6.222| + |7 - 6.222| + |4 - 6.222| + |7 - 6.222| + |6 - 6.222|]/9 <em>MAD = 1.136</em>
SECOND BOWLER: <span>10,6,8,8,5,5,6,8,9 </span>Mean = (Sum of all data)/(Number of data points) = (<span>10+6+8+8+5+5+6+8+9</span>)/9 <em>Mean = 7.222</em> Mean absolute deviation or MAD = [∑(|Data Point - Mean|]/Number of Data Points MAD = [|10 - 7.222| + |6 - 7.222| + |8 - 7.222| + |8 - 7.222| + |5 - 7.222| + |5 - 7.222| + |6 - 7.222| + |8 - 7.222| + |9 - 7.222|]/9 <em>MAD = 1.531 </em> The mean absolute deviation represents the average distance of each data to the mean. Thus, the lesser the value of the MAD is, the more consistent is the data to the mean. <em>B</em><em>etween the two, the first bowler is more consistent.</em>
He two equations given are x^2 + y^2 = 26 And x - y = 6 x = y +6 Putting the value of x from the second equation to the first equation, we get x^2 + y^2 = 26 (y + 6) ^2 + y^2 = 26 y^2 + 12y + 36 + y^2 = 26 2y^2 + 12y + 36 - 26 = 0 2y^2 + 12y + 10 = 0 y^2 + 6y + 5 = 0 y^2 + y + 5y + 5 = 0 y(y + 1) + 5 ( y + 1) = 0 (y + 1)(y + 5) = 0 Then y + 1 = 0 y = -1 so x - y = 6 x + 1 = 6 x = 5 Or y + 5 = 0 y = - 5 Again x = 1 So the solutions would be (-1, 5), (1 , -5). The correct option is option "C".
