Compute a 75% Chebyshev interval around the mean for x values and also for y values. Grid E: x variable 11.92 34.86 26.72 24.50 38.93 8.59 29.31 23.39 24.13 30.05 21.54 35.97 7.48 35.97 Grid H: y variable 27.86 13.29 33.03 44.31 16.58 42.43 39.61 25.51 39.14 16.58 47.13 14.70 57.47 34.44 According to Chebyshev's Theorem, [1 - (1/k^2)] proportion of values will fall between Mean +/- (k*SD) k in this case equal to z z = (X-Mean)/SD X = Mean + (z*SD) 1 - 1/k^2 = 0.75 - 1/k^2 = 0.75 - 1= - 0.25 1/k^2 = 0.25 k^2 = 1/0.25 k^2 = 4 k = 2 Therefore, z = k = 2 First, determine the mean and standard deviation of x Mean(x) = 25.24 SD(x) = 9.7873 Required Interval for x is: Mean - (z * SD) < X < Mean + (z * SD) 25.24 - (2 * 9.7873) < X < 25.24 - (2 * 9.7873) 25.24 - 19.5746 < X < 25.24 + 19.5746 5.6654 < X < 44.8146 Next, determine the mean and standard deviation of y Mean(y) = 32.29 SD(y) = 9.7873 Required Interval for y is: Mean - (z * SD) < Y < Mean + (z * SD) 32.29 - (2 * 13.1932) < Y < 32.29 - (2 * 13.1932) 32.29 - 26.3864 < Y < 32.29 + 26.3864 5.9036 < X < 58.6764