Compute a 75% Chebyshev interval around the mean for x values and also for y values.

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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