Final answer:
The standard deviation of the data set {1, 1, 5, 7, 8} with a mean of 4.4, a median of 5, a mode of 1, and a range of 7 is approximately 2.94.
Step-by-step explanation:
The student is tasked with finding the standard deviation of the ordered data set {a,b,c,d,e} given specific statistical measures. With the given median of 5, it is deduced that c=5. As the mode is 1, and the data is ordered, it can be assumed that at least two elements in the set are equal to 1. With the range given as 7, and the smallest value (the mode) being 1, the largest value in the set must be 1+7=8. Therefore, we can infer that e=8. The mean is given as 4.4, which allows us to set up the equation a+b+c+d+e=5*4.4=22. We know c=5 and e=8, and if a=b=1 (assuming the mode repeats only twice, as it's at minimum), we have 1+1+5+d+8=22, resulting in d=7. Now we have the complete set {1, 1, 5, 7, 8}. To find the standard deviation, we first calculate the variance. The variance is the average of the squared differences from the mean. Variance = [(1-4.4)^2 + (1-4.4)^2 + (5-4.4)^2 + (7-4.4)^2 + (8-4.4)^2] / 5. This gives Variance = [11.56 + 11.56 + 0.36 + 6.76 + 12.96] / 5 = 43.2 / 5 = 8.64. Finally, the standard deviation is the square root of the variance, which is approximately √8.64 ≈ 2.94.