Find the range and standard deviation for the set of numbers.111, 122, 134, 146, 150, 159, 193

Answer:For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.Step-by-step explanation:1. Let's find the range for the set of numbers given:Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.Range = 193 - 111Range = 822. For calculating the standard deviation, we should calculate first the mean and the variance, this way:Mean = Sum of all the terms / Number of the terms of the setMean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7Mean = 1,015/7Mean = 145Now, we proceed to calculate the variance this way:Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sampleLet's calculate the squared distances of each term in the set from the mean:111 - 145 = - 34 ⇒ - 34² = 1,156122 - 145 = - 23 ⇒ - 23² = 529134 - 145 = - 11 ⇒ - 11² = 121146 - 145 = 1 ⇒ 1² = 1150 - 145 = 5 ⇒ 5² = 25159 - 145 = 14 ⇒ 14² = 196193 - 145 = 48 ⇒ 48² = 2,304Now replacing with the real values:Variance = (1,156 + 529 + 121  1+ 25 + 196 + 2,304)/7Variance = 4,332/7Variance = 618.86 (Rounding to two decimal places)Finally, we can calculate easily the standard deviation:Standard deviation = √VarianceStandard deviation = √ 618.86Standard deviation = 24.88 (Rounding to two decimal places)