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.
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 - 111
Range = 82
2. 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 set
Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7
Mean = 1,015/7
Mean = 145
Now, 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 sample
Let's calculate the squared distances of each term in the set from the mean:
111 - 145 = - 34 ⇒ - 34² = 1,156
122 - 145 = - 23 ⇒ - 23² = 529
134 - 145 = - 11 ⇒ - 11² = 121
146 - 145 = 1 ⇒ 1² = 1
150 - 145 = 5 ⇒ 5² = 25
159 - 145 = 14 ⇒ 14² = 196
193 - 145 = 48 ⇒ 48² = 2,304
Now replacing with the real values:
Variance = (1,156 + 529 + 121 1+ 25 + 196 + 2,304)/7
Variance = 4,332/7
Variance = 618.86 (Rounding to two decimal places)
Finally, we can calculate easily the standard deviation:
Standard deviation = √Variance
Standard deviation = √ 618.86
Standard deviation = 24.88 (Rounding to two decimal places)