Find the range and standard deviation for the set of numbers.

111, 122, 134, 146, 150, 159, 193

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 - 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)