Answer :

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 - 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)

Thanks for taking the time to read Find the range and standard deviation for the set of numbers 111 122 134 146 150 159 193. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada