Answer to Question #177132 in Statistics and Probability for Kim Galvez

Question

1. Find the range, the standard deviation, and the variance for the given samples. Round non￾integer results to the nearest tenth. 

a. 1, 2, 5, 7, 8, 19, 22 

b. 3, 4, 7, 11, 12, 12, 15, 16 

c. 2.1, 3.0, 1.9, 1.5, 4.8 

d. 5.2, 11.7, 19.1, 3.7, 8.2, 16.3

2. A mountain climber plans to buy some rope to use as a lifeline. Which of the following would 

be the better choice? Explain why you think your choice is the better choice. 

Rope A: Mean breaking strength: 500 lb; standard deviation of 100 lb 

Rope B: Mean breaking strength: 500 lb; standard deviation of 10 lb

3. Evaluate the accuracy of the following statement: When the mean of a data set is large, the 

standard deviation will be large. Explain.

Answer 1

1. By using Excel functions:

Range = MAX(x₁,x₂..x_n) – MIN(x₁,x₂..x_n)

Standard deviation = STDEV.S(x₁,x₂..x_n)

Variance = VAR.S(x₁,x₂..x_n)

2. The mean breaking strength is same for both the ropes is 500lbs. so better choice depend upon the standard deviation of rope.

Minimum dispersion means the consistent results, that mean the rope can be used lifeline.

Since, the standard deviation of second rope is smallest.

Hence, the second option is better for using the rope as a lifetime.

3. If the mean of a data set is larger, it means that there is a large dispersion in the values. This implies that the range of data is large. Hence, the standard deviation of the data is large.