Chapter 10.2, Problem 10IP

To determine

To find: The measure of variability of his golf score. Explain what measures of variability tell you about data.

Answer to Problem 10IP

Measure of variability = 10.

Explanation of Solution

Given Information:Rondell’s golf score at the end of high school golf tournament were $\text{-1,-2,4,-6,3,-1}\text{and}\text{-3}$ .

Golf scores are $\text{-6,-3,-2,-1,-1,3,4}$

Range: To find the range subtract the highest value from the lowest

Highest = 4

Lowest = -6

A measure of variability = highest-lowest

  $\begin{array}{l}\text{=}\text{4-(-6)}\\ \text{=}\text{4+6}\text{=}\text{10}\end{array}$

Quartiles: $\text{{-6,-3,-2}, {-1,3,4}}$

First quartile = Median $\text{{-6,-3,-2}}=-3$

Third quartile = median $\text{{-1,3,4}}\text{=}\text{3}$

Interquartile range = $\text{3-(-3)}\text{=}\text{6}$

Outliers = $\text{6}\times \text{1}\text{.5}\text{=}\text{9}$

Subtract 9 from the first quartile and add 9 to the third quartile

  $\text{-3}\text{-9}\text{=}\text{-12,}\text{3+9}\text{=}\text{12}$

Any value is less than -12 or greater than12

  $\text{{-6,-3,-2,-1,-1,3,4}\}$

There are no outliers.

One-fourth of Rondell’s scores were lower than -3.one fourth was higher than 3. Half of his scores were in the interval -3 to 3. The fact that there are no outliers indicates that the score is evenly distributed.