Researchers developed a method for ranking the total driving performance of golfers The method requires knowing a golfer's average driving distance (yards) and driving (percent of drives that land in the fairway). The values of these two variables are used to compute a driving performance index. Twenty driving performance index observations are listed in the table below. Use this information to complete parts a through c. 1.27 2.91 2.01 200 1.23 1.8 168 2.93 2.39 1.82 3.85 2.37 3.21 1.42 1.92 1.27 2.26 1.81 2.16 1.24 a. Find the mean median, and mode for the 20 driving performance index values. What is the mean? bar (x)= (Round to three decimal places as needed.)

To find the mean, median, and mode of the 20 driving performance index values, we will follow these steps:<br /><br />### Mean<br />The mean is calculated by summing all the values and dividing by the number of values.<br /><br />Given values:<br />\[ 1.27, 2.91, 2.01, 200, 1.23, 1.8, 168, 2.93, 2.39, 1.82, 3.85, 2.37, 3.21, 1.42, 1.92, 1.27, 2.26, 1.81, 2.16, 1.24 \]<br /><br />First, sum all the values:<br />\[ 1.27 + 2.91 + 2.01 + 200 + 1.23 + 1.8 + 168 + 2.93 + 2.39 + 1.82 + 3.85 + 2.37 + 3.21 + 1.42 + 1.92 + 1.27 + 2.26 + 1.81 + 2.16 + 1.24 = 68.94 \]<br /><br />Next, divide by the number of values (20):<br />\[ \bar{x} = \frac{68.94}{20} = 3.447 \]<br /><br />So, the mean is:<br />\[ \bar{x} = 3.447 \]<br /><br />### Median<br />The median is the middle value when the data is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.<br /><br />First, order the values:<br />\[ 1.23, 1.24, 1.27, 1.27, 1.42, 1.81, 1.81, 1.82, 1.92, 2.01, 2.16, 2.26, 2.37, 2.39, 2.93, 3.21, 3.85 \]<br /><br />Since there are 20 values, the median will be the average of the 10th and 11th values:<br />\[ \text{Median} = \frac{1.92 + 2.01}{2} = \frac{3.93}{2} = 1.965 \]<br /><br />So, the median is:<br />\[ \text{Median} = 1.965 \]<br /><br />### Mode<br />The mode is the value that appears most frequently in the data set. <br /><br />From the ordered list, we can see that the value 1.27 appears twice, which is more frequent than any other value.<br /><br />So, the mode is:<br />\[ \text{Mode} = 1.27 \]<br /><br />### Summary<br />- Mean: \( \bar{x} = 3.447 \)<br />- Median: \( 1.965 \)<br />- Mode: \( 1.27 \)