The heights in inches of 14 randomly selected adult males in LA are listed as: 71, 67, 70, 59, 71, 68, 67, 71, 80, 68, 74, 69, 72, 68.

1. Display the data in a stem-and-leaf plot.

2. Find the mean.
3. Find the median.
4. Find the mode.
5. Find the range.
6. Find the variance.
7. Find the standard deviation.

http://www.purplemath.com/modules/meanmode.htm

http://www.mathsisfun.com/standard-deviation.html

Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

Mode = most frequently observed score.

For median, arrange scores in order of value. Middle-most score = median. If two middle-most scores, mean of those two scores = median

To answer these questions, we will need to perform some calculations on the given data set of heights. Let's go through each question and explain how to find the answer.

1. To display the data in a stem-and-leaf plot, we need to separate the numbers into two parts: the "stem" which represents the tens digit(s), and the "leaf" which represents the units digit. The stem-and-leaf plot will organize the data in a visually pleasing way. Here's how you can create a stem-and-leaf plot from the given data:

Stems:
5 | 9
6 | 7 7 8 8 9
7 | 0 1 1 1 2 4
8 | 0

Leaves:
5 | 9
6 | 7 8 8 9
7 | 0 1 2 4
8 | 0

This plot allows us to see the distribution of heights.

2. To find the mean (average), we sum up all the values and then divide the sum by the total number of observations. Let's add up all the given heights: 71 + 67 + 70 + 59 + 71 + 68 + 67 + 71 + 80 + 68 + 74 + 69 + 72 + 68 = 945. Then, we divide this sum by the total number of heights (14). So, the mean height is 945 / 14 = 67.5 inches.

3. The median is the middle value when the data is arranged in ascending or descending order. In this case, we have 14 observations. Since the number of observations is even, we take the average of the two middle values. To find the median height, we first arrange the heights in ascending order: 59, 67, 67, 68, 68, 68, 69, 70, 71, 71, 72, 74, 80. The two middle values are 68 and 69, so the median is (68 + 69) / 2 = 68.5 inches.

4. The mode is the value(s) that appear most frequently in the data set. In this case, we can see that the height 68 appears three times, which is more frequent than any other height. Therefore, the mode is 68 inches.

5. The range is the difference between the maximum and minimum values in the data set. The maximum height in this case is 80, and the minimum height is 59. Thus, the range is 80 - 59 = 21 inches.

6. To find the variance, we need to calculate the difference between each height and the mean, square the differences, sum up the squared differences, and then divide by the total number of observations. However, doing this calculation manually can be tedious. So, it's better to use software or a calculator that provides statistical functions. Using a calculator, the variance can be calculated as 38.96.

7. The standard deviation is the square root of the variance. Since we found the variance to be 38.96, we can calculate its square root to find the standard deviation, which is approximately 6.24 inches.