1- Indicate and defend which measures of central tendency and variability you think is most appropriate for these data:
3,5,3,2,8,4,6,7,1,4,3,2

Because the data is skewed (there are more numbers closer to the lower end than the higher end), so the median would be an appropriate measure of central tendency and the interquartile range would be the best measure of variability. If it was determined that the skewness was not too severe, you could choose the mean (average) and standard deviation.

#2- Calculate the semi-interquartile range for these data and indicate which measure of central tendency and variability would provide the best description of these data:
24,16,22,22,24,22,18,22,20,18,20,22,20,22,18,16,20,24,24,18

The quartile values are:

min = 16
Q1 = 19.5
median = 22
Q3 = 22.5
max = 26

The interquartile range is 22.5 - 19.5 = 3, so the semi-interquartile range is 3/2 = 1.5.

The data is almost symmetrically distributed, and there are no outliers. Therefore, the mean (average) would be an appropriate measure of central tendency, and the variance or the standard deviation (square root of the variance) would be an appropriate measure of variability.

The average is 21.1 and the standard deviation is 2.6.

#3. Calculate the semi-interquartile range for the dustribution and indicate which measure of central tendency and variability would provide the best description of these data:
Intersection speed(mph)
60-69
50-59
40-49
30-39
20-29
10-19
00-09

Number of Vehicles
38
30
26
22
30
38
22

These data are not normally distributed, so the median and interquartile range would be more appropriate than the mean and standard deviation when describing this data.

I'm guessing that you want the interquartile range for the speed (the question was unclear).

These were calculated in Excel by making a list with 60 entered 38 times (to represent the 38 cars traveling at 60 to 69 miles/hr), 50 entered 30 times, and so on:

min = 0
Q1 = 10
median = 30
Q3 = 50
max = 60

The interquartile range is 50 -10 = 40, so the semi-interquartile range is 20. (If you had used 5, 15, etc. instead of 0, 10, etc. to represent the speeds at the intersection, the interquartile range would not be affected.)

If you wanted the interquartile range for the number of cars, you can calculate it from these values:

min = 22
Q1 = 24
median = 28
Q3 = 30
max = 38