A. The following data represent the legal costs (in thousands of dollars) for 31 municipalities for a specific year.

62   21   40   37   40   2   125   29   9   48   21   150   23   112   50   24  

38   76   20   118   260   36   18   20   7   67   455   204   92   24   52

For your convenience,

1. Compute the mean, the mode, the median, and the midrange.

(mean = 73.5, mode = 20, 21, 24, and 40, MD = 40, MR = 228.5)

2. Compute the range, the variance, and the standard deviation.

(R = 453, variance = 8506.5, standard deviation = 92.2)

3. Compute the z score for the values of 2 and 455.

(For x = 2, z = - 0.78; for x = 455, z = 4.1)

4. From part 3, can you conclude that 2 and 455 are outliers? Why?

(2 is not an outlier because its z score is not less than -3; 455 is an outlier because its z score is greater than 3.)

5. Find the 1st quartile and the 3rd quartile.

(Q1 = 21, Q3 = 92)

6. What is the percentile of 37?

(P = 44%)

7. What is the score of the 40^th percentile?

(c = 12.4, round up to 13^th. The 13^th score is 36)

8. Construct a Boxplot and describe the shape.

(Boxplot – do it yourself.  Shape – extremely right skewed)

9. Construct the interval for none outliers. Are there any outliers in the data set?

(Interval for none outliers are - 85.5, and 198.5. Outliers are 204, 260 and 455 because they are outside the interval.)

B. The data shown represent the percentage of unemployed males and females for a sample of countries of the world. Using the whole numbers as stems and the decimals as leaves, construct a back-to-back stem and leaf plot and compare the distributions of the two groups (hint: compare the central location, variation, and shape of distribution.)

Females: 8.0   8.6  7.0   8.6   8.8  6.8  9.2  5.9  7.2  4.6  5.6  7.7  8.0  8.7  4.5  6.5  3.4  9.4  2.9

Males:  5.6  4.6  2.2  5.6  3.1  5.9  6.6   8.7  6.0  5.2  5.6  4.4  7.7  6.6  6.0   4.6  3.1  4.1  7.7

Answer: