Question

A researcher randomly selected n = 30 drivers who were issued speeding tickets in a city. There are four variables in this data set: (1) ID number, (2) age, (3) sex, and (3) size of the car that s/he drove when s/he got the speeding ticket.   *Sex (1 = Males, 2 = Females); Size_car (1 = Small, 2 = Medium, 3 = Large).

Data

ID	AGE	SEX	SIZE_CAR
1	18	1	2
2	28	1	2
3	44	1	3
4	20	2	2
5	39	2	2
6	53	2	3
7	28	1	1
8	18	1	1
9	24	2	1
10	21	1	2
11	35	1	3
12	38	1	3
13	22	1	1
14	29	1	2
15	63	1	3
16	22	1	3
17	45	2	2
18	36	2	2
19	16	1	1
20	56	1	3
21	20	2	1
22	23	1	2
23	58	1	1
24	32	1	3
25	25	2	2
26	28	1	2
27	21	1	1
28	51	2	3
29	26	2	1
30	45	1	2

Problem #1: Data preparation using SPSS (Statistical Package for the Social Sciences) Create a SPSS data file and enter all information. Define (name) the variables (4 variables; Id – Size_Car). Enter your data. DOUBLE check your data for accuracy of data entry. Label the VALUES: Sex (1 = Males, 2 = Females); Size_car (1 = Small, 2 = Medium, 3 = Large). (4 points). Show me the scores on all 4 variables for the first 5 cases.   Open MS Word file, “computer1_answers.” You are going to add your answers to this file.    Problem #2: Draw Graphs (2 points). Construct a graph (either a bar-graph or a histogram) that best represents each of the three variables: Age, Sex, and Size_Car. For example, you have to think about what graph (a bar [for a nominal/ordinal scale] or a histogram [for an interval/ratio scale]) will be the better for Age variable.   There should be three graphs (one for each variable). (1.5 points) What is the shape (skewedness? -- positively or negatively? normal?) of Age distribution?   Add your explanation. (1.5 points) What conclusion can you draw from the Sex distribution and from Size_Car? For example, you can say how many males or females received the speeding tickets?   How many of the people who received the speeding ticket were driving a small car, a medium car, or a large car?    Problem #3    (1.5 points) For Age, Sex, and Size_Car variables, find the mode, median, and mean. (1.5 points) What would be the best measure of central tendency for Age variable? What would be the best measure of central tendency for Sex variable? What would be the best measure of central tendency for Size_Car variable? Please justify your answer (“I chose mode for XXX variable because XXXX… For XX variable, I chose mean because XXX……..”). Problem #4 (1.5 points) Calculate the mean and standard deviation (SD) of Age separately by sex. In other words, I want you to show me the mean and SD of Age variable for male and for female, separately. (1.5 points) Compare males and females on the means and standard deviations of Age.   What do those values indicate?

Answer 1

A SPSS data file is created as explained. The variable view of the file is

And the data view is

Problem 2:

In this Data, Age is a quantitative Variable (ratio scale), we can use histogram to study the age distribution of the drivers who were issued speeding tickets

It can be seen that the age distribution is positively skewed. Since most of the values are on the left side of the histogram and some large values falls on the right, it is right skewed (i.e.,) positively skewed.

Since the variable Sex is nominal scale, bar graph will be better to represent Sex distribution of the drivers who were issued speeding tickets

It can be seen that 20 males received speeding tickets and 10 females received speeding tickets.Males were issued speeding tickets than females.

Since the variable Size_car is ordinal scale, bar graph will be better to represent car size of the drivers who were issued speeding tickets

12 alI 10 Large Medium Small Size Car

Of the drivers, who were issued speeding tickets, 9 were driving small cars and 12 were driving medium cars and the remaining 9 were driving large cars.

Problem 3:

Since Age is a quantitative variable and it does not have outliers, Mean will be an appropriate measure of central tendency.

Since Sex is a nominal variable, Mode will the best measure of central tendency for the variable Sex. Mode can be used to find which is the most common category.

The variable Size_car is an ordinal variable, thus medium will be a good measure of central tendency.

Problem 4:

The average age of the male drivers who were issued speeding tickets were 32.25 and average age of the female drivers who were issued speeding tickets were 33.90. The age of Male drivers who were issued speeding tickets were less than the female drivers who were issued speeding tickets.Since the standard deviation of male drivers were more than the female drivers,we can say that the age of Male drivers who were issued speeding tickets were more spread than the female drivers who were issued speeding tickets.