Describing Discrete Data

As we said, discrete data have natural categories. Hence to describe a discrete data set, simply classify the data into their categories. For example, suppose we ask our 20 students their stronger hand; i.e., whether they are left (L) or right (R) handed. The responses are:

Hand L  R  R  R  R  L  R  R  R  R
     R  R  R  R  L  R  R  R  R  R

Hence this is discrete data with two categories R or L. Classifying the data, we obtain

R    L
17   3

This is the distribution   of the data. It is indeed the distribution, there is no other.

A picture of the sample distribution is given in Figure 1.1:

  

Figure 1.1: Historam of Strong Hand

Note how informative this picture is. It tells you immediately that there are many more right-handed people in the sample than left-handed. More than 5 times as many. This picture is much more informative than the 20 L's and R's listed above.

One   of interest here is the   sample proportion of left-handers in the sample which is 3/16 or .1875 (19%). Later in the course, we will discuss how to use the sample proportion to   estimate the true proportion of left-handed people in the university (population).

Exercise 2.2.1  

1.

Obtain the distribution of hair color for the above 20 students. Then draw a histogram of it by hand. Obtain the sample proportion of blonds.

2.

Obtain the distribution of hair color for the above 20 students using the summary module.

3.

Sometime ago, Carrie had a deck of 59 baseball cards. The data recorded from this deck is given in Appendix A. The fourth column of this data gives the stronger hand of the baseball player, 0 for right-handed and 1 for left-handed. Obtain the distribution of the strong hand of a baseball player and obtain a histogram of it by hand.

4.

Repeat the exercise using the summary module to draw the histogram.

5.

Note that about 11% of the males in America are left-handed. Obtain the sample proportion of left-handed baseball players. Does it seem high compared to 11%? If so, can you think of a reason why it would be high?

6.

Obtain the distribution and obtain the proportion of ones in the following sample.

Data
1 1 1 1 0 0 0 1 1 0 
1 0 0 0 1 0 0 0 1 0 
0 0 1 1 1 0 0 1 1 1 
0 0 0 1 0 1 0 0 1 0