**Frequency Distributions**

Imagine that a large class of students is given a quiz. We examine the results in the form of tables and graphs.

**Practice 1**

In our hypothetical class, 130 students take a 10-question quiz. The results are described to us in long-winded verbal form. Here's what we're told: "Nobody missed all the questions (that is, got a score of 0 correct); 4 people got 1 correct answer; 7 people got 2 correct answers; 10 people got 3 correct answers; 15 people got 4 correct answers; 24 people got 5 correct answers; 22 people got 6 correct answers; 24 people got 7 correct answers; 15 people got 8 correct answers; 7 people got 9 correct answers; and 2 people wrote perfect papers (that is, got 10 correct answers)."

Portray these results in the form of a table, showing the test scores in ascending order from top to bottom in the left-hand column, and the absolute frequencies for each score in the right-hand column.

**Solution 1**

Table 8-1 shows the results of the quiz in tabular form. Note that in this depiction, the lowest score is at the top, and the highest score is at the bottom. The table is arranged this way because that's how we are asked to do it.

**Table 8-1 **Table for Practice 1. The lowest score is at the top and the highest score is at the bottom.

**Practice 2**

How else can the data from Practice 1 be arranged in a table?

**Solution 2**

The quiz results can be portrayed in a table upside-down relative to Fig. 8-1, that is, with the highest score at the top and the lowest score at the bottom (Table 8-2), and it shows us the information just as well.

**Fig. 8-1. **Illustration for Practice 1-3.

**Table 8-2 **Table for Practice 2. This is the same data as that shown in Table 8-1, but with the highest score at the top and the lowest score at the bottom.

The table can also be arranged with the columns and rows interchanged, so it has 2 rows and 11 columns (not counting the column with the headers). This can be done in either of two ways: the lowest score at the left and the highest score at the right (Table 8-3A), or the highest score at the left and the lowest score at the right (Table 8-3B).

**Table 8-3A **Table for Practice 2. This is the same data as that shown in Table 8-1, but with the data arranged horizontally. The lowest score is at the left and the highest score is at the right.

**Table 8-3B **Another table for Practice 2. This is the same data as that shown in Table 8-1, but with the data arranged horizontally. The highest score is at the left and the lowest score is at the right.

**Practice 3**

Render the data from Practice 1 in the form of a vertical bar graph, showing the lowest score at the left and the highest score at the right. Do not put numbers for the absolute frequency values at the tops of the bars.

**Solution 3**

Figure 8-1 shows the results of the quiz as a vertical bar graph, without absolute frequency values shown at the tops of the bars. The advantage of showing the numbers, if there's room to do so, is the fact that it eliminates the need for the observer having to guess at the values. In this graph, it would be a "tight squeeze" to show the numbers, and the result would look crowded and might even cause confusion in reading the graph.

**Fig. 8-1. **Illustration for Practice 1-3.

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