$15,000 up to 18,000 18,000 up to 21,000 21,000 up to 24,000 24,000 up to 27,000 27,000 up to 30,000 30,000 up to 33,000 33,000 up to 36,000 Step 4: Tally the vehicle selling prices into the classes. To begin, the selling price of the first vehicle in Table 2–4 is $23,197. It is tallied in the $21,000 up to $24,000 class. The second selling price in the first column of Table 2–4 is $18,021. It is tallied in the $18,000 up to $21,000 class. The other selling prices are tallied in a similar manner. When all the selling prices are tallied, the table would appear as: Class Tallies $15,000 up to $18,000 ||| $18,000 up to $21,000 ||| $21,000 up to $24,000 || $24,000 up to $27,000 ||I $27,000 up to $30,000 ||| $30,000 up to $33,000 |||| $33,000 up to $36,000 || |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| Step 5: Count the number of items in each class. The number of observations in each class is called the class frequency. In the $15,000 up to $18,000 class there are 8 observations, and in the $18,000 up to $21,000 class there are 23 observations. Therefore, the class frequency in the first class is 8 and the class frequency in the second class is 23. There is a total of 80 observations or frequencies in the entire set of data. Often it is useful to express the data in thousands, or some convenient units, rather than the actual data. Table 2–7, for example, reports the vehicle selling prices in thousands of dollars, rather than dollars. Now that we have organized the data into a frequency distribution, we can sum- marize the pattern in the selling prices of the vehicles for the AutoUSA lot of Whit- ner Autoplex in Raytown, Missouri. Observe the following: 1. The selling prices ranged from about $15,000 up to about $36,000. 2. The selling prices are concentrated between $18,000 and $27,000. A total of 58, or 72.5 percent, of the vehicles sold within this range.
Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation 31 3. The largest concentration, or highest frequency, is in the $18,000 up to $21,000 class. The middle of this class is $19,500. So we say that a typical selling price is $19,500. By presenting this information to Ms. Ball, we give her a clear picture of the distri- bution of selling prices for last month. We admit that arranging the information on selling prices into a frequency dis- tribution does result in the loss of some detailed information. That is, by organizing the data into a frequency distribution, we cannot pinpoint the exact selling price, such as $23,197 or $26,237. Further, we cannot tell that the actual selling price for the least expensive vehicle was $15,546 and for the most expensive $35,925. However, the lower limit of the first class and the upper limit of the largest class convey essentially the same meaning. Likely, Ms. Ball will make the same judgment if she knows the lowest price is about $15,000 that she will if she knows the exact price is $15,546. The advantages of condensing the data into a more understand- able and organized form more than offset this disadvantage. Selling Prices ($ thousands) Frequency 15 up to 18 8 18 up to 21 23 21 up to 24 17 24 up to 27 18 27 up to 30 8 30 up to 33 4 33 up to 36 2 Total 80 TABLE 2–7 Frequency Distribution of Selling Prices at Whitner Autoplex Last Month Self-Review 2–2 The commissions earned for the first quarter of last year by the 11 members of the sales staff at Master Chemical Company are: (a) What are the values such as $1,650 and $1,475 called?