Salaries of College Coaches The data are the salaries (in hundred thousands of dollars) of a sample of 30 colleges and university coaches in the United States. Construct a frequency distribution for the data using 8 classes. (The data in this exercise will be used for Exercise 11 in Section 2–2.)
164 | 225 | 225 | 140 | 188 |
210 | 238 | 146 | 201 | 544 |
550 | 188 | 415 | 261 | 164 |
478 | 684 | 330 | 307 | 435 |
857 | 183 | 381 | 275 | 578 |
450 | 385 | 297 | 390 | 515 |
The given data is
164 | 225 | 225 | 140 | 188 |
210 | 238 | 146 | 201 | 544 |
550 | 188 | 415 | 261 | 164 |
478 | 684 | 330 | 307 | 435 |
857 | 183 | 381 | 275 | 578 |
450 | 385 | 297 | 390 | 515 |
The procedure for constructing a grouped frequency distribution for the numerical data follows:
Step 1:
Highest value:
Lowest value:
Add the width to the smallest data value to get the lower limit of the next class. Keep adding until there are 8 classes, as shown, Subtract one unit from the lower limit of the second class to get the upper limit of the first class. Then add the width to each upper limit to get all the upper limits
.
The first class is
Second class is etc.
Step 2: Tally the data.
Step 3: Find the numerical frequencies from the tallies.
The completed frequency distribution is
The cumulative frequency distribution:
Cumulative frequency distribution shows the number of data values less than or equal to the upper class boundary of a specific class. Usually, we construct ascending cumulative frequency distribution. The cumulative frequency for the first class is ; for the second class it is ; for the third class it is and so on.