SECTION 2.1 Frequency Distributions and Their Graphs 41 Constructing a Frequency Distribution from a Data Set The data set lists the cell phone screen times (in minutes) for 30 U.S. adults on a recent day. Construct a frequency distribution that has seven classes. 200 239 155 252 384 165 296 405 303 400 307 241 256 315 330 317 352 266 276 345 238 306 290 271 345 312 293 195 168 342 SOLUTION 1. The number of classes (7) is stated in the problem. 2. The minimum data entry is 155 and the maximum data entry is 405, so the range is 405 - 155 = 250. Divide the range by the number of classes and round up to find the class width. Class width = 250 7 Range Number of classes ≈ 35.71 Round up to the next convenient number, 36. 3. The minimum data entry is a convenient lower limit for the first class. To find the lower limits of the remaining six classes, add the class width of 36 to the lower limit of each previous class. So, the lower limits of the other classes are 155 + 36 = 191, 191 + 36 = 227, and so on. The upper limit of the first class is 190, which is one less than the lower limit of the second class. The upper limits of the other classes are 190 + 36 = 226, 226 + 36 = 262, and so on. The lower and upper limits for all seven classes are shown at the left. 4. Make a tally mark for each data entry in the appropriate class. For instance, the data entry 168 is in the 155–190 class, so make a tally mark in that class. Continue until you have made a tally mark for each of the 30 data entries. 5. The number of tally marks for a class is the frequency of that class. The frequency distribution is shown below. The first class, 155–190, has three tally marks. So, the frequency of this class is 3. Notice that the sum of the frequencies is 30, which is the number of entries in the data set. The sum is denoted by Σf where Σ is the uppercase Greek letter sigma. Class Tally Frequency, f 155–190 ||| 3 191–226 || 2 227–262 |||| 5 263–298 |||| | 6 299–334 |||| || 7 335–370 |||| 4 371–406 ||| 3 Σf = 30 Frequency Distribution for Cell Phone Screen Times (in minutes) Times Number of adults Check that the sum of the frequencies equals the number in the sample. Lower limit Upper limit 155 190 191 226 227 262 263 298 299 334 335 370 371 406 Study Tip If you obtain a whole number when calculating the class width of a frequency distribution, use the next whole number as the class width. Doing this ensures that you will have enough space in your frequency distribution for all the data entries. Study Tip The uppercase Greek letter sigma (Σ) is used throughout statistics to indicate a summation of values. EXAMPLE 1
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