Stats Page 1 of 5 Frequency Table: partitions data into classes or intervals and shows how many data values are in each class. The classes or intervals are constructed so that each data value falls exactly into one class. Steps to making a frequency table: 1. Decide how many classes or intervals you want. 2. Find the CLASS WIDTH for the number of intervals you chose. Largest data value smallest data value Class Width = desired number of classes (round to the next highest whole number) 3. Determine the data range for each class. Find the lower class limit: the lowest class that the smallest data value can fit into (usually the smallest data value) Find the upper class limit: The highest data value that can fit in a class. Class Width is the difference between the lower class limit of one class and the lower class limit of the next class. 4. Create the classes or intervals. 5. Begin tallying. 6. Total the tallies to obtain the class frequency. Class frequency is how many times the data falls into that particular class. 7. Compute the midpoint (class mark) for each class. 8. Find the class boundaries. Upper class boundaries, add 0.5 unit to the upper class limit. Lower class boundaries, subtract 0.5 unit from the lower class limit. Example 1: The following information is based off a car pooling study of one way commuting distances of workers in the downtown area. A random sample of 60 workers were surveyed. Make a frequency table for this data. One-Way Commuting Distances in Miles for 60 Workers in the Downtown Area 13 47 10 3 16 20 17 40 4 2 7 25 8 21 19 15 3 17 14 6 12 45 1 8 4 16 11 18 23 12 6 2 14 13 7 15 46 12 9 18 34 13 41 28 35 17 24 27 29 9 14 26 10 24 37 31 8 16 12 16
Stats Page 2 of 5 What is the difference between a class limit and a class boundary? Relative Frequency: The portion of all data that falls into that class All values will be less than 1. Relative frequency = class frequency f total of all frequencies n Histogram: Bar graphs are used to represent each class. The width of each bar is the class width. The height of the bar is the class frequency. If creating a relative frequency histogram, the height of the bar is the relative frequency of that class. Steps to making a histogram or relative-frequency histogram: 1. Make a frequency table (including relative frequency) with the designated number of classes. 2. Place class boundaries on the horizontal axis and frequency or relative frequency on the vertical axis. 3. For each class of the frequency table, draw a bar whose width extends between corresponding boundaries. For histograms, the height of each bar is the corresponding class frequency. For relative-frequency histograms, the height of each bar is the corresponding class relative frequency.
Stats Page 3 of 5 Example 2: The following information is based off a car pooling study of one way commuting distances of workers in the downtown area. A random sample of 60 workers were surveyed. Make a relative frequency table and histogram for this data. One-Way Commuting Distances in Miles for 60 Workers in the Downtown Area 13 47 10 3 16 20 17 40 4 2 7 25 8 21 19 15 3 17 14 6 12 45 1 8 4 16 11 18 23 12 6 2 14 13 7 15 46 12 9 18 34 13 41 28 35 17 24 27 29 9 14 26 10 24 37 31 8 16 12 16
Stats Page 4 of 5 Distribution shapes: Mound-shaped symmetrical both sides are the same when folded vertically in the middle. Uniform or rectangular a histogram in which every class has equal frequency Skewed Left or skewed right a histogram in which the one side is larger than the other. The direction of skewness is on the side of the longer tail. o Skewed left if the longer tail is on the left o Skewed right if the longer tail is on the right Bimodal a histogram in which two classes with the largest frequencies are separated by at least one class.
Stats Page 5 of 5 Example 3: How long does it take to finish the 1161-mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska? Finish times (to the nearest hour) for 57 dog sled teams are shown below. 261 271 236 244 279 296 284 299 288 288 247 256 338 360 341 333 261 266 287 296 313 311 307 307 299 303 277 283 304 305 288 290 288 289 297 299 332 330 309 328 307 328 285 291 295 298 306 315 310 318 318 320 333 321 323 324 327 a. Find the class width. Use five classes. b. Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies. c. Draw a histogram. d. Draw a relative-frequency histogram. e. Categorize the basic distribution shape as uniform, mound-shape symmetrical, bimodal, skewed left or skewed right. Class limits Class boundaries Midpoint Tally Frequency Relative Frequency Assignment: p.44 #1 4, 6ab, 9 Label your assignment Lesson 2.1