Homework Check

Unit 5 Day 5 HISTOGRAMS

How many paperclips can you hook together in 60 seconds? Frequency Distribution Histogram Paper Clips Linked Tally Frequency 0-5 5-10 10-15 15-20 20-25 25-30 30-35 How many links can you put together in one minute? Collect data and have students record on the board in a frequency distribution table. Show how to make a histogram from this by hand. Make sure that you are not just making a bar graph. The bars should be touching (like the next slide) to show the continuity of the data. Usually the lower value for each interval is marked on the x-axis on the left side of the corresponding “bar”, although you can also use the midpoint of the interval as well. Discuss with students – what is the difference between a bar graph and a histogram? (bars touching; bar graphs used with categorical data & histograms used with quantitative data divided into intervals)

Histogram Good way to display information from large data sets Width of bar (x-axis) represents interval Height of bar (y-axis) represents frequency

Histogram

Histogram Each interval bin should have the same width Each bin includes the left endpoint value but not the right endpoint value Bars always touch

Histogram: What’s the difference?

Constructing a histogram: Determine interval width 5 to 10 intervals is usually best Organize data into a frequency table Distribute data into intervals

Sample Data: How long does the 1161 mile Iditarod take? 236 244 247 256 261 266 271 277 279 283 284 285 287 288 289 290 291 295 296 297 298 299 303 304 305 306 307 309 310 311 313 315 318 320 321 323 324 327 328 330 332 333 338 341 360 Construct a bin width of 25.

Lower Limit Upper Limit Interval Frequency 235 260 235≤x<260 4 285 260≤x<285 9 310 285≤x<310 25 335 310≤x<335 16 360 335≤x<360 3

235 260 285 310 335 360

Distribution Shapes Symmetrical Uniform (rectangular histogram) Skewed left – longer tail on the left side Skewed right – longer tail on the right side Bimodal – two classes with the largest frequencies are separated by at least one class

Distribution Shapes