1. Homework Check

2. Unit 5 Day 5
HISTOGRAMS

3. 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)

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

5. Histogram

6. 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

7. Histogram: What’s the difference?

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

9. 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.

10. 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

11. 235
260
285
310
335
360

12. 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

13. Distribution Shapes