1. Good afternoon Happy Thursday
Let’s warm up with questions 1-3 on page 3 of the Stats Packet.

2. Unit 1 Day 4
HISTOGRAMS

3. Histogram Graphical representation of a data set
Shows cluster of values and gaps in data
Good way to display information from large data sets
Width of bar (x-axis) represents interval
Height of bar (y-axis) represents frequency

4. Histogram

5. Histogram
Each interval bin should have the same width
Level of detail shown depends on bin width
Rule of Thumb: Bin Width = 15% of the range
Bars always touch
Each bin includes the left endpoint value but not the right endpoint value

6. Histogram: What’s the difference?

7. Constructing a histogram:
Determine interval width
(Largest value – Smallest value)÷Desired number of intervals
5 to 10 intervals is usually best( we decided 7 yesterday)
Organize data into a frequency table
Distribute data into intervals

8. Using Calculator
In put data: Stat-> Edit L1. TO organize data: Stat-> SortA-> input(L1) To Graph: 2nd y=, turn plot on, Under Type select the histogram. Hit Graph, Zoom 9 (Data)

9. Adjusting Window
To adjust the interval size, Change Xscl: Trace: To see min and max for each interval You can change the x:max and x:min to adjust start. From

10. Good afternoon Happy Friday!!!
Let’s start with a cumulative frequency tables. It is the same as a normal frequency table, with an additional column, where we sum up the frequencies so far.

11. Cumulative frequency tables
Intervals
Tally
Frequency
Cumulative Frequency
5-10 II 2
10-15
15-20
III 3 5
20-25
IIII II
25-30
IIII
30-35

12. Cumulative graph
This will be a line or curve with points (x,y). Not a histogram. The upper bound of each interval will be the x coordinate. The cumulative frequency will be the y coordinate.

13. 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
Maximum time is 360 hours and minimum time is 236 hours.
Say we want 5 intervals.
Interval width = range of data/5 = 124/5 = 24.8 ≈ 25
So, construct a bin width of 25.
Create a frequency table and histogram

14. 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

15. 235
260
285
310
335
360

16. 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

17. Distribution Shapes