1. Describing Distributions Numerically
Chapter 5

2. I. Types of Numeric Displays
Symmetric
Skewed
Center
Spread
Outliers
Mean
Range and Standard Deviation
> 2 standard deviations from the mean
Median
Interquartile Range (IQR) and Range
LQ – 1.5(IQR)
UQ + 1.5(IQR)

3. Effect of skew on mean

4. II. Boxplots Divide the data into quarters. Construction
Order the data in ascending order.
Circle the data point in the middle (if odd # of data) Or Circle the two middle data points and take the average (if even # of data points).
Repeat step two for each of the halves.
Put a line at the lower Quartile (LQ), Median, Upper Quartile(UQ)
Calculate any outliers, put them on line as • or *
Make a box out of the LQ, Med and UQ. Draw out ‘whiskers’ from the box out to the max and min values (excluding the outliers)

5. C. Example
18, 19, 18, 21, 35, 18, 17, 18, 19, 20, 21, 18, 21, 19
17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 35
MED = 19 LQ UQ

6. Calculation of outliers (fence)
LQ – 1.5(IQR)
UQ + 1.5(IQR)
IQR = UQ – LQ
IQR = = 3
18 – 1.5(3) = 13.5
Lower fence is 13.5
Anything below this is an outlier
IQR = UQ – LQ
IQR = = 3
(3) = 25.5
Upper fence is 25.5
Anything above this is an outlier

7. C. Example
18, 19, 18, 21, 35, 18, 17, 18, 19, 20, 21, 18, 21, 19
17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 35
MED = 19 LQ UQ 17 35

8. III. Numerical Summaries in the Calculator.
Sum of X
Sample Standard Deviation
Population Std. Dev
Sample size
LQ (25% data below)
UQ (25% data above)
The last box is called the 5 Number Summary

9. Math Scores Example I:\Math Department\TI-84-Emulator\Wabbitemu.exe
604
587
585
582
579
558
540
534
532
531
530
526
525
520
519
511
505
502
496
491
482
479
476
472
469
467
466
448
447
429
428
422
403
392
345
337
275
I:\Math Department\TI-84-Emulator\Wabbitemu.exe

10. I:\Math Department\TI-84-Emulator\Wabbitemu.exe