Describing Distributions Numerically Chapter 5

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)

Effect of skew on mean

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)

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

Calculation of outliers (fence) LQ – 1.5(IQR) UQ + 1.5(IQR) IQR = UQ – LQ IQR = 21-18 = 3 18 – 1.5(3) = 13.5 Lower fence is 13.5 Anything below this is an outlier IQR = UQ – LQ IQR = 21-18 = 3 21 + 1.5(3) = 25.5 Upper fence is 25.5 Anything above this is an outlier

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

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

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

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