Describe the spread of the data:

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Describe the spread of the data: 9.4 Measures of Variation Describe the spread of the data: * Range * IQR (Interquartile Range) * 9.5 M.A.D. (Mean Absolute Deviation)

RANGE Range: 52 - 11 = 41 The ages of people in line vary by no more than 41 years

Q1 = first quartile (median of lower half of data) Example finding the IQR (Interquartile Range): Five Number Summary LV = least value Q1 = first quartile (median of lower half of data) Median = middle number Q3 = third quartile (median of upper half of data) GV = greatest value

Five Number Summary 220 230 230 240 240 245 250 250 250 260 260 270 LV Q1 Median Q3 GV LV: 220 Q1 235 Median: 247.5 Q3: 255 GV: 270 IQR = Q3 - Q1 IQR = 255 - 235 = 20

IQR EXPLORER GEOGEBRA https://static.bigideasmath.com/protected/content/dc_ca/tools/iqr_6_9_4/iqr_6_9_4.html

CALCULATING THE OUTLIER Outliers are data values that are more than 1.5 times the IQR lower than Q1 or 1.5 times the IQR greater than Q3 To check for outliers find these values: Bottom Boundary: Q1 – 1.5(IQR) Top Boundary: Q3 + 1.5(IQR) If any of your data values are smaller than the bottom boundary, or larger than the top boundary, they are outliers

EXAMPLE CALCULATING OUTLIERS 350 356 364 376 382 390 396 400 468 Q1 = 360 MEDIAN Q3 = 398 IQR = 398-360 = 38 Q1 – 1.5 (IQR) = 360 – 1.5(38) = 360 – 57 = 303 Q3 + 1.5 (IQR) = 398 + 1.5(38) = 398 + 57 = 455 Yes … 468 is bigger than 455. No values are lower than 303.

SUMMARY: STEPS TO FIND OUTLIER 1. Find the IQR 2. Multiply the IQR by 1.5 3. Subtract 1.5(IQR) from Q1 4. Add 1.5 (IQR) to Q3 5. Look at your data values and see if any of them are lower than the number found in step 3(bottom boundary) or greater than the number found in step 4 (top boundary). 6. This is your outlier if you have one.