& STATISTICAL SAMPLING Nevada Math Project ISSUES IN PROBABILITY & STATISTICAL SAMPLING

WHAT DO PEOPLE THINK? How Tall are Dragons? HOW BIG ARE STARS?

But you can’t ask everyone! You have a Question! But you can’t ask everyone! SO YOU NEED A SAMPLE!

NO BIAS PLEASE!

So you take a random sample and compute statistics about it. You hope it reflects information about the entire population! SO YOU NEED A RANDOM SAMPLE SO YOU AVOID BIAS

RANDOM NUMBERS ARE THE KEY

Stratified Random Sample

USUALLY SAMPLES ARE REPRESENTAIVE BUT OCCASIONALLY …. CHAOS

MEAN ABSOLUTE DEVIATION MAD & MEDAD MEAN ABSOLUTE DEVIATION DATA EXAMPLE: {2,14,2,4,3} DO BOX PLOT 2 𝑸 𝟏 = 𝟐+𝟐 𝟐 =𝟐 2 𝑸 𝟐 =𝟑 4 𝑸 𝟑 = 𝟒+𝟏𝟒 𝟐 =𝟗 14 14 9 2 3

MEAN ABSOLUTE DEVIATION MAD & MEDAD MEAN ABSOLUTE DEVIATION DATA EXAMPLE: {2,14,2,4,3} Find mean, median, mode, standard deviation, MAD

STANDARD DEVIATION DATA EXAMPLE: {2,14,2,4,3} Standard Deviation MEAN = 5 so Variance is the average of (2−5) 2 =9 (Count this twice) (4−5) 2 =1 (3−5) 2 =4 (14−5) 2 =81 The Variance = 9+9+1+4+81 5 = 104 5 =20.8 Standard Deviation = 𝟐𝟎.𝟖 ≈𝟒.𝟓𝟔