Center and Spread IB SL: Statistics Day 2

Measures of Center MEAN MEDIAN

2,3,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,8,8,8,9,9 Find the mean and median

Grouped Discrete # of Siblings # of studens 12 1 15 2 8

Continuous If given a frequency table we can only find an estimate of the actual mean and only a range in which the median lies. Age # of Bus Drivers 21 - 11 26 - 14 31 - 33 36 - 38

Sometimes we have to work backwards Your test scores thus far are 87, 76, 90, 92, 80, and 85. What would you need on the next test to have a B average? (at least 84.5)

Find a given that 3, 0, a, a, 4, a, 6, a and 3 have an average of 4.

𝑥 =13.9 𝑎𝑛𝑑 𝑛=10 𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑎𝑡𝑒 𝑖=1 10 𝑥 𝑖 𝑥 =13.9 𝑎𝑛𝑑 𝑛=10 𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑎𝑡𝑒 𝑖=1 10 𝑥 𝑖

Which one is Best???? Mostly depends on shape. The most appropriate measure of center is the one that will best describe the most typical observation If your data is roughly symmetric, use 𝑥 Otherwise, use the MEDIAN

Sometimes people lie… The selling prices of the last 10 houses sold in a certain subdivision were: $146,400 $127,600 $211,000 $192,500 $256,400 $132,400 $148,000 $129,500 $131,400 $162,500

SPREAD

4 ways to measure Range IQR Variance Standard Deviation

2,3,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,8,8,8,9,9

Variance and St. Dev 𝑣𝑎𝑟= 𝑥− 𝑥 2 𝑛 IB denotes standard deviation as sn but the calculator will show it as σn 𝑣𝑎𝑟= 𝑥− 𝑥 2 𝑛

Short Example x 3 7 6 8 11

What about grouped data? Add in one small thing…FREQUENCY! 𝑠 𝑛 = 𝑓 𝑥− 𝑥 2 𝑛