Tuesday, 9/17
➢ Population mean: µ = Σx/N (N=number of data values in population
➢ Population variance: δ = Σ(x-µ)2/N
➢ Population standard deviation: δ = √Σ(x-µ)2/N
Professor went through example discussing how to find mean and standard deviation
➢ Sample coefficient of variation(CV): CV = (s/x) * 100
→ Where x is the mean, and s is the standard deviation
➢ Population coefficient of variation(CV): CV = (δ/µ) * 100
→ Where µ is the population mean, and δ is the population standard deviation
Professor went through example with class determining coefficients of variation
➢ Chebyshev’s Theorem-for any set of data and for any constant k greater than 1, the
proportion of the data that must lie within k standard deviations on either side of the
mean is at least: 1-(1/k2)
→ Tells us the minimum percentage of data that fall between the mean and any specified
number of standard deviations on either side of the mean
➢ For any set of data...
→ At least 75% of the data falls in the interval from (µ-2δ) to (µ+2δ)
→ At least 88.9% of the data falls in the interval from (µ-3δ) to (µ+3δ)
→ At least 93.8% of the data falls in the interval from (µ-4δ) to (µ+4δ)
➢ Percentile of a distribution is a value such that P% of the data fall at or below it and (100-
P)% of the data fall at or above it
→ If a test score is at the 89th percentile, then 89% of scores are at or below it
➢ Quartiles divide data into fourths; Q1 is 25th percentile, Q2 is median, Q3 is 75th percentile
→ Q1: median of the lower half of the data
→ Q3: median of the upper half of the data
→ Interquartile range: Q3-Q1
Professor went through example with class calculating Q1 and Q3
➢ Population mean: µ = Σx/N (N=number of data values in population
➢ Population variance: δ = Σ(x-µ)2/N
➢ Population standard deviation: δ = √Σ(x-µ)2/N
Professor went through example discussing how to find mean and standard deviation
➢ Sample coefficient of variation(CV): CV = (s/x) * 100
→ Where x is the mean, and s is the standard deviation
➢ Population coefficient of variation(CV): CV = (δ/µ) * 100
→ Where µ is the population mean, and δ is the population standard deviation
Professor went through example with class determining coefficients of variation
➢ Chebyshev’s Theorem-for any set of data and for any constant k greater than 1, the
proportion of the data that must lie within k standard deviations on either side of the
mean is at least: 1-(1/k2)
→ Tells us the minimum percentage of data that fall between the mean and any specified
number of standard deviations on either side of the mean
➢ For any set of data...
→ At least 75% of the data falls in the interval from (µ-2δ) to (µ+2δ)
→ At least 88.9% of the data falls in the interval from (µ-3δ) to (µ+3δ)
→ At least 93.8% of the data falls in the interval from (µ-4δ) to (µ+4δ)
➢ Percentile of a distribution is a value such that P% of the data fall at or below it and (100-
P)% of the data fall at or above it
→ If a test score is at the 89th percentile, then 89% of scores are at or below it
➢ Quartiles divide data into fourths; Q1 is 25th percentile, Q2 is median, Q3 is 75th percentile
→ Q1: median of the lower half of the data
→ Q3: median of the upper half of the data
→ Interquartile range: Q3-Q1
Professor went through example with class calculating Q1 and Q3
