CHE 315 – Lecture 59/9/05

Statistics

Quiz 2

1. An iron ore was analyzed by dissolving a 1.1324-g sample in concentrated HCl. After precipitation, filtration and washing, the residue was ignited to give 0.593 g of pure Fe2O3 (159.69 g/mol). What was the % Fe (55.847 g/mol) in the iron ore?

2. Stormwater running off of parking lots have typical copper (63.55 g/mol) concentrations of 100 ppb. Convert that concentration to molarity.

Arithmetic mean (average)

n321i

i

ii

x....xxxx

n

xx

Best way to express results if data is symmetrical

Standard Deviation

Measures how closely the data is clustered around the mean

Degrees of freedom: n-1

1n

)xx(s i

2i

Variance = s2

Relative standard deviation – (coefficient of variance)

x

s100

Gaussian distribution

Approximate µ by and σ by s

22 2)x(e2

1y

x

z

Used to express deviations from the mean in multiples of the standard deviation

s

xxxz

Probabilities

RangePercentage of measurements

µ + 1σ 68.3

µ + 2σ 95.5

µ + 1.96σ 95

µ + 3σ 99.7

Confidence intervalRange of values that will contain the true mean of the population to a given probabilityC.I. when s is large? small?C.I. when n is large? small?

n

tsx

Advantages to larger sample size– More confident of true value

Disadvantages of larger sample size– Money– Time– Not enough sample

z vs. t

t tends to z at large n’sValues of both in tables depend on confidence level– t also depends on degrees of

freedom

→ t for a single measurement

→ t for n measurementsns

xt

s

xt

xz