stats midterm formulas

frequency

number of times

percentage

number of times / total # of data points

ex: 4 times / 40 people = 10%

mean

aka xbar, mu

• sum of values / number of data points or sample of people

• (xi x frequency + xii x frequency …) / sample of people

• ex: (27×0 + 48×1…)/150

variance

• s²

• n = total number of data points

• s² = (1/n-1) sum(xi-xbar)² + sum(xii-xbar)²…

• ex: (1/150-1) (27(0-1.42)² + 48(1-1.42)²…

standard deviation

= s, sigma

• square root s²

z score

z = (x - xbar)/ s

(x is given)

• ex: (1-1.42)/0.899441 =

• z = -0.466957

how to get groups for 5 quarter summary

sort data in ascending order

ex:

• 1-27 uses machine 0 times

  • 27 + 48 (48 is number of people that use the machine 1x a day) = 75

• 28-75

  • 75 + 60 (60 ppl use machine 2x a day)

location of 1st quartile

L1 = (1/4)(n+1) (n = total number of data points)

location of second quartile

L2 = (2/4)(n+1)

location of third quartile

L3 = (3/4)(n+1)

first quartile

Q1 = (1-0.75)(37th value)+0.75(38th value)

→ using 1 because 37th and 38th value corresponds bc people between 28-75 use coffee machine

second quartile

Q2 = (1-0.5)(number value) + (0.5)(number value)

third quartile

Q3 - (1-0.25)(number value) + (0.25)(number value)

yhat

= a +bx

Use to find estimated regression equation or least squares regression line

• the estimate of y value

• (x = people waiting or value given, plug in x to get predicted time

b

= r(s_y/s_x)

a

= ybar - b(xbar)

how to solve probability

1. find distance of value from mean

   1. x - mu (x is value, mu is mean)

2. divide distance by standard dev (sigma) for z score

3. match to rule

   1. 1 → 68

   2. 2 → 95

   3. 3 → 99.7

4. plug z score into equation

   1. p(mu - z score (sigma) <= x <= mu + z score (sigma) = z score percentage

5. plug in mu and sigma

6. solve

probability equation for value between two values

p(mu - z score (sigma) <= x <= mu + z score (sigma) = z score percentage

→ p(100 - 2 (15) <= x <= 100 + 2 (15) = 95%

p(70 <= x <= 130) = 95%