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Chapter 3 Formulas
Sample Mean = 𝑥̅ =
∑ 𝑥
𝑛
Population Mean = 𝜇 =
∑ 𝑥
𝑁
Weighted Mean =
∑(𝑥𝑤)
∑ 𝑤
Range = Max – Min
Sample Standard Deviation = 𝑠 =
∑(𝑥−𝑥̅ )
2
𝑛− 1
Population Standard Deviation = 𝜎 =
∑(𝑥−𝜇)
2
𝑁
Sample Variance = 𝑠
2
∑(𝑥−𝑥̅ )
2
𝑛− 1
Population Variance = 𝜎
2
∑( 𝑥−𝜇
)
2
𝑁
Coefficient of Variation = CVar = (
𝑠
𝑥
̅
∙ 100 ) % Z-Score = 𝑧 =
𝑥−𝑥̅
𝑠
Percentile Index = 𝑖 =
(𝑛+ 1 )∙𝑝
100
The interquartile range = IQR = Q 3
– Q
1
Outlier Lower Limit = Q 1
- (1.5·IQR) Outlier Upper Limit = Q 3
+ (1.5·IQR)
Empirical Rule: z = 1, 2, 3 68%, 95%, 99.7% Chebyshev’s Inequality = (( 1 −
1
( 𝑧
)
2
TI- 84
Enter the data in a list
and then press
[STAT]. Use cursor
keys to highlight
CALC. Press 1 or [ENTER] to select 1:1-Var Stats. Press [2nd], then press the number key
corresponding to your data list. Press Enter to calculate the statistics. Note: the calculator always defaults
to L1 if you do not specify a data list.
TI- 89
Press [APPS], select FlashApps then press
[ENTER]. Highlight Stats/List Editor then
press [ENTER]. Press [ENTER] again to select
the main folder. To clear a previously stored list
of data values, arrow up to the list name you want to clear, press
[CLEAR], then press enter. Make sure the cursor is in the list, not
on the list name and type the data pressing [ENTER] after each
one. Enter all x-values in one list. Press [F4], select 1: 1-Var Stats.
To get the list name to the List box, press [
nd
] [Var-Link], arrow down to list1 and press [Enter]. This will
bring list1 to the List box. Select [Enter] to enter the list name and then enter again to calculate. Use the
down arrow key to see all the statistics.
Chapter 4 Formulas
Sum of Two Dice Standard Deck of Cards
Second Die
1 2 3 4 5 6
First Die
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Complement Rules: 𝑃(𝐴) + 𝑃(𝐴
𝐶
𝐶
𝐶
Mutually Exclusive Events: P(A ∩ B) = 0
Union Rule: P
A ∪ B
= P
A
+ P
B
− P(A ∩ B) Independent Events: P
A ∩ B
= P
A) ∙ P(B
Intersection Rule: P(A ∩ B) = P(A) ∙ P(B|A)
Conditional Probability Rule: 𝑃(𝐴|𝐵) =
𝑃(𝐴∩𝐵)
𝑃(𝐵)
Fundamental Counting Rule: m 1
·m 2
···m n
Factorial Rule: n! = n·(n – 1)·(n – 2)···3·2·
Combination Rule: n
C
r
𝑛!
( 𝑟!
( 𝑛−𝑟
) !
)
Permutation Rule: n
P
r
𝑛!
( 𝑛−𝑟
) !
TI-84 Combinations/Permutations : Enter the number “trials” (n) on the home screen. Press [MATH].
Use cursor keys to move to the
PRB menu. Press 2 for
permutation (2: n
P
r
), 3 for
combination (3: n
C
r
). Enter the
number of “successes” (r). Press
[ENTER] to calculate.
TI- 89
Combinations/Permutations :
Press [
nd
] Math > 7:Probability
Press 2 for permutation (2: n
P
r
3 for combination (3: n
C
r
). Enter
the sample size on the home
screen, then a comma, then enter
the number of “successes” then
end the parenthesis. Press
[ENTER] to calculate.
Chapter 5 Formulas
Discrete Distribution Table: 0 ≤ 𝑃(𝑥) ≤ 1
P(x) = 1
Discrete Distribution Mean: 𝜇 = ∑(𝑥 ∙ 𝑃(𝑥))
Discrete Distribution Variance:
2
2
2
Discrete Distribution Standard Deviation:
2
TI-84 Calculator Instructions for Mean, Variance & Standard Deviation
Select [STAT] then (1:Edit). Make sure the cursor is in the list, not on the list name
and type the desired values pressing [ENTER] after each one. For x and P(x) data
pairs, enter all x-values in one list. Enter all corresponding P(x)-values in a second
list. Press [STAT]. Use cursor keys to highlight CALC. Press 1 or [ENTER] to select
1:1-Var Stats. Press [2nd], then press the number key corresponding to your x list,
then a comma, then [2nd] and the number key corresponding to your P(x) values.
(Should look like this 1-Var Stats L 1
,L
2
) Press Enter to calculate the statistics. Where
the calculator says 𝑥̅ this is μ the population mean and σ x
is the population standard
deviation (square this number to get the population variance).
upper value of x into each cell. Press [ENTER]. This is the cumulative distribution function and will
return you the probability between the lower and upper x-values, inclusive.
Chapter 6 Formulas
Uniform Distribution:
1
𝑏−𝑎
, for 𝑎 ≤ 𝑥 ≤ 𝑏
P(X ≥ x) = (
1
𝑏−𝑎
P(X ≤ x) = (
1
𝑏−𝑎
P
1
≤ X ≤ 𝑥
2
1
𝑏−𝑎
2
1
Standard Normal Distribution:
μ = 0, σ = 1
Z - score: 𝑧 =
𝑥−𝜇
𝜎
Central Limit Theorem:
Z-score: 𝑧 =
𝑥̅ −𝜇
(
𝜎
√𝑛
)
Normal Distribution Probabilities:
P(X ≤ x) = P(X < x)
TI-84: normalcdf(-1E99,x,μ ,)
P(X ≥ x) = P(X > x)
TI-84: normalcdf(x,1E99,μ ,)
P(𝑥
1
≤ X ≤ 𝑥
2
) = P(𝑥
1
< X < 𝑥
2
TI-84: normalcdf(x 1
,x 2
,μ ,)
Inverse Normal Distribution:
P(X ≤ x) = P(X < x)
TI-84: invNorm(area,μ,)
P(X ≥ x) = P(X > x)
TI-84: invNorm(1–area,μ,)
P(𝑥
1
≤ X ≤ 𝑥
2
) = P(𝑥
1
< X < 𝑥
2
TI-84: x 1
= invNorm(area/2,μ ,)
x 2
=invNorm(1–area/2,μ ,)
Chapter 7 Formulas
TI-84: Press the [STAT] key, arrow over to the [TESTS] menu,
arrow down to the [A:1-PropZInterval] option and press the
[ENTER] key. Then type in the values for X, sample size and
confidence level, arrow down to [Calculate] and press the [ENTER] key. The
calculator returns the answer in interval notation. Note: sometimes you are not given
the x value but a percentage instead. To find the x to use in the calculator, multiply 𝑝̂
by the sample size and round off to the nearest integer. The calculator will give you
an error message if you put in a decimal for x or n. For example if 𝑝̂ = 0.22 and n =
124 then 0.22*124 = 27.28, so use x = 27.
TI-89: Go to the [Apps] Stat/List Editor , then select 2
nd
then F7 [Ints], then select 5: 1 - PropZInt. Type
in the values for X, sample size and confidence level, and press the [ENTER] key. The calculator returns
the answer in interval notation. Note: sometimes you are not given the x value but a percentage instead. To
find the x value to use in the calculator, multiply 𝑝̂ by the sample size and round off to the nearest integer.
The calculator will give you an error message if you put in a decimal for x or n. For example if 𝑝̂ = 0.
and n = 124 then 0.22*124 = 27.28, so use x = 27.
Confidence Interval for One Proportion
𝛼/ 2
𝑝̂𝑞̂
𝑛
𝑥
𝑛
TI-84: 1-PropZInt
Sample Size for Proportion:
∗
∗
𝑧
𝛼 ⁄ 2
𝐸
2
Always round up to whole number.
If p is not given use p * = 0.5.
E = Margin of Error
Confidence Interval for One Mean
Use z-inteval when σ is known.
Use t-interval when s is known.
If n < 30, population needs to be normal.
z-interval
𝛼/ 2
𝜎
√𝑛
TI-84: ZInterval
Z-Critical Values
TI-84: 𝑧
𝛼/ 2
= invNorm(1–area/2,0,1)
T-Critical Values
TI-84: 𝑡
𝛼/ 2
= invT(1–area/2,df)
t-interval, df = n – 1
𝛼 2
⁄ ,𝑛− 1
𝑠
√
𝑛
TI-84: TInterval
Sample Size for Mean
𝛼 2
⁄
2
Always round up to whole number.
TI-84: Press the [STAT] key, arrow over to the [TESTS]
menu, arrow down to the [7:ZInterval] option and press the
[ENTER] key. Arrow over to the [Stats] menu and press the
[ENTER] key. Then type in the population or sample standard
deviation, sample mean, sample size and confidence level, arrow down to [Calculate] and press the
[ENTER] key. The calculator returns the answer in interval notation.
