BSTAT Exam 2

College of the Ozarks Fall 2025

What are the components of central tendency

Mean, median, and mode

Variation is measured using:

range, interquartile range, variance, standard deviation, and coefficient of variation.

Range

largest # - smallest #

Interquartile range 

Quartile 3 - Quartile 1

Coefficient of variation =

Standard deviation/mean

sample mean

Sample Variance

S

Sample Standard Deviation

𝜇

population mean

population variance

Population standard deviation

n

sample size

N

population

Sample computed measurement =

statistic 

population computed measurement =

parameter

What does the 5-number summary consist of?

1. smallest number 

2. Quartile 1 

3. Median 

4. Quartile 3 

5. Largest Number

these convert a number to be expressed as standard deviations

z-scores (z-score of 2 means our number is two standard deviations away from the mean)

how to find z-score on excel

=STANDARDIZE(x,mean,standard dev)

How is an outlier determined?

if it is at least 3 standard deviations away from the mean.

NOT normally distributed

Chebyshev’s theorem

in Chebyshev’s theorem, what % of the data must be withing 2 standard deviations of the mean?

75%

in Chebyshev’s theorem, what % of the data must be withing 3 standard deviations of the mean?

89%

in Chebyshev’s theorem, what % of the data must be withing 4 standard deviations of the mean?

94%

According to the Empirical Rule, what % of the data must be within 1 standard deviation of the mean?

68%

According to the Empirical Rule, what % of the data must be within 2 standard deviation of the mean?

95%

According to the Empirical Rule, what % of the data must be within 3 standard deviation of the mean?

99.7%

Normally distributed with 0 skewness

Empirical Rule (Bell-shaped)

Discrete Random variable

a random variable that may assume a finite number of values

Finite =

Discrete

Probability Distribution

A list or function that shows all the possible outcomes of a random event and their corresponding probabilities.

E(x) =

average or mean

Calculate probability distribution:

Mean = x*f(x)

Standard Deviation

Sum(x-E(x))² f(x) FORMULA WILL BE ON TEST

4 Properties of binomial distribution

1. the experiment consists of a sequence of n identical trials

2. the outcomes are possible on each trial. We refer to one outcome as a success and the other outcomes as a failure.

3. the probability of a success (p), cannot change from trial to trial. and the probability of a failure, (1-p) does not change from trial to trial

4. the trials are independent

the probability of a success =

p

the probability of a failure =

1-p

Properties of Poisson distribution

1. Events are independence

2. Constant rate 

3. Discrete events (two events cannot occur at the same time)

4. mean=variance

5. STANDARD DEVIATION = the mean

The Standard Deviation of a poisson distribution =

Mean