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Statistics
Statistics Unit Vocabulary - Honors Algebra Two
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Terms in this set (42)
Statistics
The science of collecting, organizing, displaying, and analyzing data in order to draw conclusions and make predictions
Population
The entire group of interest to the statistician
Sample
A subset of population that represents the population (Used when it is not possible to obtain data about every member of a population)
Variable
characteristic of a population that can assume different values called data
Data
Different values; Information
Univariate Data
Data that includes only one variable
Descriptive Statistics
The branch of statistics that focuses on collecting, summarizing, and displaying data
Measures of Center (Central Tendency)
Measures of average; a single number used to represent what is average or typical
Mean
The sum of values in a set of data divided by the total number of values n in the set
Median
The middle value or the mean of the two middle values in a set of data when the data is arranged in numerical order
Mode
The value or values that appear most often in a set of data. A set of data can have no mode, one mode, or more than one mode.
Measures of Spread (Variation)
What statisticians use to describe how widely the data values vary and how much values differ from what is typical. Most common measures of spread are range, variance, and standard deviation.
Range
The difference between the greatest and least values in a set of data
Variance
The variance in a set of data is the mean of the squares of the deviations or differences from the mean
Standard Deviation
The standard deviation in a set of data is the average amount by which each individual value deviates or differs form the mean. It is the square root of the variance formula for population standard deviation.
Quartiles
Three position measures that divide a data set arranged in ascending order into four groups, each containing about 25% of the data. The median marks the second quartile , Q2, and separates the data into upper and lower halves.
Lower Quartile
Q1 is the median of the lower half
Upper Quartile
Q3 is the median of the upper half
Five-Number Summary
The three quartiles, along with the minimum and the maximum
Interquartile Range (IQR)
The difference between Q3 and Q1 (The interquartile range contains about 50% of the values)
Outlier
An extremely high or extremely low value when compared to the rest of the values in the set. Look for data values that are beyond the upper or lower quartiles by more that 1.5 times the interquartile range
Survey
Data are collected from responses given by members of a population regarding their characteristics, behaviors, or opinions
Observational Study
Member of a sample are measured or observed without being affected by the study
Experiment
The sample is divided into two groups
- experimental group that undergoes a change
- control group does not undergo the change
comparison of the two
Random Sample
Members of the population are selected entirely by chance
Bias
An error that results in a misrepresentation of members of a population
Parameter
a population characteristic
ex. all men over 50; students k-12
Distribution
Shows the observed or theoretical frequency of each possible data value
Negatively Skewed Distribution
Mean < Median
The majority of the data are on the right of the mean
Symmetric Distribution
Mean ≈ Median
The data are evenly distributed on both sides of the mean
Positively Skewed Distribution
Mean > Median
The majority of the data are on the left of the mean
Random Variable
The numerical outcome of a random event
Discrete Random Variables
Discrete random variables represent countable values
Continuous Random Variables
Continuous random variables can take on any value
Probability Distribution
A probability distribution for a particular random variable is a function that maps the sample space to the probabilities of the outcomes in a sample space. Can be represented by tables, equations, or graphs
Theoretical Probability Distribution
A theoretical probability distribution is based on what is expected to happen
Experimental Probability Distribution
A distribution of probabilities estimated from experiments
Law of Large Numbers
States that the variation in a data set decreases as the sample size increases
Normal Distribution
A continuous, symmetric, bell-shaped distribution of a random variable
Empirical Rule
Can be used to determine the area under the normal curve at specific intervals
z-Value
Represents the number of standard deviations that a given data value is from the mean
Standard Normal Distribution
A normal distribution with a mean of 1 and a standard deviation of 1
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Verified questions
STATISTICS
(a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, and (c) explain what it would mean to make a Type II error. According to the CTIA-The Wireless Association, the mean monthly revenue per cell phone was $48.79 in 2014. A researcher suspects the mean monthly revenue per cell phone is different today.
STATISTICS
A production line operation is tested for filling weight accuracy using the following hypotheses. $$ \begin{array} { l l } { \text { Hypothesis } } & { \text { Conclusion and Action } } \\ { H _ { 0 } : \mu = 16 } & { \text { Filling okay; keep running } } \\ { H _ { \mathrm { a } } : \mu \neq 16 } & { \text { Filling off standard; stop and adjust machine } } \end{array} $$ The sample size is 30 and the population standard deviation is $\sigma = .8 .$ Use $\alpha = .05$. a. What would a Type II error mean in this situation? b. What is the probability of making a Type II error when the machine is overfilling by .5 ounces? c. What is the power of the statistical test when the machine is overfilling by .5 ounces? d. Show the power curve for this hypothesis test. What information does it contain for the production manager?
STATISTICS
The statement represents a claim. Write its complement and state which is $$ H _ { 0 } $$ and which is $$ H _ { a } $$ . $$ \mu \neq 2.28 $$
PROBABILITY
At least one normal six-sided die with numbers 1 to 6 on its faces. Several dice would be useful to speed up the experimentation. Toss two dice 360 times. Record the sum of the two numbers for each toss in a table. $$ \begin{matrix} \text{Sum} & \text{Tally} & \text{Frequency} & \text{Rel. Frequency}\\ \text{2}\\ \text{3}\\ \text{4}\\ \vdots\\ \text{12}\\ & \text{Total} & \text{360} & \text{1}\\ \end{matrix} $$
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