Statistics is the science of conducting studies to collect, organize, summarize, and draw conclusions from data. *(this is not the same as a statistic)*
What is a variable?
A variable is a characteristic or attribute that can take on different values. If it's obtained by chance, then it's a "random" variable. Different values are called DATA. Variable = imprint on the coin. Random Variable is the process of recording the results. Data are the individual recorded results.
What are the two main areas of STATS?
1) Descriptive-strictly observational
2) Inferential - draw conclusion now; hypothesis testing; predictive about the future
What it is a sample?
This consists of some collection of the subject being studied. It's any subset of the entire group being studied. A sample obtained by chance (or random #'s) is a random sample.
What is a population?
A population consists of all subjects (or objects) being studied.
EX: A recent survey found that, on average, about 33% of Americans vote for president every 4 years. POPULATION: Americans SAMPLE: Americans over 50
What is a discrete variable?
This is a variable that takes on a countable number of values.
What is a continuous variable?
A continuous variable take on an uncountable number of values.
What is a countable set?
This is when you can pair your set of values with the positive integers (1,2,3,4,5...)
What is an uncountable set?
Too many values to pair
What are the types of studies?
Observational Study and Experimental Study
What is an independent variable?
The variable being manipulated.
What is the dependent variable?
This is the resultant variable (Y)
What is a frequency distribution?
This is the organization of raw data using classes (categories) and frequencies (#of things in a class).
What is the method for constructing a frequency distribution?
1. Use between 5 and 20 classes (categories) and, if possible, make the class width odd. (so the mid will be a whole number)
2. make the classes mutually exclusive
3. make the classes exhaustive
4. use continuous classes
5. make the width of the classes equal
what is a frequency?
the number of things in a class
what is a class?
what are the steps to constructing a frequency distribution
1) get points
2) create chart
3) determine width of each class
two values occur with the same greatest frequency
A graph of a data set obtained by drawing a horizontal line from the minimum data value to Q1, drawing a horizontal line from Q3 to the maximum data value, and drawing a box whose vertical sides pass through Q1 and Q3 with a vertical line inside the box passing thorugh the median or Q2
Chebyshev's Theorem 134
The proportion of values from a data set that will fall within k standard deviations of the mean will be at least 1 -1/k^2, where k is a number greater than 1 (k is not necessarily an integer).
coefficient of variation 132
this is denoted by CVar, is the standard deviation divided by the mean. The result is expressed as a percentage.
data array 109
Data set in order.
deciles divide the data distribution into 10 groups
empirical rule 136
in normal distribution (bell shaped):
1) 68% of the data will fall within 1 standard deviation of the mean
2) 95% of the data will fall between 2 standard deviations of the mean
3) 99.7% of the data will fall between 3 standard deviations of the mean
exploratory data analysis (EDA) 162
the act of analyzing data to determine what information can be obtained by using stem and leaf plots, medians, interquartile ranges, and boxplots
five-number summary 162
five specific values for a data set that consist of the lowest and highest values, Q1, Q3, and the median.
interquartile range (IQR) 151
the difference between Q1 and Q3 and is the range of the middle 50% of the data
the mean is the sum of values divided by the number of values. SigmaX/n The symbol is X with a line over the top of it
the mid point of the data array. the symbol is MD
the sum of the lowest and the highest values in the data set, divided by 2. The symbol is MR. lowest value + highest value/2
modal class 112
class with the largest frequency
the value that occurs the most
more than two values that occur with the same greatest frequency
negatively skewed or left skewed distribution 117
majority of the data falls to the right of the median with a tail to the left
an extremely high or an extremely low data value when compared with the rest of the data values
characteristic or measure obtained by using all the data values from a specific population
divide the data set into 100 equal groups
positively skewed or right skewed distribution 117
majority of the data is left of the median. tail is to the right of the median.
divide the distribution into 4 groups separated by: Q1, Q2, Q3
the highest value minus the lowest value. Sybol R is used.
range rule of thumb 133
a rough estimate of standard deviation s~range/4
resistant statistic 165
relatively less affected by outliers.
standard deviation 127
square root of the variance. the symbol is the lower case sigma. o with the line from the forehead.
square root of data value minus population mean divided by population size
characteristic or measure obtained by using the data values from a sample.
symmetric distribution 117
data values are evenly distributed on both sides of the mean.
one value that occurs with the greatest frequency
the average of the squares of the distance each value is from the mean. The symbol for the population variance is lowercase sigma squared.
population variance equation = sigma(Data value - population mean)/population size
weighted mean 115
used when the values are not all equally represented.
equation = sum of the weights*values/sum of the weights
z score or standard score 142
obtained by subtracting the mean from the value and dividing the result by the standard deviation. This is used to compare relative positions of data from the results of others
categorical frequency distribution 38
used when the data are categorical (nominal)
raw data value is placed into a quantitative or qualitative category
class boundaries 39
the upper and lower values of a class for a grouped frequency distribution whose values have one additional decimal place more than the data and end in the digit 5
class midpoint 40
found by adding the upper limit and lower limit and dividing by 2.
class width 39
found by subtracting the upper limit from the lower limit
cumulative frequency 54
the sum of the frequencies accumulated up to the upper boundary of a class in the distribution
cumulative frequency distribution 42
a distribution that shows the number of data values less than or equal to a specific value
the number of data values contained in a specific class
frequency distribution 37
the organization of raw data in table form, using classes and frequencies
frequency polygon 53
a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of classes. The frequencies are represented by the heights of the points
grouped frequency distribution 39
when the range of the data is large, the data must be grouped into classes that are more than one unit in width.
a graph that displays the data by using contiguous vertical bars (unless the frequency of the class is 0) of various heights to represent the frequencies of the classes
lower class limit 39
smallest data value that can be included in the class
a graph that represents the cumulative frequencies for a the classes in a frequency distribution
open ended distribution 41
no specific end or no specific beginning
Pareto Chart 70
used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest
pie graph 73
a circle divided into sections or wedges according to the percentage of frequencies in each category of the distribution
raw data 37
data are in original form
relative frequency graph 56
proportions instead of raw data as frequencies
stem and leaf plot 80
a data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes
Time Series Graph 72
represents data that occur over a specific period of time
ungrouped frequency distribution 43
range of data is relatively small, a frequency distribution can be constructed using single data values for each class