Statistics Fall 2010

Statistics is the science of conducting studies to collect, organize, summarize, and draw conclusions from data. *(this is not the same as a statistic)*

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.

• 1) Descriptive-strictly observational
• 2) Inferential - draw conclusion now; hypothesis testing; predictive about the future

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.

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

This is a variable that takes on a countable number of values.

A continuous variable take on an uncountable number of values.

This is when you can pair your set of values with the positive integers (1,2,3,4,5...)

Too many values to pair

Observational Study and Experimental Study

The variable being manipulated.

This is the resultant variable (Y)

This is the organization of raw data using classes (categories) and frequencies (#of things in a class).

• 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

the number of things in a class

a category

• 1) get points
• 2) create chart
• 3) determine width of each class
• 4)

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

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).

this is denoted by CVar, is the standard deviation divided by the mean. The result is expressed as a percentage.

Data set in order.

deciles divide the data distribution into 10 groups

• 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

the act of analyzing data to determine what information can be obtained by using stem and leaf plots, medians, interquartile ranges, and boxplots

five specific values for a data set that consist of the lowest and highest values, Q1, Q3, and the median.

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

class with the largest frequency

the value that occurs the most

more than two values that occur with the same greatest frequency

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

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.

a rough estimate of standard deviation s~range/4

relatively less affected by outliers.

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.

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

used when the values are not all equally represented.

equation = sum of the weights*values/sum of the weights

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

used when the data are categorical (nominal)

raw data value is placed into a quantitative or qualitative category

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

found by adding the upper limit and lower limit and dividing by 2.

found by subtracting the upper limit from the lower limit

the sum of the frequencies accumulated up to the upper boundary of a class in the distribution

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

the organization of raw data in table form, using classes and frequencies

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

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

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

no specific end or no specific beginning

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

a circle divided into sections or wedges according to the percentage of frequencies in each category of the distribution

data are in original form

proportions instead of raw data as frequencies

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

represents data that occur over a specific period of time

range of data is relatively small, a frequency distribution can be constructed using single data values for each class

largest data value included in the class