prob stats 2nd

frequency distribution

• a group of data sorted into categories showing the number of observations in each of the non-overlapping classes

• used to organize nominal-level or ordinal-level type of data

categorical, interval ratio

the data are grouped into classes:

stem and leaf plot

• method is to some extent overcomes the loss of actual observations brought about by the histogram

stem

leading digit/s

leaf

trailing digit

John Tukey

who introduced stem and leaf plot?

histogram

• a graph in which the classes are marked on the horizontal axis (x-axis) and the class frequencies on the vertical axis (y-axis)

frequency polygon

• a graph that displays the data using points which are connected by lines

cumulative frequency

• a graph that displays the ________ for the classes in a frequency distribution

pareto chart

• It represents frequency distribution for a categorical data (or nominal-level) & frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest.

bar chart or graph

• bases of the rectangles are arbitrary intervals whose centers are the codes. the height of each rectangle represents the frequency of that category. it is also applicable for categorical data (or nominal-level)

pie chart or circle graph

• divided into portions that represent the relative frequencies (or percentages) of the data belonging to different categories. 

• the data in the _____ should be categorical or nominal-level.

time series graph

• represents data that occur over specific period of time under observations

• shows for a trend or pattern on the increase or decrease over the period of time

pictograph

• immediately suggests the nature of the data being shown

• a combination of the attention-getting quality and the accuracy of the bar chart

• appropriate pictures arranged in a row (sometimes in a column) present the quantities for comparison. 

scatter plot

• used to examine possible relationships between two numerical variables

• two variables are plotted in x-axis and y-axis

title, all axes, zero, disfigure

Guidelines for developing graphs/charts

• the graph or chart should include a _____

• the scales for ____ should be included

• the scales on the y-axis should start at ____

• the graph or chart should NOT _____ the data

labeled, unncessary, simplest

Guidelines for developing graphs/charts

• the x-axis and y-axis should be properly ______

• the graph or chart should NOT contain ______ decorations

• the ________ possible graph or chart should be used for any data set

measures of central tendency

• a single value that represents a data set

• its purpose is to locate the center of a data set

• commonly referred to as an average 

mean

• a set of data has only ONE ______

• applied for interval and ratio data

• all values in the data set are included

mean

• very useful in comparing two or more data sets

• affected by the extreme small or large values on a data set

• cannot be computed for the data in a frequency distribution with an open-ended class

outlier

an extremely low or extremely small value is called

arithmetic mean

• the only common measure in which all values plays on equal role meaning to determine its values you would need to consider all the values of any given data set

ungrouped data

•  raw data. It is just arranged (for example, from highest to lowest).

grouped data

• organized in a table form, usually with classes or intervals.

median

• The midpoint of the data array

• Note: Data Array is a data set arranged in order whether ascending or descending

• appropriate measure of central tendency for data that are ordinal or above, but is more valuable in an ordinal type of data

median

• unique, there is only one _______ for a set of data

• found by arranging the set of data from lowest or highest (vice versa) & getting the value of the middle observation

median

• not affected by the extreme small or large values

• it can be computed for an-open ended frequency distribution 

• can be applied for ordinal, interval and ratio data

mode

• found by locating the most frequently occurring value

• easiest average to compute

• there can be more than one mode or even no mode in any given data set

mode

• not affected by the extreme small or large values

• can be applied for nominal, ordinal, interval and ratio data

weighted mean

• useful when various classes or groups contribute differently to the total

• found by multiplying each value by its corresponding weight and dividing by the sum of the weights

normal distribution or gaussian distribution

• continuous probability distribution that describes data that clusters around the mean

• it applies to variables where values tend to gather around the average.

bell-shaped

• the graph in Normal Distribution or Gaussian Distribution is shaped as what?

• It has a highest point (peak) at the mean. 

gaussian function or bell curve

• normal distribution is also called as what???

1733 by abraham moivre

• the normal curve was first developed mathematically in ______ by __________

1924 by karl pearson

• the work of abraham moivre was later rediscovered in

1783 by pierre-simon laplace

• used the normal curve in ____ by ______ to describe errors in measurements

1809 by Carl Friedrich Gauss

• was applied in _____ by ______ to analyze astronomical data.

bell-shaped, equal and center, unimodal, symmetric

1. the distribution is shaped as _____

2. the mean, median and mode are ______ and are located at the ______ of the distribution

3. the normal distribution is _______

4. the normal distribution is ______ about the mean (the shape are same on both sides)

continuous, asymptotic, 1.00 or 100%

1. the normal distribution is ________ (infinitely to the left and right side)

2. normal curve is ________ (it never touches the x axis)

3. total area under the normal distribution curve is ____ or ______

68%, 95%, 99.7%

1. the area under the part of a normal curve that lies within 1 standard deviation of the mean ___%; within 2 standard deviation, about ___%; and with 3 standard deviation, about ____%

standard normal distribution

• A normal distribution can be converted into a standard normal distribution by obtaining the z value

• A z value is the signed distance between a selected value, designated X (sa formula), and the mean, u (basta ung sa formula), divided by the standard deviation.

• It is also called as z scores, the z statistics, the standard normal deviates, or the standard normal values. in terms of formula:

range

• The difference of the highest value and the lowest value in the data set. 

standard deviation

• It is a statistical term that provides a good indication of volatility. 

  • Volatility = measure of risk  

• It measures how widely values are dispersed from the average.   

• It is calculated as the square root of variance

variance

• It is a mathematical expectation of the average squared deviations from the mean