STATISTICS OF ONE VARIABLE. By: Mankiran , Jasmeet , Manahil , Jasvinder , and Josh MDM4UO Mr. Seto. 2.1 Data Analysis With Graphs. Statistics : the gathering, organization, analysis, and presentation of numerical information
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By: Mankiran, Jasmeet,
Manahil,Jasvinder, and Josh
Statistics: the gathering, organization, analysis, and presentation of numerical information
Application: the scientific research, commercial advertising, sports, economics, etc
Population: the entire group/set you wish to measure or draw conclusions from.
Range: difference between the highest and lowest values in a set of data
Raw Data: unprocessed information collected for study and research
Sample: A “subset” of the population; the only way to analyze the population by sampling
Variable: the quantity being measured
Intervals: set of all numbers between two given numbers
Intervals: a set of all numbers between two given numbers
Here are a class’ scores obtained on a data-management examination. Construct a frequency table
Find the range: 96-39= 57
Determine the number of intervals we want: 9
Interval size= range/# of intervals
Interval size= 57/9= 6.3= approximately 6
Construct a histogram, frequency polygon, and
Cumulative frequency polygon
Frequency Cumulative Polygon
Mean: Sum of the values of a variable divided by the number of values
Median: The middle value when they are ranked from highest to lowest
Mode: The most frequent value
Outlier: Datum that are distant from the majority of the data set
Weighted Mean: Measure of central tendency that reflects the relative importance of the data
Ex. The following info was gathered from a group of teenagers, and the number of hours they spent on cell phone in a week. Find the mean, and mode median, from the grouped interval.
Find the mean:Median:
Look at number of teens which is 2.5
Deviation is the difference between an individual value and the mean for the data
Standard Deviation is the tool to measure or quantified by a number
Variance is the mean of the squares of the deviations for a set of data
Example: A set of all marks for Will in calculus. Find the standard deviation and variance, using formula.
∑(x-u)2 = 524
Measures of Spread – Cont’d standard deviation and variance, using formula.
Z = x – μ
(x-Q3) >(1.5 x IQR) or
(Q1-x) > (1.5 x IQR)
Sampling Bias Example: if a school band was surveyed on whether the funds collected for the football equipment should be given to the school band for new instruments.
Non- response Bias Example: if every 10th person entering the malls main entrance was asked to volunteer to complete a questionnaire on shoes, and only 75% of these people are willing to respond.
Measurement Bias Example: If Sandalwood wanted to know if lanyards are efficient methods of uniform and they asked Ms. Gyutt to stand in the main atrium and take a tally of the number of students that who actually wore or had their lanyards visible.
Response Bias Example: A group of students witnessed a fellow student being bullied. The principal requests students to come forward to give insight as to what exactly happened. He fears that the other students may not want to reveal any information that they witnessed because of being labelled or targeted by other bullies.