intro stat
DESCRIPTION
Introductory Lesson in StatisticsTRANSCRIPT
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INTRODUCTION TO STATISTICS
Prepared by:Joshua Erdy A. Tan
Professional Teacher
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I. Basics of StatisticsII. Statistical Description of DataIII. Measures of Central Tendency
Outline of Discussion
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Define the basics of statistics. Compute for the accurate statistical data. Reflect on learning statistics in everyday
lives.
Objectives
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Basics of Statistics
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Science of collection, presentation, analysis, and reasonable interpretation of data.
Presents a rigorous scientific method for gaining insight into data.
Give an instant overall picture of data based on graphical presentation or numerical summarization irrespective to the number of data points.
Statistics
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Methods used to determine the variability and reliability of data.
Statistical Methods
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Taxonomy of Statistical Methods
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Statistical Description of Data
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Statistics describes a numeric set of data by its:
Center Variability Shape
Statistics describes a categorical set of data by:
Frequency, percentage or proportion of each category
Statistical Description of Data
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Any characteristic of an individual or entity. It can take different values for different individuals.
Variables
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• Nominal - Categorical variables with no inherent order or ranking sequence such as names or classes (e.g., gender). Value may be a numerical, but without numerical value (e.g., I, II, III). The only operation that can be applied to Nominal variables is enumeration.
• Ordinal - Variables with an inherent rank or order, e.g. mild, moderate, severe. Can be compared for equality, or greater or less, but not how much greater or less.
Types of Variables
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• Interval - Values of the variable are ordered as in Ordinal, and additionally, differences between values are meaningful, however, the scale is not absolutely anchored.
• Ratio - Variables with all properties of Interval plus an absolute, non-arbitrary zero point, e.g. age, weight, temperature (Kelvin).
Types of Variables
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Tells us what values the variable takes and how often it takes these values.
Distribution
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Unimodal - having a single peak Bimodal - having two distinct peaks Symmetric - left and right half are mirror
images.
Types of Distribution
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Consider a data set of 26 children of ages 1-6 years. Then the frequency distribution of variable ‘age’ can be tabulated as follows
Frequency Distribution
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Frequency DistributionFrequency Distribution of Age:Age 1 2 3 4 5 6Frequency 5 3 7 5 4 2
Age Group 1-2 3-4 5-6
Frequency 8 12 6
Grouped Frequency Distribution of Age:
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Cumulative FrequencyAge 1 2 3 4 5 6Frequency 5 3 7 5 4 2Cumulative
Frequency5 8 15 20 24 26
Age Group 1-2 3-4 5-6Frequency 8 12 6Cumulative Frequency 8 20 26
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Measures of Central Tendency
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Mean The most popular and well known measure
of central tendency. It is equal to the sum of all the values in the
data set ( ) divided by the number of values ( ) in the data set.
Formula:
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Mean
Staff 1 2 3 4 5 6 7 8 9 10
Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k
For example, consider the wages of staff at a factory below:
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Mean To get the mean (represented by x) , you need to add the salaries of staff members and divide it by the number of staff members.x = (15,000 + 18,000 + 16,000 + 14,000 + 15,000 + 15,000 + 12,000 + 17,000 + 90,000 + 95,000)/10x = 30,700
Answer: The mean salary for these ten staff is $30.7k.
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Median The middle score for a set of data that has
been arranged in order of magnitude.
Formula: e = (x + y)/2
Where:e = medianx = smallest middle marky = largest middle mark
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Median Suppose we have a data below:
To get the median, find the smallest and largest middle mark.
(x) Smallest middle mark: 55(y) Largest middle mark: 56
65 55 89 56 35 14 56 55 87 45 92
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Median Then solve using the formula:
e = (x+y)/2e = (55+56)/2e = 55.5
Answer: The median is 55.5.
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Mode The most frequent score in the data set.
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Mode Suppose we have a data below:
To get the mode (X), find the most occuring/frequent score in the data above.
X = 55Answer: The mode is 55 since it appears/occurs more than the other numbers.
69 55 89 56 35 14 56 55 83 55 91
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Range The difference between the lowest and highest values.
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Range In A(4, 6, 9, 3, 7) the lowest value is 3,
and the highest is 9. To get the Range of A:
R = highest value – lowest valueR = 9 – 3R = 6
Answer: The range of set A is 6.
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