INTRODUCTION TO STATISTICS

Prepared by:Joshua Erdy A. Tan

Professional Teacher

I. Basics of StatisticsII. Statistical Description of DataIII. Measures of Central Tendency

Outline of Discussion

Define the basics of statistics. Compute for the accurate statistical data. Reflect on learning statistics in everyday

lives.

Objectives

Basics of Statistics

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

Methods used to determine the variability and reliability of data.

Statistical Methods

Taxonomy of Statistical Methods

Statistical Description of Data

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

Any characteristic of an individual or entity. It can take different values for different individuals.

Variables

• 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

• 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

Tells us what values the variable takes and how often it takes these values.

Distribution

Unimodal - having a single peak Bimodal - having two distinct peaks Symmetric - left and right half are mirror

images.

Types of Distribution

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

 

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:

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

Measures of Central Tendency

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:

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: 

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.

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

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

Median Then solve using the formula:

e = (x+y)/2e = (55+56)/2e = 55.5

Answer: The median is 55.5.

Mode  The most frequent score in the data set. 

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

Range  The difference between the lowest and highest values.

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.

END