Chapter 8 addisional content
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This document discusses key concepts in statistics including descriptive statistics, variables, data sets, and statistical notation. It summarizes raw call center wait time data into a frequency table and histogram. Descriptive statistics are used to organize and summarize large amounts of data in order to see patterns and trends. Variables can be either discrete, taking countable values, or continuous, taking any real number value. Statistical software packages help perform complex calculations and analysis involved in descriptive and inferential statistics.
![2013/05/10
1
STATISTICS
X-Kit Textbook
Chapter 8 & 9 (Learning more about Sample Data)
Precalculus Textbook
Appendix B: Concepts in Statistics
Par B.2 (Measures of Central Tendency & Dispersion)
ORGANISE& SUMMARISERAW DATA
Raw Data
Discrete Data
Ungrouped
Frequency
Table
Grouped (low
frequency)
Continuous
Data
Grouped
Frequency
Table
Call Centre Data: waiting times (in seconds)
for 35 randomly selected customers
C1 2 3 4 5 6 7 8 9 10 11 12
75 37 13 90 45 23 104 135 30 73 34 12
C13 14 15 16 17 18 19 20 21 22 23 24
38 40 22 47 26 57 65 33 9 85 87 16
C25 26 27 28 29 30 31 32 33 34 35
102 115 68 29 142 5 15 10 25 41 49
DISCRETE DATA
TERMINOLOGY EXPLANATION
Variableof Interest? Waiting times (in seconds).
Continuous orDiscrete
Data?
Continuous Data – workingwith
measures of time.
Raw Data? A list of different values. Data hasnot
been processed in anyway.
Numberof Observation? 35
Frequency? The numberof times a data value
appears.
FrequencyTable Grouped FrequencyTable
FREQUENCY TABLE
Class Intervals TallyMarks Frequency
0 ≤ 𝑥 ≤ 25 //// //// 10
25 < 𝑥 ≤ 50 //// //// / 11
50 < 𝑥 ≤ 75 //// / 6
75 < 𝑥 ≤ 100 /// 3
100 < 𝑥 ≤ 125 /// 3
125 < 𝑥 ≤ 150 // 2
HISTOGRAM: CONTINUOUS DATA
0
2
4
6
8
10
12
Intervals
[0;25]
(25;50]
(50;75]
(75;100]
(100;125]
(125;150]](https://image.slidesharecdn.com/chapter8addisionalcontent-130607064116-phpapp01/85/Chapter-8-addisional-content-1-320.jpg)
Chapter 8 addisional content
- 1. 2013/05/10 1 STATISTICS X-Kit Textbook Chapter 8 & 9 (Learning more about Sample Data) Precalculus Textbook Appendix B: Concepts in Statistics Par B.2 (Measures of Central Tendency & Dispersion) ORGANISE& SUMMARISERAW DATA Raw Data Discrete Data Ungrouped Frequency Table Grouped (low frequency) Continuous Data Grouped Frequency Table Call Centre Data: waiting times (in seconds) for 35 randomly selected customers C1 2 3 4 5 6 7 8 9 10 11 12 75 37 13 90 45 23 104 135 30 73 34 12 C13 14 15 16 17 18 19 20 21 22 23 24 38 40 22 47 26 57 65 33 9 85 87 16 C25 26 27 28 29 30 31 32 33 34 35 102 115 68 29 142 5 15 10 25 41 49 DISCRETE DATA TERMINOLOGY EXPLANATION Variableof Interest? Waiting times (in seconds). Continuous orDiscrete Data? Continuous Data – workingwith measures of time. Raw Data? A list of different values. Data hasnot been processed in anyway. Numberof Observation? 35 Frequency? The numberof times a data value appears. FrequencyTable Grouped FrequencyTable FREQUENCY TABLE Class Intervals TallyMarks Frequency 0 ≤ 𝑥 ≤ 25 //// //// 10 25 < 𝑥 ≤ 50 //// //// / 11 50 < 𝑥 ≤ 75 //// / 6 75 < 𝑥 ≤ 100 /// 3 100 < 𝑥 ≤ 125 /// 3 125 < 𝑥 ≤ 150 // 2 HISTOGRAM: CONTINUOUS DATA 0 2 4 6 8 10 12 Intervals [0;25] (25;50] (50;75] (75;100] (100;125] (125;150]
- 2. 2013/05/10 2 FREQUENCY TABLE Class Intervals Frequency Cumulative Frequency 0 ≤ 𝑥 ≤ 25 10 10 25 < 𝑥 ≤ 50 11 10 + 11 = 21 50 < 𝑥 ≤ 75 6 21 + 6 = 27 75 < 𝑥 ≤ 100 3 27 + 3 = 30 100 < 𝑥 ≤ 125 3 30 + 3 = 33 125 < 𝑥 ≤ 150 2 33 + 2 = 35 OGIVE: CUMULATIVE FREQUENCIES 0 5 10 15 20 25 30 35 40 0 25 50 75 100 125 150 Cumulative Frequency Cumulative Frequency STATISTICS IS … Collection of Data Analysis of Data Interpretation of Data Presentation of Data DESCRIPTIVE STATISTICS Use graphs, charts & tables Calculation of various statistical measures To organise and summarise information To reduce information to a manageable size and place into focus INFERENTIAL STATISTICS Population The complete collectionofindividuals,items,or data under consideration in a study Sample The portion ofthe population selected for analysis Inferential Statistics Consists oftechniques for reachingconclusions about a populationbaseduponinformation containedin a sample Example: Population–all registeredvoters Sample – a telephone surveyof600registered voters VARIABLE,OBSERVATION AND DATA SET • A variable is a characteristic of interest concerning the individual elements of a population or a sample. • Represent a variable by a letter such as x. • An observation is the value of a variable for one particular element from the sample or population. • A data set consists of the observations of a variable for the elements of a sample.
- 3. 2013/05/10 3 QUANTITATIVE VARIABLE: DISCRETE AND CONTINUOUS VARIABLE • A quantitative variable is determined when the description of the characteristic of interest results in a numerical value. • A discrete variable is a quantitative variable whose values are countable (results from counting). • A continuous variable is a quantitative variable that can assume any numerical value over an interval (results from making a measurement). EXAMPLE DISCRETE VARIABLE POSSIBLE VALUES FOR THE VARIABLE The number of individuals in groups of 30 with a type A personality 0, 1, 2, 3, ..., 30 EXAMPLE CONTINUOUS VARIABLE POSSIBLE VALUES FOR THE VARIABLE The cholesterol reading for those individuals having cholesterol readings ≥ 200mg/unit All real numbers between 200 and 𝑏 (largest cholesterol reading of all such individuals) QUALITATIVE VARIABLE: • A qualitative variable is determined when the description of the characteristic of interest results in a nonnumeric value. • Classified into two or more categories. • The categories for qualitative variables are often coded for purpose of performing computerised statistical analysis. EXAMPLE Qualitative variable Possible categories Gender Male, female SUMMATION NOTATION 𝒙 = 𝒕𝒉𝒆 𝒔𝒖𝒎𝒎𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝒙 •Sigma notation (Greek symbol). •Operation of sums - 𝒙. •Operation of sums of squares - 𝒙 𝟐 ; 𝒙 𝟐 . •Operations of sums of cross products - 𝒙𝒚.
- 4. 2013/05/10 4 EXAMPLE X 0.1 0.2 0.3 0.4 0.5 Y 2 4 6 8 10 Calculate: 1. 𝐱 𝟐 2. 𝐱𝐲 3. 𝐱 𝟐 4. 𝐱 𝐲 COMPUTER SOFTWARE AND STATISTICS •The techniques of descriptive and inferential statistics involve lengthy repetitive computations as well as the construction of various graphical constructs. •Statistical packages: SAS, SPSS, MINITAB, EXCEL, STATISTIX