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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]

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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.

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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.

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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