LBSRE1021 Data Interpretation Lecture 3

1
LBSRE1021 Data InterpretationLecture 3

• Location and Dispersion

2
OBJECTIVES

• State some basic definitions
• Prepare a frequency distribution using given
  data.
• Plot a frequency distribution as a bar chart.
• Explain the terms Location and Dispersion

3
OBJECTIVES
4
Definition

• Statistics
• The organisation of data to enable meaningful
  analysis.

5
Definitions

• Population Every member of the group in which
  you are interested e.g. the consumers of a
  certain product, the employees of a company
• Sample A sub-set of the population on which
  measurements may be made that approximate to
  those of the population

6
More definitions

• Variable Something which can be measured or
  counted.
•  eg. age, weight, salary, no. children
• Frequency The number of times a particular value
  of a variable occurs.

7
Frequency Distribution
8
Grouped Frequency Distribution
9
Bar Chart
10
Measures of Location
11
Measures of Location Mean
12
Measures of Location Median
13
Measures of Location Mode
14
Dispersion
15
Dispersion Quartiles
16
Dispersion Quartiles

• QUARTILES
• The quartiles are four values in a data set.
• First Quartile (Q1) is a value such that 25 of
  items in the data set have this value or less.
• Second Quartile (median) is a value such that 50
  of items in the data set have this value or less.
• Third Quartile (Q3) is a value such that 75 of
  items in the data set have this value or less.
• Fourth Quartile is a value such that 100 of
  items in the data set have this value or less.

17
Quartiles Example

• Switchboard data refers to the number of
  telephone calls to a switchboard each hour for
  two days
• Day 1 26 25 30 31 27 27 26 29
• Day 2 30 32 27 28 26 27 28 29
• To find the first quartile and the third quartile
  arrange the 16 data items in ascending order as
  follows
• 25 26 26 26 27 27 27 27 28 28 29 29 30 30 31 32

18
QuartilesExample

• The first quartile will be the value of the (n
  1) 1/4 item.
• The third quartile will be the value of the (n
  1) 3/4 item.
• In this case Q1 will be the value of the 4.25th
  item. By interpolation, the first quartile will
  be 26.25
• between 26 and 27.
• Q3 will be the value of the 12.75th item. So the
  third quartile will be 29.75
• between 29 and 30.
• (Q2 is the value of the (n 1)/2 item, i.e. the
  Median)

19
Deviation
20
Dispersion Variance

• Deviations from the mean (x - x) are
• - ve and -ve
• - sum to zero
• (x - x )2 is always ve
• Average of square of deviations is the
• Variance å ( x - x )2
• n

21
Standard Deviation
22
S.D. Example
23
Central Tendency

• The mean and Standard Deviation describe the
  area of central tendency and spread of data

Mean
(Mode and Median same if symmetrical)
Spread
24
Coefficient of Variance