Advanced Mathematics for Business
Topic 1:
Introductory Management Statistics
© NCC Education Limited
Title of Topic Topic 1 - 1.2
Role of Mathematics in Business
Senior managers will use mathematics to assist
when making business decisions, for example:
• How many goods to produce
• What prices to charge
• How many employees are required
• Whether to invest in new capital assets
• Whether to develop a new range of products
• Whether to fund a new marketing campaign
Title of Topic Topic 1 - 1.3
Scope and Coverage
This topic will cover:
• Data types
• A revision of summary statistics
• Index numbers
Title of Topic Topic 1 - 1.4
Learning Objectives
By the end of this topic students will be able to:
• recognise nominal, ordinal, interval and ratio
data types
• recognise and use mode, median, mean, range,
standard deviation and coefficient of variation
• calculate Laspeyres and Paasche index
numbers
• use index numbers to calculate percentage
changes and to deflate series
Title of Topic Topic 1 - 1.5
Data Types (Level of
Measurement)
• Nominal
Low
• Ordinal
Information Content
• Interval
• Ratio
High
Title of Topic Topic 1 - 1.6
Nominal Data 名目数据 (Named)
• Data which can only be categorised.
• The data can be counted but not ordered, measured or
expressed as a ratio.
• Examples include:
• Gender (male or female)
• Job role (administration, production, accounting, sales)
• Product type (fruit cake, chocolate cake, cream cake)
• Summary statistics:
• Mode 众数
Title of Topic Topic 1 - 1.7
Count
• Parts in stock
3
10
9
6
8
7
2
11
6
7
5
12
7
5
8
5
7
8
6
5
9
4
6
10
1
8
3
6
11
6
2
10
7
9
7
4
8
8
4
4
9
5
7
9
3
Part number
7
• Return
6
8
5
9
4
3
10
2
11
1
12
Total
for
Frequency
7
next point
6
6
5
5
4
3
3
2
2
1
1
45
• Mode
- The number or category that occurs the most
Title of Topic Topic 1 - 1.8
Ordinal 序数 (Ordered)
• Data which can be ranked and counted but can
not be measured or expressed as a ratio.
• Examples include:
• Employee grades (A, B, C …)
• Voting preferences (best candidate, second best
…)
• Product preferences
• Summary statistics:
• Mode, median 中位数
Title of Topic Topic 1 - 1.9
Order
• Score on rating scale
3
10
9
6
8
7
2
11
6
7
5
12
7
5
8
5
7
8
• Median
6
5
9
4
6
10
1
8
3
6
11
6
2
10
7
9
7
4
8
8
4
4
9
5
7
9
3
Score
1
2
3
4
5
6
7
8
9
10
11
12
Frequency
1
2
3
4
5
6
7
6
5
3
2
1
Cumulative
frequency
1
3
6
10
15
21
28
34
39
42
44
45
- Value of middle item of ordered data, (N +1)/2 term
Title of Topic Topic 1 - 1.10
Interval Data 等距数据
• Data which can be placed along a scale, ranked,
measured and counted but cannot be expressed
as a ratio.
• Examples:
– Centigrade temperature scale (10C, 15C, 20C)
– IQ score (100, 115, 130)
• Summary statistics:
– Mode, median, mean
– Range, standard deviation
Title of Topic Topic 1 - 1.11
Measure
• Temperature C
3
10
9
6
8
7
2
11
6
7
5
12
7
5
8
5
7
8
6
5
9
4
6
10
1
8
3
6
11
6
2
10
7
9
7
4
8
8
4
4
9
5
7
9
3
Temperature (x)
1
2
3
4
5
6
7
8
9
10
11
12
Total
• Mean
- total value of all data / number of data
Frequency (f)
1
2
3
4
5
6
7
6
5
3
2
1
45
fx
1
4
9
16
25
36
49
48
45
30
22
12
297
 = mean = 297/45 = 6.6C
Title of Topic Topic 1 - 1.12
Standard Deviation
Title of Topic Topic 1 - 1.13
Measure
Temperature Frequency
(x)
(f)
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
6
9
5
10
3
11
2
12
1
Total
45
fx
1
4
9
16
25
36
49
48
45
30
22
12
297
x-
-5.6
-4.6
-3.6
-2.6
-1.6
-0.6
0.4
1.4
2.4
3.4
4.4
5.4
(x - )2
31.36
21.16
12.96
6.76
2.56
0.36
0.16
1.96
5.76
11.56
19.36
29.16
f(x - ) 2
31.36
42.32
38.88
27.04
12.80
2.16
1.12
11.76
28.80
34.68
38.72
29.16
298.8
Title of Topic Topic 1 - 1.14
Standard deviation
Ratio 比率数据 (Scale with Natural
Zero)
Title of Topic Topic 1 - 1.15
• Data which can be placed along a scale, ranked,
measured, counted and expressed as a ratio.
• Examples
– Kelvin temperature scale
– Time spent in queue (10, 20, 30 minutes)
– Differences on interval scales
• Summary statistics
– Mode, median, mean
– Range, standard deviation, coefficient of variation
变动系数, skewness
Title of Topic Topic 1 - 1.16
Ratio
Queuing time Frequency
(x)
(f)
1
1
2
2
etc.
etc.
11
2
12
1
total
45
fx
1
4
etc.
22
12
297
x-
-5.6
-4.6
etc.
4.4
5.4
(x - )2
31.36
21.16
etc.
19.36
29.16
f(x - ) 2
31.36
42.32
etc.
38.72
29.16
298.8
Data types (Discrete 离散 &
Continuous 连续)
Title of Topic Topic 1 - 1.17
• Discrete data
– Can take a countable number of values
• Number of products built (1,237,502)
• Number of questions correct in test (4)
• Continuous
– Can take an uncountable number of values
• Length of fabric cut (45.9847248738…metres)
• Time in queue (23 minutes
5.2084792…seconds)
Title of Topic Topic 1 - 1.18
Recap and Review
Summary.
四个数据类型（Nominal, Ordinal,
Interval and Ratio ）、五个关键公式
（平均、众数、中位数、标准差、变动
系数）、两种数据（离散和连续）
Any questions?
Title of Topic Topic 1 - 1.19
Index numbers 指数数据
Title of Topic Topic 1 - 1.20
Simple Price Index - 1
Consider chocolate bar, set 2014 as base year
Title of Topic Topic 1 - 1.21
Simple Price Index - 2
• Compare the prices of snack products over time
Title of Topic Topic 1 - 1.22
Year
Chocolate Bar
Price
Index
Sandwich
Price
Index
Bag of Crisps
Price
Index
Jan 2014
0.47
100.00
1.85
100.00
0.60
100.00
Jan 2015
0.52
110.64
1.92
103.78
0.61
101.67
Jan 2016
0.56
119.15
2.00
108.11
0.63
105.00
Title of Topic Topic 1 - 1.23
Percentage Change Between
Index Numbers
year
chocolate bar
index
annual %
sandwich
price
index
bag of crisps
price
index
Jan 2014
100.00
-
100.00
-
100.00
-
Jan 2015
110.64
10.64
103.78
3.78
101.67
1.67
Jan 2016
119.15
7.69
108.11
?
105.00
?
Title of Topic Topic 1 - 1.24
Rebasing Price Relatives
• Reasons for changing base period;
- Mature series => large indices, relevance of base
period
- Compare different indices which have used
different base years
Title of Topic Topic 1 - 1.25
Rebasing Price Relatives
Title of Topic Topic 1 - 1.26
Simple Aggregate Indices
Title of Topic Topic 1 - 1.27
Laspeyres (Base Weighted) Price
Index
Title of Topic Topic 1 - 1.28
Example
Title of Topic Topic 1 - 1.29
Paasche (Current Weighted) Price
Index
Title of Topic Topic 1 - 1.30
Example
Title of Topic Topic 1 - 1.31
Weighted Index Numbers
Weighted Index Numbers 加权指
数
Title of Topic Topic 1 - 1.32
Eggs
Flour
Fat
Sugar
Lemons
Gas
w
18
16
5
14
2
45
100
R
151.00
225.70
94.60
405.00
256.40
319.40
2718.00
3611.20
473.00
5670.00
512.80
14373.00
27358.00
Title of Topic Topic 1 - 1.33
Deflating Data - 1
Title of Topic Topic 1 - 1.34
Deflating Data - 2
Title of Topic Topic 1 - 1.35
Summary
At the end of this presentation, you should be able to:
• Recognise nominal, ordinal, interval and ratio data
types
• Recognise and use mode, median, mean, range,
standard deviation and coefficient of variation
• Calculate Laspeyres and Paasche index numbers
• Use index numbers to calculate percentage
changes and to deflate series
Title of Topic Topic 1 - 1.36
References
• ONS
www.statistics.gov.uk/statbase/product.asp?vlnk=8
68, accessed 20 December 2015
Topic 1 – Introductory Management
Statistics
Any Questions?