Making sense of numbers - a half-day workshop

Making sense of numbers

An introductory half-day workshop

Facilitated by: Ian J Seath

Apply some basic principles for displaying tables of data

Select appropriate types of chart to analyse and present data

Decide how big a sample to choose in order to be confident in the results

Explain why an “average” could be very misleading

MOST PEOPLE HATE MATHS!

“A Mathematician is a device for turning coffee into theorems.”Paul Erdos (Hungarian Mathematician)

An aeroplane flies round the four sides of a 100 mile square

It flies at 100 mph on side 1, 200 mph on side 2, 300 mph on side 3 and 400 mph on side 4.

What is its average speed? 100 m.p.h.

300 m.p.h.

200 m.p.h.400 m.p.h.100

milessquare

The Golden Rules of Measurement No measurement without recording

No recording without analysis

No analysis without action

PRESENTING TABULAR DATA

“As you can clearly see…”

Badly presented data makes it hard to understand & improve performance Very few people need absolutely accurate numbers (Actuaries,

Accountants, Scientists and Engineers are common exceptions) So, for most management information, rounded data will be easier to

handle

Which of these is easier to identify the biggest percentage increase in orders?

Orders for product ABC have increased from 4,725 to 6,321 p.a. whereas DEF orders have increased from 3,015 to 4,643 p.a.

ABC orders have increased from 4,700 to 6,300 whereas DEF orders have increased from 3,000 to 4,600 p.a.

Tip 1: Round to “2 effective digits” It’s much easier on the eye and to do a bit of

mental arithmetic on the second example and say that an increase of 1,600 ABC Orders is about a third (33%) and an increase of 1,600 DEF Orders is about half (50%)

Applied with common sense, rounding to two effective digits usually makes numbers easier to cope with and to get a quicker understanding of what’s going on

Which is easier to read?

Sales (£k) Profit (£k)

2014 25,000 2,4002013 22,000 2,0002012 18,000 1,6002011 14,000 1,0002010 10,000 650

2010 2011 2012 2013 2014

Sales (£k) 10,000 14,000 18,000 22,000 25,000

Profit (£k) 650 1,000 1,600 2,000 2,400

Tip 2: Columns of data are almost always easier to read than rows Put the latest data, or the biggest numbers, at

the top of the table You may not be able to do this with time-based

Columns of data allow the eye to scan up and down more easily

How would you improve this?

Sales (£k) Q1 Q2 Q3 Q4

Customer A 34.4 32.1 27.7 32.2

Customer B 148.6 139.6 144.3 166.5

Customer C 305.7 284.4 245.3 377.8

Customer D 25.8 29.2 24.9 27.8

Customer E 256.7 242.1 212.9 243.0

Customer F 68.5 73.3 67.9 84.6

Better?

Sales (£k) Q1 Q2 Q3 Q4 Average

Customer C 310 280 250 380 310

Customer E 260 240 210 240 240

Customer B 150 140 140 170 150

Customer F 69 73 68 85 74

Customer A 34 32 28 32 32

Customer D 26 29 25 28 27

Average 142 132 120 156 140

What can you conclude from this?

# of Orders Q1 Q2 Q3 Q4

Customer A 370 350 320 350

Customer B 160 150 150 180

Customer C 47 51 46 63

Customer D 42 40 36 40

What else would you want to know?

Better?

# of Orders Q1 Q2 Q3 Q4 Average

Customer A 370 350 320 350 348

Customer B 160 150 150 180 160

Customer C 47 51 46 63 52

Customer D 42 40 36 40 40

Average 155 148 138 158 150

Tip 3: When to use Tables for data Use tables when you have small data sets or

if you need people to see the exact numerical values in your results

Round the data to two effective digits unless readers need the precise numbers

6 basic rules from Prof. ASC Ehrenberg Andrew Ehrenberg was a statistician and marketing scientist

For over half a century, he made contributions to the methodology of data collection, analysis and presentation

Ref: Rudiments of Numeracy http://www.maths.leeds.ac.uk/~sta6ajb/math1910/p4.pdf

1. Rounding to 2 effective digits2. Row and column averages3. Figures are easier to compare in columns4. Order rows and columns by size5. Spacing and layout6. Graphs vs. Tables

HOW MUCH DATA DO YOU NEED?

“Anecdotes are not statistics.”

Sampling In many cases, we obtain data through

sampling; often because it is simply not possible to measure every single item, or to log every activity, transaction or incident

The purpose of sampling is to collect an unbiased subset which will give you a manageable amount of data

When you take samples, they should be representative (statistically valid and reliable) and economic to collect (quick and cost-effective)

Population vs. Sample

Customer Satisfaction Unhappy Happy

If we surveyed every single customer over a year to find out how happy they were with our services, this is what we might find.

One person’s sample of 10 customers

How happy are customers according

to this sample?

Another person’s sample of 10 customers

How happy are customers according

to this sample?

The “right answer” depends on sample size

Your ability to be confident about Customer satisfaction depends on sample size.If you pick too small a sample you could, purely by chance, find very different results and draw the wrong conclusions.

http://www.surveysystem.com/sscalc.htm

Terms you need to understand Confidence Interval (Margin of Error)

The plus-or-minus figure usually reported in newspaper or television opinion poll results

If you pick a CI of 5 and 83% of your sample picks ‘Happy’, you can be “sure” that the 78-88% of the entire population would have picked ‘Happy’

Confidence Level Tells you how “sure” you can be that the population

would pick an answer within the Confidence Interval A 95% CL is most commonly used and means, for the

example above, you can be 95% sure that the true population is between 78 and 88%

Example

+ or - 3

6000 orders p.a.

= 75 customers per month

You might, therefore, say if 83% ofCustomers are ‘Happy’:“We are 95% confident that between 80 and 86% of customers are Happy”

You can also work out the CI for a known

sample size

Tip 4: Sampling guidelines

With static populations (e.g. customers, staff), use random sampling; for example using Random Number Tables to decide what (and when) to sample Random sampling means that every unit in a population will have

an equal probability of being chosen in the sample

With time-based data, collect data in sub-groups of 5 values, equally spaced in time (e.g. services are delivered, or transactions are carried out continuously over a period of time – call handling in a contact centre) If it is not feasible to take sub-groups, take individual values at

regular intervals; e.g. every 10th or 100th

To make meaningful comparisons… We must all be measuring the same thing

Definition of the Performance Indicator e.g. an average customer satisfaction score of 8.5

(out of 10) is not the same as 85% of customers are “satisfied”

We must be collecting statistically valid samples

THE “MISLEADING” AVERAGE

“Lies, damned lies and statistics.”

On average our rope is 2

cm thick !

That’s good to know !

Supplier

Customer

Do you know what “average” means? The length of time (in days) taken for 10

customer orders to be despatched was recorded

What was the average time it took (from order placed to despatch)?

Order 1

Order 2

Order 3

Order 4

Order 5

Order 6

Order 7

Order 8

Order 9

Order 10

6 6.5 7 7 7 7.5 8 8 10 13

Mean, Median and Mode

Arithmetic Mean - the sum of values divided by the number of values, often called “the average” (8.0 in our example)

Median - the middle value when all the values are arranged in order[or the mean of the two middle values if there is an even number in the list] (7.25 in our example)

Mode - the most frequently occurring value (7 in our example)

If the Mean = the Median, the data is distributed symmetrically

The Median and Mode are not affected by extreme values in a set of data, unlike the Mean

Which “average” would you use & why?

16 data points23 data points

Here are two “response time” histograms

You also need to understand Variation

Bell-shaped Skewed

PlateauBi-modal

What a Histogram might tell you Bell-shaped - a symmetrically shaped distribution which typically

represents data randomly distributed, but clustered around a central value

Positive or negative skews - where the average value of the whole set of data is to the left (-) or right (+) of the central value. Look out for specification limits at the boundaries of the distribution which might be causing data to be dropped from the population. More extreme shapes are also known as “precipices”

Bimodal - where there are two peaks. Usually indicates two sets of data (e.g. two teams or locations), with different Means have been mixed

Plateau - occurs where several sets of data have been mixed (e.g. from a number of customers/locations/groups)

GRAPHS AND CHARTS“A picture paints a thousand words.”

Graphs and Charts

Tip 5: When to use Graphs for data Use graphs when you have more than ten

data points, or if you want to show people “the big picture”, not detailed data

Use graphs when you need to show trends, over time

Don’t clutter a graph with too many different sets of data; it’s usually better to split the data into separate graphs

Pie Charts The data points in a Pie

Chart are displayed as a percentage of the whole pie

Good for: showing proportions, at a glance

No good for: showing trends or comparisons over time

Bar Charts In Bar Charts, categories are

typically organised along the horizontal axis and values up the vertical axis

Bar Charts illustrate comparisons among individual items, but do not show proportions as in a Pie Chart

Good for: showing quantities of responses in different categories; often best when sorted into biggest to smallest

Not good for: showing data over time (use a Line Graph instead)

Histograms In Histograms, a variable (e.g.

Time, Length, Height) is displayed along the horizontal axis and frequency up the vertical axis

Good for: showing the variation in a set of data and to help decide if the Mean or Median are the best choice of average to quote

Not good for: showing variations over time

N.B. Excel also calls these “Bar Charts”

PARETO ANALYSIS“Separate the vital few from the trivial many.”

Pareto Analysis

80% of problems or errors are often due to only 20% of the causes (The “Vital Few”)

The remaining 80% of causes account for only 20% of the problems or errors (The “Trivial Many”)

CausesProblemOccurrences

Also known as the 80:20 rule

80% The “Vital Few”

Causes

The “Trivial Many”Causes

Most ofthe

problems

Pareto Diagram A Pareto Diagram is a particular

type of Bar Chart Category data is presented in

decreasing size, from left to right and a Cumulative % line is also drawn

Good for: showing the 80:20 Rule – highlighting the few categories that account for the majority of performance or issues

Not good for: showing data over time (use a Line Graph instead)

Example: Reasons for delayed orders

Causes Frequency Cumulative Frequency

% Cumulative %

A. Unclear supporting information

47 47 54 54

B. Staff absenteeism 18 65 21 75

C. Non-approved signatory (> £500)

6 71 7 82

D. Customer not informed of date

6 77 7 89

E. Computer problems 5 82 6 95

F. Quotations policy 3 85 3 98

G. Other 2 87 2 100

Example: Reasons for delayed orders

IS PERFORMANCE IMPROVING?

“Two data points do not indicate a trend.”

Line Graphs In a Line Graph, time data is

distributed evenly along the horizontal axis, and all value data is distributed up the vertical axis

Good for: showing how results have changed over time (trends)

Not good for: comparing lots of different sets of results (too many lines make it hard to see what's going on)

N.B. Excel enables you to overlay a statistically derived trend line

What can you conclude from this Line Graph?Are weekly Orders increasing, decreasing, or not changing?

4 Week Moving Average

Weekly orders are decreasing (from around week 10)

4 Week Moving Average

Control Charts Statistical Process

Control Charts are a particular type of Line Graph

They enable you to determine whether variations are due to “Special” or “Common” causes

The Control Limits are based on process variation (s), not specification tolerances

WORKSHOP REVIEW“Learning points for action at work?”

ian.seath@improvement-skills.co.uk

07850 728506

@ianjseath

uk.linkedin.com/in/ianjseath

Prepared byIan J SeathImprovement Skills Consulting Ltd.

Making sense of numbers - a half-day workshop

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