DATA:
DATA ANALYSIS, PROBABILITY AND STATISTICS, AND GRAPHING
In the workplace the common thing would be -- we measure everything. If someone
is measuring something and they are taking samples and they see that is it going
out of the acceptable margin. I mean, they need to be able to stop everything and
get someone to find out what is happening. Upper and lower limits, check that against a
blueprint and see that the upper and lower limits have been put in properly, then
compare that with how it was running earlier that day. Someone has got to understand;
it could be a supervisory level. Someone's got to be putting in the data properly. It
is computerized, of course, but it is only as good as the information that someone
is putting in. We try to tell people, numbers have got to make sense. They have
got to make sense. You have to be able to see if for twenty-five days it has been operating
like this and suddenly it looks like this. What does your gut tell you? There is
something wrong here. Something is going out, that kind of thing. Look at the chart.
People should have enough understanding and knowledge to read all the results of all
our quality measure that we post on a regular basis. And if they see something that
they don't understand, they need to question that. Say, 'what is that?' How does
that impact that? Where does that come from? Everyone of those things impacts something
else. In a workplace setting, there is this domino effect. Everything builds on
the next thing. From the time that raw material comes in the door and one process
after another through departments takes place. You are adding value, but you are also
adding costs. We need to catch those numbers if they start to go out of alignment.
Again going back to -- people need to see the big picture first. The numbers stand
out, how things operate. So they see the big math picture. You get to the big math picture
through all these tiny calculations.
Overview
Adults make decisions based on data in their daily lives and in the workplace. According
to Equipped for the Future, "Adults are also interested in learning and strengthening
the skills associated with using information to have an impact on the world. They identify the need to develop the problem solving and critical thinking skills that
have to do with analyzing and reflecting on information in order to make good decisions.
. ." (p. 24) Reading charts and graphs, interpreting the data, and making decisions based on the information are key skills to being a successful worker and an informed
citizen. Being an informed citizen includes understanding statistics and probability
as well. Adults
41
cannot make reasonable decisions unless they understand from where the statistics come.
Charts and graphs are essential in the workplace. According to SCANS documentation,
tomorrow's workers must have reading skills that enable employees "to read well enough
to understand and interpret diagrams, directories, correspondence, manuals, records, charts, graphs, tables, and specifications. Without the ability to read a diverse
set of materials, workers cannot locate the descriptive and quantitative information
needed to make decisions or to recommend courses of action." (p. xvi)
Data from charts and graphs are used to make decisions. Graphs are useful tools in
that they organize data so that information becomes clearer. This organized information
can then be used to draw conclusions, to make decisions, or to influence others.
Data is organized in a variety of fashions, from charts and graphs, to computer-generated
spreadsheets.
In comparing the comments made by stakeholders --often individuals in managerial positions
-- with those made by adult learners, several interesting distinctions were noted.
Stakeholders tended to use the data in charts and graphs to make inferences and
decisions. Adult learners, on the other hand, were more inclined to use charts and
graphs in a more literal way - simply to gather information. Adult learners who created
charts and graphs used them to help themselves while stakeholders (management) used
charts and graphs to influence others. In addition, adult learners claimed either to
not have a use for charts and graphs or felt they used them when they needed information.
Stakeholders shared a concern for the lack of "chart literacy".
Key Findings
Data collection, analysis, and graphing are essential in the workplace. SCANS proposes
five competencies needed by employees for success in the workplace. The competency
Information clearly suggests that data analysis and graphing are necessary skills
for tomorrow's employees. An example of the level of proficiency for the competency
Information includes the ability to ". . . analyze statistical control charts to
monitor error rate. Develop, with other team members, a way to bring performance
in production line up to that of best practice in competing plants." (p. xx)
Many industries, manufacturing in particular, now use statistical control processes
(SPC) to monitor their processes in order to ensure quality products. Often the
front-line employee is required to collect the data used for charting the manufacturing
process; therefore, employees at all levels should be knowledgeable about and comfortable
with using a variety of charts. As more and more quality teams -- consisting of
a variety of employees -- are charged with the task of ensuring quality products,
employees will need to have an understanding of probability and sampling. During a focus
42
group session, when asked how math is used in the workplace, an adult learner responded,
"Sometimes I have SPC graphs. It kind of determines if something is wrong with the machine and pretty simple things, nothing really major. One out of 6 is bad, shut
the machine down. A lot of times we don't count the parts. They'll just be in a
can and we write down on an overlay. You know, if you red tag some parts that are
no good, you tag -- nothing really major."
It is interesting to note that only stakeholders seem to be acutely aware of the need
to have the ability to read and interpret statistical process control charts. "There
are two other areas and we mentioned this before about statistical process control.
Our industry is moving into really using numbers to determine whether the production
process is functioning or not. And they are using the concept of time as well as
numbers. How fast it takes to do a particular process. Budgetary hourly rates is
another phrase that is kicked around. . . " Yet another stakeholder commented, "In the
workplace today, employers want everyone to understand quality. Any chart or graph
that shows production uses statistics."
Other forms of charting are also used in the workplace to make decisions as well as
gauge accuracy. One learner shared how he uses blueprints to determine whether a
part is within tolerance: "Basically at work every day, you know, just looking at
parts, I use a blueprint. That gives you a tolerance, a couple thousandths here, couple
thousandths there, sometimes 5, -2, and if you've got a part that's right on the
borderline of tolerance you want to decide if you want to just keep on running it
or fix it or basically see what kind of problem it is going to cause." And another adult learner
has an idea of what will be required of her in the workplace: For myself, I m hoping
to get into social work. So I need to be able to read and understand graphs (for
statistics). That way, I ll be able to compare past trends with current trends and
hopefully predict results. Also making my own graphs. At least I think that s what
statistics will be like.
Statistical knowledge is important in problem-solving and decision-making. Adults,
often without even realizing it, make decisions based on statistical information.
It may be via the television, radio, or it may be through print materials. The
following adult learner made her decision based on what she had seen in a magazine. "That
reminds me of a fee that I thought was too high. There was a newsletter I wanted
to subscribe to, but it charged $35 a year, and I couldn't understand why a little
paper would cost so much. But then on the inside it showed a circle graph, with sections like
a pie, and it showed what the money was spent for. Then I could see that it really
was a reasonable amount to pay." It is important that adults know that they are
using statistical information in their reasoning. A stakeholder weighed statistical information
to decide whether it was relevant to him: "I was reading an article about what to
look for if a kid is using drugs. And I thought about my 14-year old grandson and how different it is now that he is a teenager. I had to take my random knowledge
of a person and decide whether it was statistically relevant to drug use." Another
stakeholder agreed that sta
43
tistical information does influence decision-making.
"You're seeing different information that you need to reason and draw conclusions based on
this. Is this a good sale, not a good sale, and so forth depends on the whole reasoning
process -- looking at graphs and charts -- looking at your paycheck and whatever
-- just being presented with information and attempting to draw conclusions."
Statistical information is used to communicate information and sometimes influence
others. Understanding the flood of statistical information allows adults to make
more informed decisions. A teacher said it very well, "[When] we understand math,
we can use it to take control of our lives. Do our own figures so as not to be the victim
of scams." A stakeholder explained how she thought a nice graph could be an influencing
agent: ". . . Not only did he do nice histograms and circle graphs but inside he
did it by ethnic, by cities that the students are from, and so forth, and then he has
a final chart on the money that he's asking on the back. I think it is a nice piece
of work. On the back is a financial chart which could hopefully affect the budget."
Graphs, tables, and statistics make data easier to understand. Adults create graphs
for clarity and understanding, for themselves as well as for others. Sometimes seeing
the data in chart form makes the decision making process easier since the information is clearer. The following adult learner provides an example of how charts helped
them see the issues more clearly. "When I bought my car, I put a $1000 down payment
on it. I owed them like $8000 on it for five years which I was gonna end up paying
a lot of interest . . . so I made a plan to pay as soon as possible so I save the interest.
So I figured out how much I could spare each month. I did a budget so I would send
them like 2 payments, 3 payments a month. I did a graph to see how far it would
go. So like in a year and two months I called the company and I asked them how much
money I save from all the interest from me paying early and I end up with almost
$2000 and I ask them if I can take this $2000 I saved and add it to what I pay and
they said I could."
Even when the charts and graphs are not initiated by adults, they do tend to make
the information easier to digest. From an adult learner, "I watch this thing on PBS.
It's like this physics show -- and it's actually enjoyable. They give images and
graphs; they give you things about different theories with physics. It is hard to understand,
but the way they put it on TV, it's very simplified. You can actually see it with
your eyes." There are those, however, who don't agree that charts make understanding information easier. A stakeholder commented, "Right now all the changes that
are going on. There's ATM. You can't go to a bank anymore necessarily and talk
to a person. Statements are getting more, well, they are supposed to be easier to
read . . . things are constantly changing on them, you know."
44
Charts and graphs are also used for record keeping such as spreadsheets and data bases.
According to the SCANS report (p. xviii), employees of the near future will need
to be able to use spreadsheet programs for tasks such as monitoring expenditures
There is a concern for the lack of understanding and ability to read and interpret
statistical information, including charts and graphs. There is also worry about the
use and misuse of statistical information. While adult learners did not have this
concern, stakeholders and instructors agree that adults do tend to have difficulty deciphering
what the numbers and charts mean. Stakeholders shared their concerns: "I think
transferability is really hard for adults. To know a concept is one thing, but to
be able to look at a table and say, 'I understand this table, or I can read this table,
or I can interpret what this means' is hard to do." "I tried something in the workforce
here about a month ago based on quality where we measure quality based on the number of errors per 1000 lines shipped. We benchmark ourselves against Toyota, Ford,
Chrysler, and all the other automotive people. I had a lot of blank stares going
back from the audience. They could not associate what I was trying to talk about
. . . statistics to the competition. They simply had a block saying, 'But we're different.'
Math is math and I was having a hard time with that comparison. They were not able
to connect. I kind of lost them on that one. So we are going to try again going
back to more graphs I guess is probably the best way to try to communicate this. You know,
'A picture is worth a thousand words.' I'll try that out next time."
Yet another stakeholder believed that understanding statistical data involved much
more than just looking at numbers in a literal sense. "I'd like to also suggest
that, underlying understanding of statistics and some key aspects of both measurement
and number sense lies the fuzzy yet critical domain of proportional reasoning. Consider,
for example, that people's ability to understand and communicate about (rather than
compute) what an average or percents, understand notions of sampling and representation, make sense of and make choices about probability and risk (e.g., likelihood of
accidents, errors out of XXX products), and anything that is decreasing/ increasing/changes
its magnitude, relies heavily (though of course not exclusively) on deep understanding of proportions, rates, ratios, relations, and relative comparisons, which are
all parts of the same conceptual system that mathematicians (and I'm not one of them)
call Rational number concepts. "
Adults use charts, graphs, and statistical information in their roles as workers,
parents, and citizens. As workers, adults used data to monitor the quality of the
products being made. They also make decisions based on the data. A stakeholder uses
blueprints and statistical process control charts: "People that I work with have to know
at least the basic math skills in order to perform the SPC and we do a lot of blueprint
reading -- a lot of math involved in reading a blueprint." A learner explained how
he uses a variety of skills to do his job. "My daily job was office manager. My responsibilities
were to do a daily cash reconciliation, post accounts receivable, accounts payable,
45
keep up with hourly employee time cards and keep track of everyone's vacation and sick time. I always made decisions using amounts, money, graphs, and basic
addition and subtraction skills. I used all these skills on a daily basis to reconcile
and solve any problems regarding my specific job requirements."
As citizens, adults need to understand the data that they are continually being bombarded
with -- through all forms of media. This stakeholder clarified the importance of
understanding data as it relates to elections. "I want to switch from workplace to
community and society and all that data that we get inundated with -- try to make,
you know, what's going on in the world -- what does it mean to win a primary and
say that is 14 electoral votes and, all of a sudden, you're supposed to be the front
runner and how do you gauge the real significance of that. Then the next week you're blown
out of the water supposedly because something else happens. I remember the election
last year when the polls and the data, they became the driving force themselves as
you watched one go up and one go down. How do people really assess that because it is
such a big part -- you're talking about one arena, but locally, we're having a school
tax referendum. People are being surrounded by numbers in which they've got to make
decisions. This was cut in half. Well, what does it mean that this was cut in half?
Half of what? Is it really that big of a difference . . or whatever. So I think
something in adult ed. I think we're tending to look at the work stuff a lot and
a lot of the sort of consumer needs, but I think some of the data in terms of broader societal
issues. We're tying to get people more engaged." And another stakeholder, when
asked what were the three most important math concepts that should be taught, included
statistics: " . . . As members of a community we use statistics to understand our
community better and to help create a better environment for ourselves."
Implications for Teaching and Learning
Introduce more work-related charts and graphs and other statistical information to
better prepare adult learners for the world of work. According to the Massachusetts
ABE Math Standards [pg. 50], to become successful employees, adult learners need
to have the opportunity to "systematically collect, organize and describe data; and construct,
read and interpret tables, charts and graphs". Adult learners need much more than
simple activities where they are asked to find literal bits of information in charts
and graphs. They need opportunities to collect their own data, then create their
own charts and graphs. In designing their own charts, adult learners begin to understand
how data can be represented. Employees at all levels are being required to read
and interpret charts and graphs, so adult learners need to be prepared. As one stakeholder
put it, ". . . Being able to be chart literate and being able to read those charts
and graphs that we produce and we put up in our plant everywhere; all our quality
charts -- the lowest level, entry-level employee should be able to read those."
46
Provide hands-on experience collecting, organizing, and interpreting data. It is
not enough that adult education classes give learners practice in simply reading
and finding literal information based on charts and graphs. Providing adult learners
with the actual experience of gathering data, deciding on how to represent the data, and
interpreting the results will give them a deeper understanding of statistical information.
According to The Massachusetts ABE Math Standards (p. 50), adult learners should
be able to "make inferences and convincing arguments that are based on data analysis;
and evaluate arguments that are based on data analysis." Adult learners need opportunities
to interpret charts and graphs and discuss their findings and implications with others. A stakeholder added, ". . .Need basic level of mathematics to survive,
for public discourse -- the use, abuse, and misuse of statistics today -- how and
why -- more observation -- reading charts and polls. Why they're done and how they're
used."
Connecting to the Four Purposes
Stakeholders interviewed for this project were concerned about many adults' inability
to read and interpret statistical information. This suggests that many adults, at
least when it comes to statistical information including charts and graphs, need
to become more literate for access and information. The National Adult Literacy Survey
includes the literacy tasks of reading and interpreting statistical information under
the heading of quantitative literacy. In fact, while most adult learners viewed
charts and graphs as a medium for accessing information, there were a few exceptions as illustrated
by this interaction between three adult learners and the focus group facilitator.
BB [facilitator]: "How about if you're reading the paper and you see a graph comparing the number of high school dropouts in 1965 and 1995. Can you read and understand
information presented that way?" M [first learner]: "You need to know the number
of students in '65 compared to the number of students in '95." C [second learner]:
I can't read graphs, no." BB: "Would it be important to you to be able to?" C:
"No." M: "Yes, it would be important. S [third learner]: "It is if you're doing
a test." BB: "Any other reason?" S: "No, not really." C: "Yes, actually it would
be important to know." S: "My brother-in-law uses his computer to graph his income, you
know?" M: "The light bill is a graph."
The creation of charts and graphs based on data collection is one method of giving
voice to the data. Literacy as voice requires that adults be able to communicate
to others; charts, graphs, statistics are each a means of communicating what the
data is suggesting.
As seen in earlier examples, adults use statistical information to guide their decision-making.
They often create charts and graphs to clarify the problem, then make decisions
based on the interpretation they give. The following adult learner provides an example of how adults use charts and graphs to take action and make decisions: "We
had to reduce our hours at work. We made a big chart on the chalkboard. We compared
four-hour shifts, eight-and ten-hour ..."
47
Return to ANPN Frameworks Table of Contents
Webmaster / Adult Numeracy Practitioners Network