The word “statistics” means different things to different people. Unfortunately, too many people associate statistics with numbers/math and they break out in hives. For most people, I think that the first thing that pops into the mind when hearing or seeing the word statistics is either “Mean, Median & Mode” or graphs of data, like bar graphs, pie charts, line graphs, etc.
The topics mentioned above are covered to varying degrees in almost all high school math courses. Even elementary schools are understanding the importance of a good foundation in statistics, and it is common to see small children collecting “things” to eventually be represented on a chart or some other visual display cours particuliers maths.
There is, of course, a great deal more to understand about statistics and there are some MUST UNDERSTAND concepts that literally everyone needs to know. But the first thing for adults to be able to do is read, understand, and analyze the information in charts and graphs. A simple everyday-life kind of example comes in my mail every month from Colorado Springs Utilities. Just a few years ago, the city utilities department added to the very boring lists of numbers of meter readings for gas, electricity, and water usage some very useful year-long line graphs of each service. These graphs are fascinating–if you know how to read them.
These graphs SHOULD, if every year were perfect and identical, look like lovely sine/cosine curves–cycling gradually up and curving and down and curving to head back up through one complete cycle for that year. My current bill just came and I always, after reading the amount and gasping, turn to the graphs. I first look to see if the graphs start and end at the same height. In theory, the amount of gas used last March should be similar to the amount of gas used this March. This year, the numbers are very different. We have had a very warm March this year and we never got that yearly Spring Break winter storm. On the graph for gas, instead of a nice gentle curve around March, there is a sharp drop in the line since the high temperatures made furnaces unnecessary.
These graphs can remind you of your vacation, because all three graphs have a drop off at the same week because the thermostat on the furnace (air conditioner) was re-set and no one was at home to use much electricity, or water. If my sprinkler system had rain sensing shut-offs, I would probably be able to tell which weeks had more rain. If water usage is steadily increasing for no apparent reason, there is likely a leak or a toilet/faucet that needs to be replaced. Graphs can have a great deal to say if you know how to interpret the information.
I find it interesting to compare the water graph to the gas graph. They are basically the same shape–except “opposite.” (This is not the correct mathematical term, but I didn’t think you wanted to hear that their periods, which are the same, are shifted 182.5 days from each other.) What I mean by opposite is that when one graph goes high (usage is up) the other graph goes down because usage is low. This indication that there is a CORRELATION between these two. In fact, there is a strong, negative, correlation between gas and water usage.
CORRELATION is one of those MUST UNDERSTAND concepts in statistics, and I will be writing several different articles just on correlation because it is THAT important!
In general, though, the word “correlation” says these seem to be related to each other in some way–they change together (at the same time). The word “strong” indicates that the pattern of change is very consistent in both amount of change and when the change occurs. The word “negative” means that when one amount increases, the other decreases. In a positive correlation, both would be high or low at the same time.
Now, is everyone listening? The #1, key, most important concept to be sure you understand about statistics is that correlation means NOTHING! Yes, you heard me correctly. Correlation means nothing! A strong correlation may be interesting, and it IS possible that one causes the other, but it is just as likely that a 3rd variable causes the other two.
Let’s check our water/gas example. Does watering my lawn (water usage goes up) cause my gas usage to go down? Of course not! Does turning up my thermostat (gas usage goes up) cause the water usage to decrease? Again, no–but there IS a connection! There is a 3rd variable that is affecting both water and gas usage–outside temperature. As the temperature climbs from 60 to 70 to 80 to 90 degrees, the furnace shuts off (gas use down), but the sprinklers become necessary (water use up), and as the temperatures fall, the sprinklers get shut down and drained while the furnace becomes necessary. Thus, gas and water use are related to each other, but a change in one does NOT cause a change in the other.