Numbers Lesson I: Introduction to Historical Statistics
Questions this lesson addresses: How can we use numbers to understand our past? You will read, use websites and a spreadsheet, answer questions, and submit your answers to the dropbox Numbers I.
For the first part of this lesson, please play a game.
Play through the game at least five times before you click “See how it works.”
Once you’ve seen how it works, play the game again.
Learning Outcomes: By the end of this lesson students will be able to-
- Identify the difference between the mean, median, and mode of a group of numbers.
- Open a spreadsheet file using Excel, Numbers, LibreOffice, or Excel Online.
- Adjust and read a wage graph.
- Identify why the number of years averaged in a graph matter.
- Identify the overall wheat price trend in England between 1264 and 1400.
- Read a spreadsheet by using tabs.
- Answer questions about the past by interpreting data.
Why do historical statistics matter?
Let’s tackle that one word at a time, backwards. Statistics matter because we use numbers to measure our lives, whether it’s the dollars in our bank account, the number of friends we have on facebook, or how full a glass is (half full?) Increasingly, statistics are used to convince us in the truth of an argument. Yet, without a basic understanding of statistics, people often fall back into the cynicism that all numbers lie. Numbers are just information, and just as we apply the PISA test to sources, so too can we apply certain standards for what is a credible statistic.
Why do statistics matter to history? Numbers show us trends, that is up or down, in parts of our lives that are important. How much food, per person, does one society provide over time? How is income distributed to a people, mostly to the rulers, or does every group have a sizable chunk? As well, numbers let us compare groups that are fare apart from each other in geographic or temporal terms. Did the Han Chinese of 100 CE have greater economic output than the Holy Roman Empire in Europe of 1000 CE? Statistics matter because we can see trends (changes over time) and comparisons.
What is an average? Questions to answer.
To start, let’s deal with a simple concept: an average. There are three types of averages, the mean, median, and model. The mean is the sum of all the numbers, divided by the total number.
For example, if we had the age of death for a single town in a single year we might ask, how old are you likely to live if you are your age right now?
First average the following ages: 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 9, 18, 18, 35, 45, 58, 72, 73, 75, 78, 88, 92, 107, 110. (25 numbers): What is the mean? Does this mean that you are going to die at this age? No, because you have already lived past 1 and likely past the ages 5,6, and 9. So, if we wanted to average the year of death for individuals above the year of 9, we’d start adding at 18.
What is the average age of death for individuals over the age of 9?
The median is the value (number) in the middle of a string of numbers. What is the median age of death for this town?
The mode is the most commonly occurring number in a string of numbers. What is the mode age of death for this town? This tell us that the most popular age of death for this town was one, even if the average (mean) age of death was higher.
As a historian, when you see the word “average” you always need to ask if it’s the mean, median, or mode and is that the most useful average for understanding the past.
If you’d like more help understanding mean, median, and mode, you can see a video here.
A brief pause for technical help.
For the next part of the lesson, you need access to a spreadsheet program. If you have Microsoft Excel or Mac Numbers on your computer you’re all set. If you don’t you’ll need to do one of two things:
- Download and install the free office software LibreOffice . This will give you give you a free version of a spreadsheet program.
OR
- Use Excel Online, the free software that’s part of your Normandale email account. First, save the document posted on D2L called “Historical Statistics for the World Economy, 1–1500 CE” to your free Microsoft OneDrive that is part of your Normandale email. The next several slides are to help folks get a spreadsheet program. If you have one, skip down to the Wages part of the lesson.
OR
- Open the spreadsheet in Google docs if you have a google account. (The way to do this is about the same as using Excel online).
Below is what Excel looks like on a Mac.
If you don’t have Excel or the LibreOffice version of it…
- Login to your Normandale email and click on the box of squares, which will show programs like below.
Choose “Excel Online”
Once you’ve opened that up, you’ll want to open a file from OneDrive. Your page will look similar, but not exactly like this one.
Once you’re in OneDrive,
Download the “Historical Statistics for the World Economy, 1–1500 CE”to your computer and
Upload the file into the OneDrive, so you can open it in Excel Online.
Numbers warm up: Reading simple graphs.
Open a browser and go to Real daily wages in pounds, England, 1260–1994 : http://data.is/1Sh8SLx and Wheat Prices, 1264–1400, in constand 1996 pounds, http://data.is/1k2CYaw
Let’s start with the wages graph. Click on the “Display” tab and make the Time period from 1260–1400.
Question: What is the highest daily wage and in what year during the period 1260–1400?
Adjust the running average.
Type “20” in the running average box.
Notice that you can no longer see 1260 as the chart needs 20 years to start the average calculation.
Notice how much smoother the chart appears when you’re averaging twenty years rather than one year.
Question: Which chart do you find explains the wage changes better, and why? Give me at least two sentences.
Next, switch to the wheat prices graph.
Adjust the “Time period” to 1264–1400.
Under “Chart type” adjust the chart to a “Relative line chart.”
Note the left measurement of the charts (y axis) changed from pounds (which is British money) to a percentage change in the wheat price with 1264 as the “0%” year.
Note that over 140 years there was little overall price change. Wheat cost the same in 1400 as in 1264.
Question: Why would the price of wheat stay the same in England? Evidence from your background reading for this week will help.
How much did we make? An introduction to big historical numbers.
Open “Historical Statistics for the World Economy: 1–1500” in D2L.
The first tab (1) is an introduction and not terribly useful to use. Tabs 2,3, and 4 will offer us more useful information.
Questions to complete the assignment
Answering the following questions by reading from the Excel Spread sheet.
Population Tab: Note you need to add three 0’s (000) to get the correct population number.
How many people lived in Western Europe (all 29 countries) and in China in the year 1000 (you will need to scroll down to see China)?
How many people lived in Africa in the year 1000?
GDP tab (on the bottom of the spreadsheet)
What was the GDP (gross domestic produce or how much stuff a country produces) of the 29 Western European countries in the years 1 and 1000?
What was the GDP of China and India combined in the year 1000?
PerCapita GDP tab (per capita means per person, or the average contribution to the total amount of production in a country)
What was the per capita GDP of the 15 West Asian Countries in the years 1 and 1000?
What was the per capita GDP of the world in the years 1, 1000, and 1500? Hint: at the bottom of the spread sheet.
Grading criteria
Student
- Identified the difference between the mean, median, and mode of a group of numbers.
- Opened a spreadsheet file using Excel, Numbers, LibreOffice, or Excel Online.
- Adjusted and read a wage graph.
- Identified why the number of years averaged in a graph matter.
- Identified the overall wheat price trend in England between 1264 and 1400.
- Answered questions about the past by interpreting data.