Data Management and Probability

This week we got to look at the familiar concept of data management and probability. As usual, we went through some fun activities and got our minds thinking. The growth mindset is still at the core of ever lesson we have had up until this point and should be the centre of every lesson taught. Kids need to know that their brain is a muscle and that every time it challenged or faced with a struggle, it has the opportunity to grow stronger. Perseverance is a a skill that all students need to develop in order to succeed. Our friend Mojo shows us how some students view academics and the school setting. You're either born smart or you're not? I don't think so!

Mean, Median, Mode, and Range
One of the fundamental concepts rooted in data management and probability is the use of mean, median, mode, and data range. The mean is the number that people are usually referring to when they talk about "the average". It can be calculated by adding up all the data values and dividing by the number of values. The median is the middle value when the data is in order. This value can be a whole number or half way between two numbers. The mode is the most frequent value in a data set. A data set can have one mode, multiple modes, or no mode at all. The range is the difference between the least value and the greatest value and shows the spread of data. Understanding these terms and their role within a set of data is necessary for developing an understanding of data management and probability.

Bar Graphs
Data can be visually represented in a multitude of ways, such as pictographs, line graphs, and circle graphs. One of the visual representations that we focused on in class is the bar graph. Bar graphs are displays that use the lengths or heights of bars to represent quantities. While there are many variations of bar graphs, our class specifically looked at is the Stem-and-Leaf Plot. The stem-and-leaf plot is a way of both organizing and displaying numerical data. In this graph, numbers are grouped together by their place value. The "stem" is determined by the digits greater place value while the "leaf" is determined by the digits lesser place value. As shown in picture to the right, the "stem" of 1 has two leaves, 6 and 7. This means that within this data set, there are the numbers 16 and 17.



Levels of Graph Comprehension
Looking at a graph requires numerous levels of comprehension. This is necessary so that information is not misinterpreted. Many graphs display information that can be looked at in different ways. An example of this is the graph to the right that focuses on tax rates. The bar on the left is much higher than the bar on the right, approximately 5 times larger. What you don't see, however, is the rest of the bar as you are focused in on the top part. The bar on the left represents a tax-rate of 35% while the bar on the left represents 39.6%. When we teach students about graphs, we need to be mindful of the three levels of comprehension. These include reading the data, reading between the data, and reading beyond the data.

Early Probability
Another focus of this weeks class was probability. Probability is a measure of likelihood. It can be expressed qualitatively or quantitatively as a fraction or decimal between 0 and 1 or an equivalent percent. When young students are asked to describe events of probability, they develop a probability language. Words like always and never as well as likely and unlikely are established early in this vocabulary and help students understand how probability plays a role in their daily lives.

One of the activities we engaged with in this class was understanding probability through the use of dice. We were asked to roll every number on the dice and record how many rolls it took us to roll each number. While the odds of a rolling a number are 1 in 6, it took most students many more rolls to completely roll every number. An even easier activity that can be used to teach young students about probability is flipping a coin. This activity would be much simpler than rolling a dice because there are only two sides on a coin, therefore the probability of every outcome is much larger than any outcome of rolling a dice.

Probability and Data Management in Our Daily Lives

Probability and data management play an important role in our lives in many different ways. Many of our actions throughout the day are based on data management and trends that we have seen throughout our lives. During this time of the year we usually have colder weather. With a higher probability of cold weather as compared to summer weather, we are more likely to wear a coat. Every December for the past 10 years, I have worn a coat at least once. This set of data helps inform me of what is to come in December as far as weather and helps determine a probability of wearing a coat.

Students already have an idea of data management and probability, they just don't know it yet. They know that they are in school from Monday to Friday during the school year and the likelihood of a snow-day is usually small. They know that they will most likely be eating pizza on Friday because they have had pizza every Friday for two months. This understanding of data management and probability is basic, but can be developed in more depth.