Understanding Statistics
Statistics is a branch of mathematics and a scientific discipline that involves the collection, analysis, interpretation, and presentation of data. It plays a fundamental role in a wide range of fields, including science, social science, business, economics, and many others. Statistics helps researchers and analysts make sense of large and complex sets of data, extract meaningful insights, and make informed decisions.
Statistics is a powerful tool for making data-driven decisions, drawing valid conclusions, and conducting scientific research. It is an interdisciplinary field with a broad range of applications, and its methods and principles are continuously evolving to address the growing complexity of data in the modern world.
Averages
In mathematics, "averages" refer to various measures of central tendency that are used to summarize a set of numerical data by providing a single representative value. There are several types of averages commonly used in mathematics:
Mean: The mean, often referred to as the "average," is the most common measure of central tendency. It is calculated by summing up all the values in a dataset and then dividing the sum by the total number of values. The mean represents the arithmetic average of the data.
How to Find the Average
It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Example 1: What is the Average(Mean) of these numbers?
7, 12, 8
- Add the numbers: 7 + 12 + 8 = 27
- Divide by how many numbers (there are 3 numbers): 27 / 3 = 9
The Mean is 9
Example 2: Look at these numbers:
3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
The sum of these numbers is 330
There are fifteen numbers.
The mean is equal to 330 / 15 = 22
The mean of the above numbers is 22
Frequency Tables
Sometimes we don't have a simple list of numbers, it might be a frequency table like this (the "frequency" says how often they occur):
| Score | Frequency |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 4 |
| 4 | 2 |
| 5 | 1 |
(it says that score 1 occurred 2 times, score 2 occurred 5 times, etc)
Mean = 2×1 + 5×2 + 4×3 + 2×4 + 1×5(how many numbers)
And rather than count how many numbers there are, we can add up the frequencies:
Mean = 2×1 + 5×2 + 4×3 + 2×4 + 1×52 + 5 + 4 + 2 + 1
And now we calculate:
Mean = 2 + 10 + 12 + 8 + 514
= 3714 = 2.64...
And that is how to calculate the mean from a frequency table!
Example: Parking Spaces per House
Isabella went up and down the street to find out how many parking spaces each house has. Here are her results:
| Parking Spaces | Frequency |
|---|---|
| 1 | 15 |
| 2 | 27 |
| 3 | 8 |
| 4 | 5 |
What is the mean number of Parking Spaces?
Answer:
The Mean is 2.05 (to 2 decimal places)
(much easier than adding all numbers separately!)
Let us explore few more Frequency Table example through Canva slides
Graphical Explanation
GeoGebra tool is also used to show graphical representation and method of finding averages. Given GeoGebra link is created to help understand how we can calculate Mean using GeoGebra.
Math nook used to demonstrate the understanding of averages using an online game.
Quiz time
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