Activity 1. What am I? (Ideal time allotment: Monday Nov 22 - 1 hour)
Directions: Complete the table below and write your answer on a separate sheet of
paper.
1.{
+ = 2
3 + 3 = 6
2.{
3 − 2 = 4
+ 2 = 3
3.{
3 + 5 = 8
3 + 5 = 1
Slope-intercept form
Slope
(equal or not equal)
y – intercept
(equal or not equal)
Number of
Solutions
Type of System
of Linear Equation
1
2
3
Answers
Answer:
11 Introduction
In every aspect of our lives, data—information, numbers, words, or images—are collected, recorded, analyzed, interpreted, and used. We encounter this information in the form of statistics too—everything from graphs of the latest home sales figures to census results, the current rate of inflation, or the unemployment rate.
Being able to make sense of data is an important skill. In Section 11.1, we will consider how to summarize a set of data by using an average value, calculated using the mean, median or mode.
In Section 11.2, we will look at how to present and understand data in tables. The focus will then move to graphs, and different types of charts that all make data easier to understand in Sections 11.3, 11.4, and 11.5. Graphs and charts are very useful for displaying the relationship between quantities quickly and in an accessible form, but these can also be used to mislead the unwary reader—so you’ll learn how to critically assess this type of information too.
Finally, in Section 11.6, you'll see some of the new types of interactive data visualizations that are becoming more common.11.0.1 What to Expect in this Unit
This unit should take around ten hours to complete. In this unit you will learn about:
The three different averages.
Understanding and constructing tables.
What to look out for in charts and graphs.
How to construct charts and graphs to display information.
11.1 Averages
Think of a trip that you or a friend might take frequently, such as shopping or going to work. How long would you say that trip takes?
You may have said something like, "Well, it usually takes about 45 minutes to get to work, but, if the traffic is heavy, it can take up to 1+ 1/2hours.” In other words, 45 minutes is a typical time, though there are exceptions. How did you decide what time to say? Did you pick a time that seemed to occur quite often, or perhaps a time that was somewhere in the middle of the times taken for recent trips?
Knowing a typical value for a data set, and also how the data is spread out around this typical value, is important for all sorts of situations.
A value that is typical of the values in a set of data is known as an average. There are different ways of calculating an average, and you will learn about three of these: The mean, the median, and the mode.
11.1.1 Calculating the Mean of a Data Set
You have probably come across the mean before; it is the most commonly used type of average and takes into account all the data.
Let’s look at an example to explore this type of average.
Suppose eight students took an exam, with the following scores:
9 7 6 7 8 4 3 9
To get a feel for the problem and to help you check that your final answer is reasonable, look at the exam scores and decide what a typical value might be. Make a note of your estimate.
To calculate the mean value, we add all the data values together and then divide this sum by the number of values.
In this example, the sum of the data values is
9+7+6+7+8+4+3+9=53.
There are eight data values. Therefore, the mean value is 53/8=6.625.
The mean exam score for these students was 6.6 (rounded to 1 decimal place).
How did this compare with the typical value you estimated at the beginning? Did you decide that 6 or 7 might be a typical value?
The mean value will always lie between the smallest value and the largest value, and will often be somewhere towards the middle, though exactly where depends on the actual values in the data set.
Remember to make a note of this in your math notebook for easy reference later.
Step-by-step explanation:
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