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Lesson 4: Statistics
Lesson Outline:
1. Probability: Getting a “Snapshot” of the Data
2. Central tendency
a. Mean
b. Median
3. Visual representations of data
a. Pie charts/graphs
b. Bar and line graphs
In this we will look at the basic statistical math skills and concepts that you will need to know for the GED® test.
In this section the work is all done with basic arithmetic. You will not need to learn any new math. You will learn some concepts and terms that are structured around addition, multiplication, and division.
PROBABILITY
The term probability means the chance of an event occurring, such as the chance of a flipped coin landing heads up.
The chance of a coin coming up heads is 1 out of 2. There are only 2 possibilities, either heads or tails. Only one will occur on a given coin flip
A probability, in math, is a number ranging from 0 to 1.
A common way to show the “probability of something happening” is with a ‘P’ followed by a parenthesis containing the event. Flipping a coin and getting heads gives us 1 type of event (heads) out of two possibilities (heads or tails).
= ½ or 0.5 or 50%
Another example:
What is the probability of drawing a heart from a deck of shuffled playing cards? (one deck has 52 cards)
In a deck of playing cards the heart is one suit out of four that the deck is evenly divided into. (The suits are diamonds, clubs, spades and hearts.)
If you draw a card from a shuffled deck, you are making a random selection. Any card has an equal chance of being picked.
There are 13 hearts out of the 52 cards. Your chance of drawing a heart is:
= 13/52
= ¼ or 25%
You have one chance out of four that you will draw a heart. This does not mean that if you draw four cards, you are guaranteed to have exactly one heart card. A probability refers to likelihood. What you actually end up with in a real life situation will not always match up with the calculation. But the more times you do it, the more times it will look like that probability. In other words, if you draw a card 100 times, the number of hearts will be closer to 25% than if you just draw four times.
To calculate the probability of multiple events, you multiply the probabilities together.
Your chances of drawing two cards and having them both come up hearts is
P(2 hearts) = P(1 heart) x P(1 heart)
= ¼ x ¼
= 1/16 one chance out of sixteen.
Getting a "Snapshot" of the Data:
Statistical information is drawn from data.
Data is usually a set of numbers. For example, the heights of a group of people or the populations of cities.
We can do things to make the data more meaningful and draw conclusions about a given group.
CENTRAL TENDENCY
The term central tendency refers to how data looks toward the middle when you put it all in order. There are two central tendency numbers that can give us a “snapshot,” or summary, of a set of data. This single number can be more meaningful and easier to work with than a long list of numbers.
a. Mean
The mean is the sum of all the data divided by how many data there are in the set. This gives us one number (called an average) that lets us know the tendency of the overall group.
If your data is a set of numbers x1  xn that is n numbers long, then:
x1 + x2 + … + xn
mean = 
n
(You can refer to this formula on the formulas page during the test.)
Example:
Calculate the mean height from the following set of data:
66 in., 61 in., 62 in., 60 in., 64 in., 69 in., 70 in.
There are seven measurements, so n =7
66 + 61 + 62 + 60 + 64 + 69 + 70
mean = 
7
= 452/7 = 64.57 inches
b. Median
The median is another number that shows the central tendency of a group of data. The formula page expresses it as “the middle value of an odd number of ordered scores, and halfway between the two middle values of an even number of ordered scores.
It is the middle value in a set of data. Half of the data values are below it and half are above it.
To find the median you must put the data set into numerical order. For example, using the data from the previous problem:
66 in., 61 in., 62 in., 60 in., 64 in., 69 in., 70 in.
we can put the numbers in order from least to greatest and get:
60 in., 61 in., 62 in., 64 in., 66 in., 69 in., 70 in.
median^
The data value in the middle is 64 inches, so that is the median.
Notice that we can pick a middle value because there is an odd number of data (7 measurements).
If we have an even number of data we must take the average or midpoint between the middle two values.
So for example, let’s say we do a survey of how many pets each family on a block owns. Respectively, they have:
3, 0, 2, 1, 6, 1 pets in each household
We first make it an ordered series
0, 1, 1, 2, 3, 4
median^
Notice that we have an even number of values (6). There is no single value exactly in the middle. So we must look to the middle two values, 1 and 2. Halfway between 1 and 2 is 1.5.
So the median (middle) value of the number of pets that the households on this block own is 1.5 pets.
Measures of central tendency like mean and median values allow us to summarize data and also give us a basis for comparing multiple sets of data.
VISUAL REPRESENTATIONS OF DATA
Another way of getting a “snapshot” of data is with actual pictures.
a. Pie charts/graphs
A pie chart (also called a pie graph) is a circle with pieshaped sections representing percentages of a group. The sections are labeled with a name and a percentage.
A pie chart is used to relate proportions of a total.
Helpful tip:
Questions with a pie chart will tend to be more about the numbers than about anything the pie itself will tell you. Focus on the percentages related to what they are asking about.
Example:
An ice cream store made $1,100 in a week.
How much of their sales came from cones and sundaes?
Ice Cream Sales for the week
Total: $1100
Cones earned 63% and sundaes earned 5%. Together they made
63% + 5% = 68% of the total sales amount.
x/1100 = 68/100
we can multiply each side by 100 to get x/11 = 168
and then multiply each side by 11 to get x = $748
b. Bar and Line Graphs
Bar and line graphs are based on a coordinate system. Remember from geometry that graphs have a horizontal and vertical dimension. They each stand for specific units such as time, dollars, etc…, so that the points or bars will correspond to values along each axis.
Example:
The following bar graph shows a company’s profit in millions of dollars.
Yearly Profit
in millions of dollars
In what year did the company have a profit of $8 million?
First, find 8 on the vertical axis and follow the imaginary horizontal line to the right until you reach the bar that is in line with it. It is the bar over the year 2005.
Problem:
Anne records the growth of her hamster and produces the following graph
How much did the hamster grow between the 2nd and 10th week?
A) .05 lbs.
B) .06 lbs.
C) .07 lbs.
D) .08 lbs.
E) Not enough information to determine answer
Find week 2 (the second unit from the left) and week 10 on the horizontal axis.
Go up to the points on the line graph and find the values, 154 and .224, and subtract to find the change in weight.
.224
 .154
.070
The answer is .07 lbs., which is answer C).
This concludes Lesson 4 and brings us to the end of the GED® Mathematics lessons.
Click on the link below to move on to the course summary.
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