Tuesday, May 12, 2020

Algebra 1- The Segment Addition Postulate

Suppose XA = 3x and AY =  4x - 6. If A is the midpoint of XY, what is the length of XY?
           3x                       4x - 6
_________________________________
X                         A                         Y
The trick in this problem is to see that if A is the midpoint, then XA = AY.

Since XA = AY, 3x = 4x - 6
Subtract 3x from both sides.

3x - 3x = 4x - 3x - 6

0  = x - 6

Add 6 to both sides of the equation.

0 + 6 = x - 6 + 6

6 = x
To compute XA, you can either use 3x or 4x - 6

Using 3x, we get XA = AY = 3 × 6 = 16
Using 4x - 6, we get XA = AY = 3 × 6 - 6 = 18 - 6 = 12
XY = XA + AY = 16 + 16 = 32
The length of XY is 32.
Assignment: 

Tuesday, May 5, 2020

Algebra 1- Joint and marginal frequency tables

Relative Frequency

How often something happens divided by all outcomes.
Football Match

Example: Your team has won 9 games from a total of 12 games played:

  • the Frequency of winning is 9
  • the Relative Frequency of winning is 9/12 = 75%
All the Relative Frequencies add up to 1 (except for any rounding error).
road

Example: Travel Survey

92 people were asked how they got to work:
  • 35 used a car
  • 42 took public transport
  • 8 rode a bicycle
  • 7 walked
The Relative Frequencies (to 2 decimal places) are:
  • Car: 35/92 = 0.38
  • Public Transport: 42/92 = 0.46
  • Bicycle: 8/92 = 0.09
  • Walking: 7/92 = 0.08
0.38+0.46+0.09+0.08 = 1.01
(It would be exactly 1 if we had used perfect accuracy)

Assignment
 Each student in a random sample of students at a local high school was categorized according to gender (male or female) and whether they supported a proposal to increase the length of the school day by 30 minutes (oppose, support, no opinion). The following table summarizes the data for this sample.
  
Opinion on Proposal to Increase Length of School Day
Oppose
Support
No Opinion
Total
Gender
Male
50
40
20
110
Female
40
40
10
90
Total
90
80
30
200


a.             What proportion of the students in this sample are male?
 
b.             What proportion of the students in this sample support the proposal?
 
c.              What proportion of the males in this sample support the proposal?
 
d. What proportion of the students in this sample who support this proposal are female?


Friday, May 1, 2020

Algebra 1 Instructional video 4/30


2 way table

Two-Way Table

Do you believe in Martians? Here is a survey of 100 college students asking that very question: Do you believe in Martians?
GenderYesNo
Male1032
Female3820
Total4852
This type of table is called a two-way or contingency table.
A two-way or contingency table is a statistical table that shows the observed number or frequency for two variables, the rows indicating one category and the columns indicating the other category. The row category in this example is gender - male or female. The column category is their choice, yes or no.
There is a lot of information we can learn from this small table. Let's look at a couple questions you could see on a test.
How many males were asked? Let's look across the male row. Ten said 'yes' and 32 said 'no.' That would be a total of 42 males.
How many college students believe in Martians? Look down the Yes column. Ten males and 38 females said 'yes.' That would be a total of 48 college students.

Example #2

A recent survey of 100 college students asked if they prefer to drink tea, coffee, or an energy drink during finals week. Here is the table created from that survey.
GenderTeaCoffeeEnergy Drink
Male21539
Female18206
Total203545
Let's look at a couple questions you could see on a test.
How many college students drink tea given that they are a female? In this question, we're looking for tea drinkers that are female. Let's look at the female row and tea column. The answer is 18.
How many students drink tea or are male? In this question, we're looking for all tea drinkers united with all males. To figure out the answer, let's highlight the Tea column and Male row. We do have an overlap at Tea and Male, so be sure not to add that twice. So our answer is Total Tea drinkers 20 plus Total Males 56 minus the overlap of 2. 20 + 56 - 2 = 74. There are 74 students that are tea drinkers or male.
Source:https://study.com/academy/lesson/what-is-a-two-way-table.html

Assignment: quizziz code: 898765

Tuesday, April 28, 2020

Instructional Video 4/28/2020


5 number summary

You only need the five values listed above (min, Q1, Q2, Q3, and max) in order to draw your box-and-whisker plot. This set of five values has been given the name "the five-number summary".

Examples

Example 1

Earlier you were asked to compute the five number summary for 0, 0, 1, 2, 63, 61, 27, 13. It helps to order the data.
0, 0, 1, 2, 13, 27, 61, 63
  • Since there are 8 observations, the median is the average of the 4th and 5th observations: 2+132=7.5
  • The lowest observation is 0.
  • The highest observation is 63.
  • The middle of the lower half is 0+12=0.5
  • The middle of the upper half is 27+612=44
The five number summary is 0, 0.5, 7.5, 44, 63

Example 2

Create a set of data that meets the following five number summary:
{2, 5, 9, 18, 20}
Suppose there are 8 data points. The lowest point must be 2 and the highest point must be 20. The middle two points must average to be 9 so they could be 8 and 10. The second and third points must average to be 5 so they could be 4 and 6. The sixth and seventh points need to average to be 18 so they could be 18 and 18. Here is one possible answer:
2, 4, 6, 8, 10, 18, 18, 20

Example 3

Compute the five number summary for the following data:
 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9, 10, 15
There are 20 observations.
  • Lower : 1
  • Q1:2+32=2.5
  • Q2:4+52=4.5
  • Q3:6+72=6.5
  • Upper : 15

Example 4

Compute the five number summary for the following data:
4, 8, 11, 11, 12, 14, 16, 20, 21, 25
There are 10 observations total in this set of data. 
  • Lowest value (minimum) : 4
  • Q1:11 (Note that this is the median of the first half of the data - 4, 8, 11, 11, 12)
  • Q2:12+142=13 (Note that this is the median of the full set of data)
  • Q3:20 (Note that this is the median of the second half of the data - 14, 16, 20, 21, 25)
  • Upper value (maximum) : 25
The five number summary is 4, 11, 13, 20, 25.

Example 5

Compute the five number summary for the following data:
3, 7, 10, 14, 19, 19, 23, 27, 29
There are 9 observations total. To calculate Q1 and Q3, you should include the median in both the lower half and upper half calculations.
  • Lowest value (minimum) : 3
  • Q1:10 (this is the median of 3, 7, 10, 14, 19)
  • Q2:19
  • Q3:23 (this is the median of 19, 19, 23, 27, 29)
  • Upper value (maximum) : 29
The five number summary is 3, 10, 19, 23, 29.
Assignment: 

Sources: https://www.purplemath.com/modules/boxwhisk2.htm