1. Drill
Put these numbers in order from least to greatest: {-2, 6, 3, 0, -5, 1, -8, 8}
b) Add the #’s together c)Subtract the smallest # from the largest #.

2. Algebra I Statistics Mean, Median, Mode
Day 2

3. Visual Memory

4. Mean
The mathematical average, the number you get when you add up all the numbers in the sample space and divide the sum by the amount of numbers there are.

5. Median
After the numbers are put in numerical order the median is the middle #.
If two numbers are in the middle you take the mean of those two #’s.

6. Mode
The number that appears the most in the sample space. If more then one number appears the most then they are both the mode.
If all numbers appear the same amount of times we say that ALL #’s are the mode.

7. Range
The difference between the largest and smallest numbers. {2, 4, 6, 7, 10}
The Range of this set is because 10 – 2 = 8

8. Find the mean, median, mode and range for these two sets of #’s
{2, 4, 4, 7, 9, 10, 11, 15}
{1, 2, 6, 6, 9, 9, 25, 30}

9. Examples
Jed’s test scores so far are 86, 95, 78, 87, and 92. What is Jed’s mean score? What is his median score?
An article in the newspaper states that the median price of a home in your neighborhood is $275,000 and the mean price is $389,000. Explain what might cause such a large difference in the two measures of central tendency.

10. Example HSA
The newspaper printed the high temperatures for last week, but the temperature for Saturday was smudged. If the mean high temperature for last week was 84 , what was the temperature for Saturday?
Day Sun Mon Tues Wed Thurs Fri Sat
Temp **

11. Outlier(s)
An outlier is a number that is far away from the rest of the data.
Ex: (2, 4, 5, 8, 10, 13, 48)
Ex: (3, 28, 31, 36, 39, 43, 46)

12. Mean vs. Median
When you have an outlier it can drastically effect the mean. The median will roughly stay the same.
When you have an outlier you should use median for the measure of central tendency.
When you do not have an outlier you should use the mean.

13. Find the mean and median for each set of data and determine which measure of central tendency is better.
{20, 21, 24, 27, 29, 30, 31, 35}
b) {12, 14, 16, 19, 22, 23, 30, 73}

14. Example
Create a box and whisker plot for this set of data:
{12, 8, 21, 16, 9, 11, 18, 22, 24, 17}

15. Interquartile Range (IQR)
The interquartile range of a set is the difference between the lower and upper quartiles. (Q3 – Q1 = IQR)
Find the IQR for the last problem we did.

16. Algebra 1 Statistics (Measures of Central Tendency) Obj: SWBAT determine which measure of central tendency is best for describing the data.

17. Measures of Central Tendency
Mean, Median, Mode and Range are all measures of central tendency, because they give us an average of all the values in a data set.
(They find the “center” of the set)

18. Outlier(s)
An outlier is a number that is far away from the rest of the data.
An outlier can dramatically change the value of the mean and range. (Non-Resistant)
But it will not drastically change the median or mode. (Resistant)

19. Example
Which one(s) of these numbers would be considered an outlier? (If any)
A) {2, 24, 25, 36, 38, 40, 42, 44, 90}
B) {1, 5, 7, 9, 11, 14, 16, 20, 25}

20. Example
Which measure of central tendency would best describe this set of data? (Why)
{2, 4, 5, 6, 8, 10, 12, 13, 14, 50}

21. Extra Stat Topics
Misleading Graphs
Matrices
Percents
Random Sample
Frequency Distributions

22. Examples
Find the mean, median, mode and range then state which measure of central tendency is the best one to use.
{2, 4, 4, 8, 10,12, 15, 15, 20, 88}
Mean: 17.8 Median: 11 Mode: 4, 15 Range: 86
We should choose the median since there is an outlier.

23. Unit B
Sampling

24. Vocabulary
Sample: A sample is a portion of a larger group, called the population.
If all units in a population are included, then it is called a census.

25. Example Population Sample
All of the light bulbs manufactured on a production line
24 light bulbs selected from the production line
All of the water in a swimming pool
A test tube of water from the pool
All of the people in the United States
1509 people from throughout the United States

26. Vocabulary
A random sample of a population is selected so that it is representative of the entire population.
A simple random sample must be selected so that every individual in the population has an equal chance of being selected.

27. Vocabulary
A stratified random sample is when the population is divided into smaller similar groups. Then a simple random sample is selected from each group.
In a systematic random sample, the items are selected according, to a specific time or item interval.

28. Vocabulary All random samples are unbiased.
A Biased Sample is when one group or portion of the population is more likely to be picked then another.

29. Types of Bias
Convenience: is when people or subjects in the population are simply picked due to the fact they are easy to contact.
Voluntary Response: is when the people is the sample are offering their time or choosing to give data (Ex: phone calls, surveys mailed out, etc..)

30. Drill
Determine the mean and median prices for 7 different cars shown below:
Which measure of central tendency best represents the average price? (Why)
Car
Price A
$18,000 E
$34,000 B
$23,000 F
$38,500 C
$26,500 G
$88,000 D
$30,000

31. Algebra I Matrices and Sampling Frequency Distribution

32. Matrices Matrices are simply used to organize and arrange data.
Example:
What is the total amount of tests taken by 9th graders?
9th th th
Tests
Quizzes HW

33. L H S W H S 9th 10th 11th 9th 10th 11th Tests Quizzes HW Tests Quizzes

34. Sampling
When taking a sample you want the sample to be random and each possible individual in the group must have an equal chance of being selected.

35. Frequency Distribution Charts
A frequency distribution chart tells you how many “items” there are in each group.
Test Score
Frequency 60 3 70 4 80 7 90 6
100 5

36. Example Find the mean, median, mode and range for this set of data.
Test Score
Frequency 60 3 70 4 80 7 90 6
100 5

37. Examples
Think of two random ways of selecting 50 students in the school for a survey. Every student in the school must have an equal opportunity to be selected.
Make a frequency distribution chart with at least 20 total numbers and find the mean, median, mode and range for the set.

38. Examples
Find the mean, median, mode and range for each set of numbers.
{2, 4, 5, 5, 7, 7, 7, 9, 10, 15}
{10, 4, 8, 12, 4, 12, 16, 20, 22}

39. Algebra 1 Box and Whisker Plots
Objective: students will be able to construct a box and whisker plot after finding the five-number summary of a set of data.

40. Five-Number Summary
The five number summary of a set of data consists of the median, the upper and lower quartiles and the upper and lower extremes.
LE, Q1 (LQ), MED, Q3 (UQ), UE

41. Extremes
The upper and lower extremes of a set of data are just the maximum and minimum numbers in the set.

42. Median (Quartiles)
The upper and lower quartiles are found by finding the median of the numbers larger then the median of the whole set and the median of the numbers lower then the median of the whole set.

43. Create a Box and Whisker Plot
{2, 4, 5, 8, 10, 14, 18}
LE (Min): LQ:
MED: UQ:
UE (Max):

44. Create a Box and Whisker Plot
{8, 10, 14, 20, 24, 38, 42, 48}
LE (Min): LQ:
MED: UQ:
UE (Max):

45. Stem and Leaf Plots

46. Drill
Create a Box and Whisker Plot for this set:
{1, 2, 3, 3, 5, 7, 8, 10}
Hint: Find Extremes, Quartiles, and the Median.

47. Stem and Leaf Plot
A stem and leaf plot is another way of arranging data to make it easier to analyze.
The last digit in the number is known as the leaf and all other digits are known as the stem.

48. Example
{31, 33, 36, 44, 58, 63, 67}
Stem
Leaf 3 4 5 8 6
3 7

49. More Examples
107
10 is the Stem
7 is the Leaf

50. Try to create a stem and leaf plot:
{11, 14, 15, 17, 17, 21, 24, 28, 31, 40}

51. Solution
Stem
Leaf 1 2 3 4

52. Example #2
11, 13, 14, 14, 32, 33, 27, 29, 10, 41, 25, 32, 39, 42, 35, 27, 19, 23, 47, 42, 20

53. Solution
Stem
Leaf 1 2 3 4

54. Solution (Cont.)
Stem
Leaf 1 2 3 4

55. Example #3
Best Buy: 30, 35, 40, 20, 25, 23, 45, 50, 55, 60, 43, 35, 32
Toys R Us: 32, 20, 15, 28, 35, 42, 34, 50, 35, 20, 26, 34
Find the mean, median,mode and range for each store.

56. DRILL Write each percent as a decimal. a) 27% b) 9%
2) Find Q3 for this set of numbers:
{3, 5, 6, 8, 12, 15, 18, 20, 21, 22}

57. Frequency Tables 90 8 80 11 70 15 60 9 Grade Frequency
A frequency table is used to tell you how many of each number are contained in the data set.

58. Review For Test 2 1) Box and Whisker Plots 2) (5 Number Summary)
3) Interquartile Range
4) Random Samples
5) Central Tendency
6) Mean, Median, Mode and Range
7) Misleading Graphs
8) Matrices
9) Stem and Leaf Plots

59. Homework
Make 5 Sets of numbers that contain 10 values in each set, with no numbers repeating and create Box-and-Whisker plots for each set of data.
Also state the IQR for each set.