1. Statistics Statistics Principles of EngineeringTM
Unit 4 – Lesson Statistics
Statistics

2. Statistics The collection, evaluation, and interpretation of data
Principles of EngineeringTM
Unit 4 – Lesson Statistics
The collection, evaluation, and interpretation of data

3. Statistics Statistics Inferential Statistics Descriptive Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Statistics
Inferential Statistics
Generalize and evaluate a population based on sample data
Descriptive Statistics
Describe collected data
Predictions are a type of inferential statistics.

4. Data Categorical or Qualitative Data
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Categorical or Qualitative Data
Values that possess names or labels Color of M&Ms, breed of dog, etc.
Numerical or Quantitative Data
Values that represent a measurable quantity
Population, number of M&Ms, number of defective parts, etc.

5. Data Collection Sampling Random Systematic Stratified Cluster
Statistics
Data Collection
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Sampling
Random
Systematic
Stratified
Cluster
Convenience
Random sampling involves choosing individuals completely at random from a population. For instance, random sampling is practiced when you put each student’s name in a hat and draw one at random.
Systematic sampling involve selecting individuals at regular intervals. For instance, choose every 4th name on the roll sheet for your class.
Stratified sampling ensures that you equally represent certain subgroups. For instance, you may randomly choose 2 males and 2 females in your class.
Cluster sampling involves picking a few areas and sampling everyone in those areas. For instance, sample everyone in the first row and everyone in the third row, but no one else.
A convenience sample follows none of these rules in particular. For instance, if you ask a few of your friends for feedback, you are performing a convenience sample.

6. Graphic Data Representation
Statistics
Graphic Data Representation
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Histogram
Frequency distribution graph
Frequency Polygons
Frequency distribution graph
Bar Chart
Categorical data graph
Histograms, bar charts, and pie charts are generally used for categorical data.
Frequency polygons are often used for numerical data
Pie Chart
Categorical data graph %

7. Measures of Central Tendency
Statistics
Measures of Central Tendency
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Mean
Arithmetic average
Sum of all data values divided by the number of data values within the array
Most frequently used measure of central tendency
Strongly influenced by outliers – very large or very small values

8. Measures of Central Tendency
Statistics
Measures of Central Tendency
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Determine the mean value of
48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

9. Measures of Central Tendency
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Median
Data value that divides a data array into two equal groups
Data values must be ordered from lowest to highest
Useful in situations with skewed data and outliers (e.g., wealth management)

10. Measures of Central Tendency
Statistics
Measures of Central Tendency
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Determine the median value of
48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55
Organize the data array from lowest to highest value.
2, 5, 48, 49, 55,
58,
59, 60, 62, 63, 63
Select the data value that splits the data set evenly.
If the data array has an even number of values, we take the average (mean) of the two middlemost values. In the example, this is 58.5.
Median = 58
What if the data array had an even number of values?
5, 48, 49, 55,
58, 59,
60, 62, 63, 63

11. Measures of Central Tendency
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Mode
Most frequently occurring response within a data array
Usually the highest point of curve
May not be typical
May not exist at all
Modal, bimodal, and multimodal

12. Measures of Central Tendency
Statistics
Measures of Central Tendency
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Determine the mode of
48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55
Mode = 63
Determine the mode of
48, 63, 62, 59, 58, 2, 63, 5, 60, 59, 55
Mode = 63 & 59 Bimodal
Determine the mode of
48, 63, 62, 59, 48, 2, 63, 5, 60, 59, 55
Mode = 63, 59, & Multimodal

13. Data Variation Range Standard Deviation Measure of data scatter
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Measure of data scatter
Range
Difference between the lowest and highest data value
Standard Deviation
Square root of the variance

14. Statistics
Range
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Calculate by subtracting the lowest value from the highest value.
Calculate the range for the data array.
2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

15. Standard Deviation s for a sample, not population Calculate the mean
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
s for a sample, not population
Calculate the mean
Subtract the mean from each value and then square it.
Sum all squared differences.
Divide the summation by the number of values in the array minus 1.
Calculate the square root of the product.
Note that this is the formula for the sample standard deviation, which statisticians distinguish from the population standard deviation. In practice, only the sample standard deviation can be measured and therefore is more useful for applications.

16. Standard Deviation
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Calculate the standard deviation for the data array.
2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 1. 2.
( )2 =
( )2 =
( )2 =
( )2 =
( )2 =
( )2 =
( )2 =
( )2 =
( )2 =
( )2 =

17. Statistics
Standard Deviation
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Calculate the standard deviation for the data array.
2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 4.
= 5,024.55 6. 5.
σ = 22.42

18. Graphing Frequency Distribution
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Numerical assignment of each outcome of a chance experiment
A coin is tossed 3 times. Assign the variable X to represent the frequency of heads occurring in each toss.
Toss Outcome
x Value
HHH 3
x =1 when?
HHT 2
HTH 2
HTT,THT,TTH
THH 2
HTT 1
THT 1
TTH 1
TTT

19. Graphing Frequency Distribution
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
The calculated likelihood that an outcome variable will occur within an experiment
Toss Outcome
X value x Px
HHH 3
HHT 2
HTH 2 1
THH 2
HTT 1 2
THT 1
TTH 1 3
TTT

20. Graphing Frequency Distribution
Statistics
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Histogram x Px 1 2
Because this is a frequency histogram, the heights of all the bars must add to 1 (1/8 + 3/8 + 3/8 + 1/8 = 1). x 3

21. Histogram Available airplane passenger seats one week before departure
Statistics
Histogram
Principles of EngineeringTM
Unit 4 – Lesson Statistics
Available airplane passenger seats one week before departure
What information does the histogram provide the airline carriers?
percent of the time
What information does the histogram provide prospective customers?
Airline carriers and passengers can see how many seats will likely be open on a flight one week prior to departure.
For instance (looking at the tallest bar) 12 percent of the time there are 5 empty seats.
Note that something is wrong with this relative frequency graph! The bars we see only add to a total of about .50 (50 percent), and they should add to 100%.
open seats