Foundation of Engineering

1. FOUNDATIONS OF
ENGINEERING

2. CHAPTER # 9
Statistics

3. STATISTICAL QUALITY CONTROL
Statistics includes scientific methods for collecting, organizing, summarizing, presenting and analyzing data
as well as making conclusions based on the data
Statistics Quality Control uses statistical methods to assess the quality of a product or process
It is extremely important manufacturing tool that is largely responsible for the success of Japanese
automobile industry
This technique was originally developed in US in the early 20th century
After World War II US abandoned the procedure because ROW industries were all destroyed so there was
no competition but now every major US industry has a quality control program
Quality is defined as “the fitness for use”. However statistical quality control defines “a high quality product
as one that closely matches the design specifications

4. SAMPLING
Sample: A small part or quantity intended to show what the whole is like
For example Gallup poll may be taken to determine how the US population will vote in next presidential
elections
Two braches of descriptive statistics i) Descriptive statistics ii) Statistics Inference
Descriptive Statistics: which seeks only to descriptive data
Statistical Inference: which seeks to make conclusions from the data
DESCRIPTIVE STATISTICS

5. DESCRIPTIVE STATISTICS
Sorting Data: To put data in a order
Range: Max - Min
Central Tendency: It is measured by mean, median and mode
Mean: Also known as arithmetic mean or average
Median: The middle of the sorted data is called Median
Mode: It is the most frequent appeared data
Variation: It is measured by Deviation, mean absolute deviation, standard deviation & variance
Deviation: It is deviation of particular data point from the mean. There are positive and are negative both. So the sum of all
deviation is equals to zero. To solve this problem we use the next ones
Mean Absolute Deviation: To avoid the above problem, we use
Standard Deviation: The most easily solution is to square the deviations because the square of (negative & positive) is
always zero
Variance: The square of standard deviation

6. EXAMPLE 9.1
Find
Mean
Median
Mode
Mean Absolute Deviation
Standard Deviation
Variance

7. HISTOGRAM
In the last example we have histogram i.e frequency v each class
Relative frequency = Frequency/n ; which is displayed on right side of the figure 9.3
Cumulative frequency It can be found by adding the frequency of a given class to the sum total of all
the lower classes. The mid pts of a rectangle can be connected to show a cumulative frequency polygon
Relative cumulative frequency: which is simply the accumulated sum of relative frequency
Note: when all the classes have been accumulated, the relative cumulative frequency is 1
For a large population e.g. in our example the production of shaft of entire day say 10,000 and we
would be able to make many more classes -> the frequency polygon becomes essentially smooth
Figure 9.3, 9.4, 9.5

8. QUINCUNX
EXAMPLE

9. NORMAL DISTRIBUTION & STANDARD
NORMAL DISTRIBUTION
The shape of the frequency polygon is the normal distribution or bell shaped curve
Relative Cumulative Frequency
Example 9.2