STATISTICAL TECHNIQUES IN ENGINEERING MANAGEMENT WORK 2 GEEN 1074 LECTURER: Question a) The three measures of “ location” for a statistical population are arithmetic mean, mode and median.
Arithmetic Mean-is the central tendency of a set of data. It is obtained by summing all the data then dividing by the number of the data to be calculated.
Mode- is the most occurring unit in a given set of data. This means that in the data given mode indicates the most recurring data contained in that data.
Median- is the most central data separating the upper and lower data into two proportional sets.
(b) Spread shows how wide the ranges of data are or how varied they are. It can be measured using range and inter-quartile range.
Range- is the measure of the difference between the highest and the lowest value of data set.
Inter-quartile range- is the set of data values between the 75th and the 25th percentile in a given set of data.
(c) Normal distribution is the distribution pattern of a set of data that is unimodal and takes the shape of a bell in a graph. It very essential in engineering to determine the equality of data distribution in a given data since it shows uniform and equal distribution in both extremes.
Central limit theorem in statistics states that in a sufficiently large population, if a random sample size from the population is taken and the mean is calculated from sample size, it will be the same or almost equal to that of the whole population. This is very useful in engineering analysis since just a sample will enable to explain a whole population therefore saving a lot of time and money.
(d) Since central limit theorem uses a sample of the population that is chosen at random it will not affect the location and the spread of the data. The data will follow the same normal distribution curve as the entire population. The mean, median and mode will be the same or approximately the same as that of the entire population.
Question 2
Statistical tools
(a) Standard Deviation- this is the determination of how your data is spread. It is commonly used to find out how far a data has deviated from the assumed value.
(b) Fixation indices- is the description of the expected level of heterozygosity in a given data. It is used to determine or measure the correlation between data drawn from different levels of a subdivided entire set of data.
(c) Analysis of Variance (ANOVA)- is set of statistical models and the procedures entailed, in which the variance in one variable is subdivided to different sources of variations. It is commonly used to test average of different groups of set of data.
(d) T-Statistic- is the measure of how far a statistic estimate is far from the calculated one. It is commonly used during hypothetical testing.
Question 3
Problem definition is very essential and must be done clearly so as to lead to a proper solution of a problem and also to guide the exercise to its objective without differing from the original quest.
Questions to ask when developing a good problem definition:
Does this data help us in achieving our goals and objectives?
How do we sample the population?
What tools do we need to collect data?
What are the methods used to achieve our objective?
Will the result of this analysis be of any good or contribution in understanding the subject?
Do we have enough funding to carry out this analysis?
What is the current state of the subject to be analyzed?
What are the risks and know about of this analysis?
What is the expected time of completion of this analysis?
What is the comparison of what we really want to measure and what available statistics allows us to measure?
Is the current statistical records available lack some information that we are analyzing?
What are the theoretical figures and results of this analysis?
What kinds of knowledge or skills are needed for this analysis?
Question 4
Because if the process inputs are correct and accurate, if the method of calculating and analyzing are correct the process output will be accurate or near accurate. If you concentrate on a process output the inputs might not be correct and even with the correct analysis the the output is bound to be wrong and therefore misleading.
Question 5
(a) Primary Data-this kind of data is collected specifically with its objective in mind. It was collected for a specific purpose. An example is data collected from staff or clients in form of questionnaires or data collected from the variation of a product in a manufacturing process.
(b) Secondary data- is data that was collected for a specific purpose but now it is being reused for another different method. For example using questionnaires and initial analysis to calculate the viability of something new or use of initial set of variations results of a product to predict the likelihood of it occurring again.
Question 6
We first calculate the average mean of the batches then calculate the average of the entire batches
The mean for the Honzaki CNC vertical milling machine= 115. 4006
The mean for the Kawda machine= 115. 597
Assumed mean = 115. 50
Standard deviation for Honzaki CNC vertical milling machine
= 115. 50-115. 4006
= 0. 0994
Standard deviation for Kawda machine
= 115. 597-115. 55
= 0. 097
Calculate for 95% confidence level
α= 1-0. 95= 0. 05
t-value= 2. 045
x= 115. 5
Maximum error
E= t*δ/n2
= 0. 0101
Confidence level
= E+x
= 115. 5101
Calculate for 99% confidence level
α= 1-0. 99= 0. 01
t-value= 3. 169
x= 115. 5
Maximum error
E= t*δ/n2
= 0. 00307
Confidence level
= E+x
= 115. 50307
