INRS Learning Unit 6 Quantitative and Qualitative Data Analysis Theme 1 Quantitative Data Analysis

Question 1

Explain the need for statistics in quantitative data analysis 4 marks .

Answer 1

• Removes guesswork
• Keeps objectivity = Must be non bias , clear reasons to prove that new suggested way of doing things is better that nthe current one .
• Defensible = means that there is a significant statistical benefit/significance shown in the results . Statistical significance goes above the expected margin or error. .

Question 2

Explain the importance of accuracy and precision in data sets 3 marks .

Answer 2

• Accuracy = free from error .
• Precision = a consistency to results that doesn’t refer to what the results they show are .
• These factors combine to create confidence .

Question 3

Explain what is meant by the range of a data set 1 mark

Answer 3

*The maximum and minimum values of a data set

Question 4

Explain how to determine the range of a data set . 1 mark

Answer 4

*Subtract the lowest value from the highest

Question 5

Determine the mean , median and mode of a data set . 6 marks

Answer 5

• Mean : Numerical average of the data . Calculated by (total number of all values added together/total number of values)
• Median : The middle value of the values provided . The values must then be placed in numerical order . If there is an even number of samples then its the average of the middle two .
• Mode : The most common value in the data set . Determined by reordering values in numerical order .

Question 6

Explain the distribution of data of a set . 2 marks

Answer 6

*How many times does each particular value occur in the data set ? Each value must then be counted to determine this .

Question 7

Calculate the standard deviation of a data set

Answer 7

*The average difference of each value in the set from the mean . (Formula won’t be tested)

Question 8

Explain the probability density function and normal distribution .

Answer 8

*The bell curve of normal distribution plots probability against values . The probabilty density is therefore the chance of a particular value occuring as shown by the given graph .

Question 9

Calculate a correlation co-efficient 8 marks

Answer 9

• Always a value from -1,0 to +1.0 .
• -1.o to -0.8 = strong negative correlation , X and Y are strongly related (Y decreases as X increases)
• -0.7 to -0.3 = weak negative correlation , X and Y may be related . Y decreases as X increases . Negative slope on the graph .
• -0.2 to +0.3 = No correlation or relationship between X and Y
• 0.4 to 0.7 = Weak positive correlation , X and Y may be related . Y increases as X increases , positive slope on the graph .
• 0.8 to 1.0 = Strong positive correlation . X and Y strongly related . X increases as Y does positive slope .

Question 10

Explain how to test a hypothesis 4 marks

Answer 10

*1/ State the hypothesis : Set and quantify your null and alternate hypotheses .
2/Set the decision criteria : Set a confidence level eg 95% mean
3/Compute the test statistic : Test stat is a normalized value which informs us of the relationship between the population and the sample .
4/Record the decision = Compare the score and test statistics .