Discuss the below:
TASK1
You are required to prepare a dataset consisting of the Income (X) in £ per week and Years of Education (Y) of 40 randomly chosen adults and then perform the following exercises. (You may enter numbers representing these characteristics of fictitious individuals, provided these are realistic).
Part A
All computer work in this section is to be performed using Microsoft Excel software. Define any term you need to use in your answer, draw appropriate diagrams and explain all relevant theory.
i. Obtain the descriptive statistics and the histogram of the data on Income and discuss whether or not standard deviation is a better measure than Semi Inter Quartile Range for this data.
ii. Now sort the data in ascending order and then delete the 5 largest and 5 smallest values. You now have 30 numbers representing income of individuals. Repeat the exercise in part (i) above for this reduced data.
Part B
All computer work in this section is to be performed using EViews software. Define any term you need to use in your answer, draw appropriate diagrams and explain all relevant theory.
iii. Obtain the descriptive statistics and the histogram of the data on Years of Education and discuss whether or not standard deviation is a better measure than Semi Inter Quartile Range for this data.
iv. Now sort the data in ascending order and then delete the 5 largest and 5 smallest values. You now have 30 numbers representing Years of Education of individuals. Repeat the exercise in part (i) above for this reduced data.
Q2: Use Excel to randomly generate 100 observations for the random variableX ~ Binomial (n, π) where n and π are numbers of your choice but are taken from the range 0.5 ≤ π ≤ 0.8 and 2 ≤ n ≤ 20 so that they do not meet the validity check.
(i) Define μ nπ andσ2= nπ(1-π) Refer to the 100 numbers you have generated. Use these numbers to estimate
a. Prob( X < μ)
b. Prob(μ-σ< X <μ+σ)
c. Prob(μ-2σ < X < μ+2σ)
(ii) Do your answers above suggest that the distribution of the generated numbers is approximately normal? Fully explain your answer.