Question

Question Five Total 25 Marks] e forecasts for the percentage rate of inflation for (0) Fourteen economists were asked to provid the third quarter of 2002. They produced the forecasts given below 12 4 1.5 15 17 1.8 1.8 9 1.9 2.12 3.2 3.9 5.0 Calculate the median, standard deviation and the interquartile range of these forecasts. 7 marks] (i) State the four characteristics of the normal distribution and comment and comment on whether the above forecasts conform to a normal distribution 5 marks] (iii) Insurance policies providing car insurance are such that the sizes of claims are normally distributed with mean ZMw10,870 and standard deviation ZMW10,610. Given a sample of 100 claims, calculate the number of claims. (a) Less than ZMW13000 (b) Between ZMw1300 and ZMW16000 2 mark] 3 marks] iv) Describe the nature and use of the following models in trend analysis. 1 mark] 2 mark] (a) Linear trend: ybo btE Log-linear trend: Inv)- bo + bit et (c) Copy and complete the table below showing the predicted value of the dependent y if bo-5 and bi-6.3 the two trend equations. Give one real world example for each trend. [4 marks] Period (t) Predicted value Linear Trend linear Trend

Answer 1

i)

From the given dataset,

Median = 1.85

Std Deviation = 1.085

Quartile 1 (Q1) = 1.55

Quartile 3 (Q3) = 2.55

IQR = Q3-Q1 = 1

ii)

From the given dataset,

Mean = 2.257

Mode = 1.5

• For a Normal Distribution, the Mean, Median & Model are equal

• From the above boxplot, we can conclude that data is skewed. A Normal distribution, is symmetric.
• The distribution is unimodal (has only one mode)