Answer to Question #231646 in Statistics and Probability for Jamilah

Question

Fertility rates for the SADC countries represent a sample of world fertility rates
(population).
(i) Find the sample mean and standard deviation of the fertility rates.
[4 marks]
(ii) Find the population mean and standard deviation of the fertility rates.
[4 marks]
(iii) Comment on the SADC vs World GDP per capita and fertilty rates.
[2 marks]
c) (i) Find the range for the world GDP per capita and fertilty rates.
[4 marks]
(ii) Find the median values for the world GDP per capita and fertilty rates.
[2 marks]
(iii) Find the interquartile range for the world GDP per capita and fertilty rates.
[4 marks]

Answer 1

If the data were available, the following formulas would apply

Part i

Sample mean $\bar{X}= \frac{\sum X}{N}$

Standard deviation $\sigma = \sqrt{\frac{\sum(x_i-\mu)^2}{N}}$

Part ii

Population mean $\mu= \frac{\sum X}{N}$

Standard deviation $\sigma = \sqrt{\frac{\sum(x_i-\mu)^2}{N}}$

Part iii

The standard deviation is a useful metric of spread or dispersion. It informs us how much the outcomes deviate from the mean on average. As a result, if the standard deviation is modest, we may conclude that the findings are near the mean, but the results are more dispersed if the standard deviation is big.

Part c(i)

The simplest measure of data variability is in the range, which is the difference between the biggest and smallest values.

Part (ii)

The median is the number that falls in the centre. The median is the value in the centre of a set of ordered data. The median is often computed for numeric variables. Still, it may also be calculated for sequential categorical data, such as the four categories in a satisfaction survey: excellent, good, satisfactory, and bad.

Part (iii)

Step 1: Arrange the numbers in ascending order.

Step 2: Determine the median.

Step 3: Put parenthesis around the values that are higher and lower than the median. It is not statistically required, but it makes Q1 and Q3 simpler to identify.

Step 4: Locate Q1 and Q3.

Step 5: To get the interquartile range, subtract Q1 from Q3.