Answer to Question #235334 in Statistics and Probability for Hastings Mambwe

Question

[1 mark]

1

b) 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

We use the table:

(i) Find the sample mean and standard deviation of the fertility rates.

[4 marks]

Solution:

sample mean:

$\bar x=\frac{5.5+2.9+4.2+6.0+3.1+3.2+4.1+4.3+1.4+4.9+3.4+2.3+2.4+5.2+4.7+3.6}{16}=3.825$

sample standard deviation:

$(5.5-3.825)^2+(2.9-3.825)^2+(4.2-3.825)^2+(6.0-3.825)^2=8.532\\ (3.1-3.825)^2+(3.2-3.825)^2+(4.1-3.825)^2+(4.3-3.825)^2=1.217\\ (1.4-3.825)^2+(4.9-3.825)^2+(3.4-3.825)^2+(2.3-3.825)^2=9.543\\ (2.4-3.825)^2+(5.2-3.825)^2+(4.7-3.825)^2+(3.6-3.825)^2=4.738$

8.532+1.217+9.543+4.738=24.03

24.03\15=1.602;

$\sigma=\sqrt{1.602}=1.266$

(ii) Find the population mean and standard deviation of the fertility rates.

[4 marks

We use full table from

to

This table contains 200 rows aтd presents the population on whole.

We copy this table in Excel and find population mean and stadard deviations by using Excel functions:

We have $\mu=2.614,\sigma=1.238$

 

ii) Comment on the SADC vs World GDP per capita and fertilty rates

SADC sample mean=3.82 greater than population mean 2.614 and for SADC standard deviation 1.266 greater than population deviation 1.238

c) (i) Find the range for the world GDP per capita and fertilty rates.

[4 marks]

Firstly we use capita table front and rear positions in World GDP per 

capita

We define range of World GDP per capita as 128647-727=$127920

From Central African Republic to Qatar.

After, we use statistical table for fertility rates table and by using smallest and biggest data in the table have:

So, range for fertility rate is 6.8-0.9=5.9 from Korea to Niger.

(ii) Find the median values for the world GDP per capita and fertilty rates.

[2 marks]

We use the same table x[1-185] which is ordered by gdp per capita, n=185- odd number of elements therefore median is x[(185+1)/2]=x[93] and in the table it is eqeals to

or median value for gdp per capita is 13463$ and corresponds to Peru.

Analogically for fertility rates we use the table from internet

from

to

Let x[1-200] ordered array corresponding to this table, we have N=200- even number elements in array and Me(x)=(x[100]+x[101])/2=(2.188+2.174)/2=2.181

because

(iii) Find the interquartile range for the world GDP per capita and fertilty rates.

[4 marks]

GDP table contains 2n+1=185 values so n=92

First by value 92 elements is x[94-185] containd even number of elemens therefore Q₁=Me(x[94-184])=(x[139]+x[140])/2=

=(4502+4247)/2=4374.5

Biggest 92 elements are x[1-92] and median of them Q₃=(x[46]+x[47])/2=

=(29924+29511)/2=29718

Thus interquartile Q_50%=Q₃-Q₁=29718-4374.5=25343.5

Fertility rates table described before contains 2n=200 elements or n=100.

Median of last 100 elenents Q₁=Me(x[101-200])=(x[150]+x[151])/2=

=(1.657+1.650)/2=1.6535

Median of first 100 elements is Q₃=(x[50]+x[51])/2=

=(3.520+3.518)/2=3.519

Interquartile Q_50%=Q₃-Q₁=3.519-1.6535=1.8655