Question $1$

$(25$ marks$)$

$1\mathrm{.}1.$ Explain in detail the four levels of Data. Provide an example for each level and outline the importance of each level in Data Science.

$[5$ Marks$]$

$1\mathrm{.}2.$ Exploratory Data Analysis is a crucial stage in Data Science. Using the tips dataset, perform the following in Python:

$[20$ Marks$]$

a$.$ Generate summary Statistics for the numerical columns. $($Hint: total$\_$bill and tip$)$

b$.$ Plot a bar chart showing tips by gender and draw conclusions.

c$.$ Create a scatter plot of tip vs total bill and explain your findings.

d$.$ Calculate the mean of the Total bill by Day.

e$.$ From the dataset, determine which day generated the highest total tips.

NB: The tips dataset is a built$-$in dataset; follow these steps to load it in Python:

import seaborn as sns

tips $=$ sns$.$load$\_$dataset$(\text{'}$tips$\text{'})$

Question $2$

$(40$ marks$)$

$2\mathrm{.}1$ Calculate the dot product of the following matrices:

$[10$ marks$]$

$\left[\begin{array}{cccc}1& 2& 3& 4\\ 5& 6& 7& 8\\ 9& 0& 1& 2\end{array}\right],\left[\begin{array}{ccc}3& 4& 5\\ 6& 7& 8\\ 9& 1& 2\\ 0& 3& 4\end{array}\right]$

NB: SHOW ALL WORKING; DO NOT USE PYTHON

$2\mathrm{.}2$ A logistics company operates a fleet of trucks to deliver goods across different cities. The company has noticed that the speed at which a truck can complete its deliveries is inversely proportional to the number of delivery stops it must make. The company's data shows that when a truck must make ten stops, it can complete its route in $5$ hours. The logistics manager wants to understand how changes in the number of stops affect the total delivery time.

a$.$ If the logistics company decides to optimise one of its routes to have only eight delivery stops, how long will it take for the truck to complete its deliveries on this optimised route?

b$.$ Additionally, calculate the time it would take if the number of delivery stops increases to $12.$

c$.$ From your calculations, provide a detailed summary of your results and draw conclusions to help the manager of the company understand the relationship between the number of delivery stops and the time taken to complete a route.

$[15$ Marks$]$

NB: SHOW ALL WORKING; DO NOT USE PYTHON