FUNDAMENTALS OF FINANCIAL STATISTICS

An Introduction to Statistics: Making Sense of the Numbers

What's the Big Idea?

Imagine you are the manager of a new Chicken Inn branch in Bulawayo. How do you decide how many chickens to cook each day? If you cook too many, you waste money. If you cook too few, you lose sales and customers get angry. You can't just guess. You need information, or what we call data. You might track your sales every day for a month, notice that you sell more on Fridays, and use that information to plan better. What you are doing is using statistics.

At its core, statistics is the science of collecting, organising, analysing, and interpreting numerical data to make better decisions. It is a powerful tool that helps us move from raw, confusing information to clear, useful knowledge. We are surrounded by statistics every day. When ZIMSTAT (the Zimbabwe National Statistics Agency) announces the monthly inflation rate, that's statistics. When an agronomist in Mashonaland Central calculates the average maize yield per hectare for a district, that's statistics.

This chapter is your introduction to this essential subject. We will learn what statistics is, why it is so important for business and government, and also understand its limitations. Mastering these basic ideas will give you the ability to understand the numbers that shape our world and to use them to your advantage.

Key Vocabulary

• Statistics: The science of collecting, analysing, and interpreting data to make decisions. It can also refer to the data itself (e.g., "sales statistics").
• Data: A collection of facts, such as numbers, words, measurements, or observations.
• Population: The complete set of all possible people or items that you are interested in studying.
• Sample: A smaller, manageable group selected from the population, which is used to represent the whole population.

The Core Concepts Explained

1. The Meaning of the Term Statistics
   The word 'statistics' can be used in two different ways:
   • As a plural noun: It refers to numerical facts or data. For example, "The latest statistics show that tourist arrivals have increased."
   • As a singular noun: It refers to the subject itself—the science and methods used to work with data. For example, "Statistics is a required module for this course."
2. The Purpose of Statistics
   The main purpose of statistics is to help us make effective decisions in the face of uncertainty. It does this by:
   • Presenting Facts Clearly: It organises complex data into a simple, definite form. An average is much easier to understand than a list of a thousand numbers.
   • Simplifying Complexity: It provides a summary of a large amount of information. For instance, the RBZ uses a single inflation figure to represent price changes across thousands of goods.
   • Allowing for Comparison: It gives us a basis to compare different groups or different time periods. Are sales this year better than last year? Statistics can tell us.
   • Helping in Forecasting: By analysing past data (e.g., rainfall patterns), we can make educated predictions about the future, which is vital for farming and business planning.
   • Informing Policy: The government uses census data on population, income, and housing to decide where to build new schools and clinics.
3. The Uses of Statistics
   Statistics is used in almost every field:
   • In Business: A company like Econet uses statistics for market research to understand customer needs. A manufacturer like Delta Corporation uses it for quality control to ensure their drinks meet standards.
   • In Economics: The Ministry of Finance and the Reserve Bank of Zimbabwe rely heavily on statistics like Gross Domestic Product (GDP), inflation rates, and employment figures to manage the nation's economy.
   • In Government Administration: Statistics are the eyes and ears of the government, helping to allocate resources efficiently, from distributing drought relief food to planning national infrastructure projects.
4. The Limitations of Statistics
   While powerful, statistics has important limitations that you must always remember:
   • It deals with groups, not individuals. Statistics can tell you the average income in a town, but it can't tell you what a specific person, like your Uncle John, earns.
   • It can be misused. Data can be manipulated to support a certain argument. You should always be critical and ask where the numbers came from. As the saying goes, "There are three kinds of lies: lies, damned lies, and statistics."
   • It only studies numerical features. Statistics is good at measuring things you can count (quantitative data), but it cannot easily measure qualitative things like honesty, friendship, or patriotism.
   • Its conclusions are only true "on average." Statistical predictions are about probability, not certainty. An economic forecast is a well-informed estimate, not a guarantee.

Worked Example: "Putting it to Work in Zimbabwe"

Scenario: The manager of a Bakers Inn in Masvingo wants to find out if customers would buy a new product: a "boerewors sausage roll." It would be a waste of money to produce thousands if nobody wants them.

• Purpose of Statistics: To make a smart, profitable business decision and avoid wasting resources.
• Use of Statistics: The manager decides to conduct market research. She prepares a simple survey and asks 100 customers over a weekend if they would be interested in the new product. This is a business use of statistics.
• Population vs. Sample: The population is all the potential customers of Bakers Inn in Masvingo. It's impossible to ask all of them. So, the manager surveys a sample of 100 customers and hopes their answers represent the entire population.
• A Limitation of Statistics: After the survey, 70% of the sample say they are interested. The manager knows this is not a guarantee of success. The result is only true on average, and the sample might not perfectly represent everyone. However, it gives her much more confidence than simply guessing.

Common Mistakes to Avoid

• Believing Statistics are 100% Fact: Remember, statistics are often based on samples and come with limitations. Always think critically about the numbers you see.
• Ignoring the Source: Not asking where the data came from. A survey conducted by a company selling a product might be biased compared to one from an independent research firm.
• Confusing the plural and singular meaning of statistics.

Collection of Data: Finding the Raw Materials

What's the Big Idea?

Think of a chef who wants to cook a delicious meal. The quality of the final dish depends entirely on the quality of the ingredients they start with. If they use rotten tomatoes, the soup will be terrible, no matter how skilled they are. It’s the same with statistics. The process of gathering information is called data collection, and it is the most important step. If we collect bad, inaccurate, or biased data, our final analysis will be useless. There is a famous saying in statistics: "Garbage in, garbage out."

So, how do we get good "ingredients"? A market researcher for a company like Schweppes might stand in a supermarket and ask people what they think of a new drink flavour. An agricultural extension officer might visit a farm in Mvurwi and measure the height of maize plants. ZIMSTAT sends people to every corner of the country to count the population during a census. These are all methods of data collection. Understanding these methods is the first step in learning how to produce trustworthy and useful statistics.

Key Vocabulary

• Primary Data: First-hand data that you collect yourself for your specific purpose (e.g., conducting your own survey).
• Secondary Data: Data that was already collected and published by someone else (e.g., using a report from ZIMSTAT).
• Qualitative Data: Descriptive, non-numerical data (e.g., a person's favourite colour, their opinion on a service).
• Quantitative Data: Numerical data that can be counted or measured (e.g., the number of people in a room, a person's age).
• Sampling: The process of selecting a representative group (a sample) from a larger population to study.

The Core Concepts Explained

1. Types of Data
   All data can be divided into two main categories:
   • Qualitative Data: This is descriptive data. It helps us understand the "why" and "how." Examples include interview responses, favourite kombi routes, or brands of soap.
   • Quantitative Data: This is numerical data. It can be further divided into two types:
     • Discrete Data: Can only be a whole number. It is counted. Examples: The number of cattle on a farm (you can't have 10.5 cattle), the number of cars passing a tollgate.
     • Continuous Data: Can take any value within a range. It is measured. Examples: A person's height (1.75m), the weight of a sack of potatoes (50.3kg), the temperature.
2. Methods of Data Collection
   We can collect data ourselves (primary data) or use data someone else has already collected (secondary data).
   • Primary Data Methods:
     • Surveys and Questionnaires: Asking people a set of questions. This can be done face-to-face, over the phone, or online. This is the most common method in business.
     • Observation: Watching and recording behaviour without asking questions. For example, counting the number of people who enter a shop.
     • Experiments: A controlled study to test a hypothesis. For example, testing which of two fertilizers produces a better yield.
   • Secondary Data Sources:
     This is data that already exists. It is often quicker and cheaper to use. Examples include reports from ZIMSTAT, the Reserve Bank of Zimbabwe, academic journals, company annual reports, and newspapers.
3. Sampling Methods
   It is usually too expensive and time-consuming to survey an entire population. Instead, we select a smaller sample.
   • Random Sampling: Every person in the population has an equal chance of being selected. This is the best way to get an unbiased, representative sample.
   • Systematic Sampling: Selecting every "nth" person from a list. For example, surveying every 10th person on a client list.
   • Stratified Sampling: First, divide the population into important subgroups (strata), then take a random sample from each group. This ensures all groups are fairly represented.
   • Convenience Sampling: Choosing people who are easy to find and survey. This method is fast and easy, but it is often very biased.

Worked Example: "Putting it to Work in Zimbabwe"

Scenario: The Ministry of Higher and Tertiary Education wants to research how students at polytechnics across Zimbabwe are using mobile data for their studies. They want to know the average amount of money students spend on data per month.

• Population: All students enrolled at every polytechnic in Zimbabwe.
• Data Collection Method: It is impossible to ask every single student. A survey using a questionnaire is the best method.
• Sampling Method: They decide to use Stratified Sampling.
  1. They divide the population into strata (each of the polytechnics).
  2. From each polytechnic, they select a random sample of 50 students. This ensures students from every institution are included.
• Types of Data Collected:
  1. "How much did you spend on data last month (in USD)?" - The answer is Quantitative (Continuous) data.
  2. "What is the main network you use for your studies?" - The answer is Qualitative data.

Common Mistakes to Avoid

• Using a Biased Sample: Only surveying students in the library about study habits. This is a convenience sample and will be biased.
• Confusing Discrete and Continuous Data: Forgetting that things that are counted are discrete, and things that are measured are continuous.
• Asking Bad Questions: Using leading or confusing questions in a questionnaire, which results in poor quality data.

Classification and Tabulation of Data: Bringing Order to Chaos

What's the Big Idea?

Imagine you have just finished harvesting and you have one massive bag filled with a mixture of maize, sorghum, and rapoko. Before you can use it, you have to sort it into separate piles. This sorting process is exactly what we do in statistics. Classification is sorting raw data into logical groups, and Tabulation is putting this sorted information into a neat table. This step is essential because it brings order to the chaos of raw data, making it easier to understand and analyze.

Key Vocabulary

• Classification: The process of arranging raw data into groups or classes according to their common features.
• Frequency: The number of times a particular value or observation appears in a data set.
• Frequency Distribution Table: A table that shows the different data classes and the frequency for each class.
• Class Interval: The range of a specific group in a frequency distribution table (e.g., "$10 up to $20").
• Tabulation: The systematic arrangement of classified data into rows and columns.

The Core Concepts Explained

The Frequency Distribution Table is the most important tool for classifying data. It shows us how "frequently" a value occurs. For example, if we survey 10 families on the number of children they have, the raw data might be: 2, 3, 1, 2, 4, 2, 1, 3, 2, 0. We can tabulate this as follows:

This table is much clearer than the original list. We can now easily see that the most common number of children is 2.

Presentation of Data: A Picture is Worth a Thousand Numbers

What's the Big Idea?

Data presentation is the art of turning the numbers in our tables into visual formats like charts and graphs. A well-designed graph can tell a story at a glance, making it easy to spot trends, make comparisons, and see relationships in our data.

Key Vocabulary

• Bar Chart: Uses bars of different heights to compare the values of different categories.
• Pie Chart: A circular chart divided into slices, used to show the proportion of each part of a whole.
• Histogram: A special type of bar chart for continuous data, where the bars touch each other.
• Line Graph: Uses points connected by lines to show how a value changes over time.

The Core Concepts Explained: Methods of Presenting Data

• Bar Charts: Perfect for comparing different, separate categories (e.g., sales figures for different branches). The bars have gaps between them.
• Pie Charts: Best for showing how a total amount is divided (e.g., budget allocation). Each slice's angle is calculated as (Value / Total) × 360°.
• Histograms: Used for continuous data from a frequency table. The bars touch to show the data is continuous.
• Line Graphs: The number one choice for showing a trend over time. The horizontal axis is always time.

Measures of Central Tendency: Finding the 'Typical' Value

What's the Big Idea?

A measure of central tendency summarizes a set of different numbers with a single, "typical" or "central" value. It helps us find a simple answer to questions like: What is the average salary? What is the most common age of our customers? These single numbers help us understand a dataset at a glance.

Key Vocabulary

• Central Tendency: A measure that represents the center point or typical value of a dataset.
• Mean: The arithmetic average, found by adding up all the values and dividing by the number of values.
• Median: The middle value in an ordered dataset.
• Mode: The value that appears most frequently.
• Outlier: An extremely high or low value that is very different from the rest of the data.

The 3 Ms: Mean, Median, and Mode

Worked Example:

A vendor's daily sales are: $20, $15, $18, $20, $22, $16, $50.

• Mean: (20+15+18+20+22+16+50) / 7 = 161 / 7 = $23.
• Median: First, order the data: 15, 16, 18, 20, 20, 22, 50. The middle value is $20.
• Mode: The value that appears most often is $20.

The high value of $50 is an outlier that pulls the mean up. Here, the median is a better measure of a "typical" day's sales.

Measures of Dispersion: How Spread Out is the Data?

What's the Big Idea?

Dispersion is a measure of how spread out or scattered the data is from the center (the mean). A small dispersion means the data points are clustered tightly together (consistent). A large dispersion means the data points are widely scattered (inconsistent). In business, understanding dispersion is just as important as knowing the average, as it helps measure risk and consistency.

Key Vocabulary

• Dispersion: The extent to which data points differ from each other or from the average.
• Range: The difference between the highest and lowest values.
• Variance: A measure of how far each number in the set is from the mean.
• Standard Deviation: The square root of the variance, and the most widely used measure of dispersion.

Worked Example:

Let's compare the sales of two vendors who both have a mean daily sale of $60:

• Vendor A's Sales (USD): 50, 55, 60, 65, 70
• Vendor B's Sales (USD): 10, 20, 60, 100, 110

Now, let's calculate the Range for both:

• Range A: 70 - 50 = $20
• Range B: 110 - 10 = $100

Analysis: Although their averages are identical, Vendor A has a much more stable business (small range), while Vendor B's business is highly inconsistent and risky (large range). The measure of dispersion revealed this important difference.