Unit 11: Biostatistics — Long Questions

Introduction
Biostatistics is a branch of statistics that applies statistical methods to biological sciences.
Biostatistics is essential for designing biological experiments, clinical trials, and epidemiological studies.

Uses of Biostatistics
The major uses of biostatistics include:

1. Designing Experiments and Studies
Introduction
Biostatistics helps in planning and structuring experiments to ensure that the data collected will be relevant and sufficient to answer the research questions.
Example
In a clinical trial testing a new drug, biostatisticians determine the sample size needed to detect a significant effect.

2. Analyzing Biological Data
Introduction
Biostatistics involves applying statistical techniques to analyse data. This analysis can uncover trends, correlations and patterns.
Example
Analyzing the growth rates of plants under different environment conditions can reveal how factors like light and water affect growth.

3. Interpreting Results
Introduction
After analyzing data, biostatistics helps interpret the result in a meaningful way.
Example
Interpreting the results of a survey on the prevalence of a disease in a population can guide public health interventions.

4. Predicting Outcomes
Introduction
Biostatistics can be used to create models that predict future outcomes based on current data.
Example
Predicting the spread of an infectious disease within a population helps in planning vaccination campaigns and allocating resources.

5. Public Health and Policy Making
Introduction
In public health biostatistics provides evidence-based insights that guide policy decision and health guidelines.
Example
Statistical analysis of a data on COVID-19 rates can lead to the implementation of COVID-19 vaccination campaign.

Examples of the uses of the Biostatistics

1. Epidemiology
Introduction
Epidemiologists use biostatistics to study the distribution and determinants of health and diseases in populations.
Example
Analysing data on COVID -19 infection rates, recovery rates and the effectiveness of vaccines involves biostatistical methods.

2. Genetics
Introduction
Biostatistics is used in genetic research to analyse the inheiritance of traits and the association of genetic variations with diseases.
Example
Genetic studies use biostatistics to identify genetic markers linked to diseases like diabetes and cancer

3. Agriculture
Introduction
In agricultural research biostatistics helps in analyzing crop yields, the effectiveness of fertilizers, and the resistance of plants to pests and diseases.
Example
Comparing the yield of different wheat varieties under various farming practices involves statistical analysis.

4. Clinical Trials
Introduction
Biostatistics is crucial in the design and analysis of clinical trials that test new treatments and drugs.
Example
Determining whether a new medication is more effective than a placebo requires rigorous statistical testing to ensure the results are statistically significant

Mean, Median and Mode
The mean, median and mode are the measures that help summarize and understand data sets.

1. Mean
Introduction
The mean also known as the average is the sum of all the values in a data set divided by the number of values. It represents the central value of a data set.

Formula
Mean = Sum of All Data Points / Number of Data Points

Examples
Consider the following data set representing the heights (in cm) of five students:
150, 160, 165, 155, 170
Mean = (150+160+165+155+170)/5 = 800/5 = 160
So the mean height is 160 cm.

2. Median
Introduction
The median is the middle value of a data set when the values are arranged to ascending or descending order. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

Steps to Calculate Median
i) Arrange the data in ascending order.
ii) If the number of values (n) is odd, the median is the value at the position (n+1)/2
iii) If the number of values (n) is even, the median is the average of the values at positions (n/2) and (n/2 + 1).

Examples
Consider the data set: 150, 160, 165, 155, 170.
i. Arrange in ascending order: 150, 155, 160, 165, 170.
ii. Number of values (n) = 5 (odd).
iii. Median is the value at position (5+1)/2 = 3.
So, the median height is 160 cm.
For an even number of values, consider the data set: 150, 160, 165, 155.
iv. Arrange in ascending order: 150, 155, 160, 165
v. Number of values (n) = 4 (even).
vi. Median is the average of the values at positions (4/2) = 2 and (4/2 + 1) = 3.
Median = (155+160)/2 = 315/2 = 157.5
So, the median height is 157.5 cm.

3. Mode
Introduction
The mode is the value that appears most frequently in a data set. A data set may have one mode more than one mode or no mode at all.

Steps to Calculate Mode
i. Count the frequency of each value in the data set.
ii. The value with the highest frequency is the mode.

Example 1
Consider the data set 150, 160, 165, 155, 160.

• Frequencies 150 (1), 160 (2), 165 (1), 155 (1).
• The value with the highest frequency is 160. So the mode of the data set is 160.

Introduction
A bar chart is a graphical representation of data using bars of different heights or lengths.

Uses
It is used to compare the quantities of different categories. Bar charts are effective for comparing different categories and visually representing the distribution of data.

Steps to Create a Bar Chart
i. Gather the data to be represented in the bar chart.
ii. Arrange the data into categories and their corresponding values.
iii. Draw a horizontal axis (x-axis) and a vertical axis (y-axis).
iv. Label the x-axis with the categories and the y-axis with the values.
v. Determine the scale for the y-axis based on the range of values in the data set. Divide the axis into equal intervals.
vi. For each category draw a bar with a height corresponding to its value. Ensure the bars are of equal width and are spaced evenly.
vii. Label each bar with its category name and value.

Example
Consider the following data representing the number of different species of plants found in a field survey:

1. Collect Data: This data is already collected in the table above.
2. Organize Data: Data is organized in the table with species and their corresponding number of plants.
3. Draw Axes: Draw the x-axis and y-axis
4. Label the x-axis with the species: A, B, C, D, E. Label the y-axis with the values i.e. number of plants.
5. Scale the Axes: The highest value is 25. Use a scale with intervals of 5 i.e. 0, 5, 10, 15, 20, 25.
6. Draw Bars: For each species draw a bar up to the corresponding number of plants.
7. Label the Bars: Label each bar with the species name and its value.

1. Mean
The mean is the average of all values in the data set.
Steps
Add all the values together:
12 + 15 + 22 + 8 + 19 + 25 + 15 = 116
Divide the total by the number of values (7)
Mean = 116/7 = 16.57

2. Median
The median is the middle value of the data set when it is arranged in ascending order.
Steps
Arrange the data in ascending order:
8, 12, 15, 15, 19, 22, 25
Identify the middle value
Since there are 7 values (odd number) the median is the 4th value.
Median = 15

3. Mode
The mode is the values that occur most frequently in the data set.
Steps
Identify the frequency of each values
8 = 1 time
12 = 1 time
15 = 2 times
19 = 1 time
22 = 1 time
25 = 1 time
The value that occurs most frequently is 15
Mode = 15

Summary of Results
Mean = 16.57
Median = 15
Mode = 15

The following bar chart representing the number of different types of fruits sold at a market in one week. The chart includes labeled axes and a title for clarity.

Number of different types of fruits sold in one week.