Class 9 Biology Notes Chapter 11

Chapter 11: Biostatistics

Exercise Solution

A. Select the Correct Answers for the Following Questions

1. What is the primary purpose of biostatistics?

a) To analyse financial data
b) To apply statistical methods to biological sciences
c) To design engineering models
d) To study historical events

Correct Answer: (b) To apply statistical methods to biological sciences

2. In biostatistics, which method is used to predict future outcomes based on current data?

a) Designing experiments
b) Drawing charts
c) Taking average
d) Analysing data

Correct Answer: (d) Analysing data (or predictive statistical modelling)

3. Which of the following best describes the mean of a data set?

a) The most frequently occurring value
b) The middle value when data is ordered
c) The sum of all values divided by the number of values
d) The difference between the highest and lowest values

Correct Answer: (c) The sum of all values divided by the number of values

4. If the data set is 5, 8, 12, 15, 20, what is the median?

a) 8
b) 12
c) 15
d) 20

Correct Answer: (b) 12

5. What is the mean of the data set: 7, 8, 9, 10, 11?

a) 7
b) 8
c) 9
d) 10

Correct Answer: (c) 9

6. When the number of values in a data set is even, how is the median calculated?

a) By choosing the middle value
b) By taking the average of the two middle values
c) By selecting the most frequent value
d) By adding all values and dividing by the total number of values

Correct Answer: (b) By taking the average of the two middle values

7. In a data set with values 3, 3, 6, 7, 8, 9, 9, what is the mode?

a) 3
b) 6
c) 7
d) Both 3 and 9

Correct Answer: (d) Both 3 and 9

8. If a data set has no repeated values, what is the mode?

a) The highest value
b) The average of the data set
c) There is no mode
d) The median value

Correct Answer: (c) There is no mode

9. In a bar chart, what does the height or length of each bar represent?

a) The total number of categories
b) The value of the corresponding category
c) The average of all values
d) The difference between the highest and lowest values

Correct Answer: (b) The value of the corresponding category

10. When constructing a bar chart, which axis usually represents the categories?

a) Vertical axis (y-axis)
b) Horizontal axis (x-axis)
c) Both axes equally represent the categories
d) Neither axis represents the categories

Correct Answer: (b) Horizontal axis (x-axis)

B. Write Short Answers

1. Define biostatistics.

Answer: Biostatistics is the branch of statistics responsible for the design, collection, analysis, interpretation, and presentation of numerical data gathered from biological, medical, and public health research.

2. What is the median of a data set?

Answer: The median is the middle value when all numbers in a data set are arranged in ascending or descending order. If there is an even number of values, it is the average of the two central numbers.

3. How is the mean calculated?

Answer: The mean (arithmetic average) is calculated by taking the sum of all numerical values in a data set and dividing that sum by the total number of values.

4. What does the height of a bar in a bar chart represent?

Answer: The height or length of a bar represents the numerical frequency, quantity, or value associated with that specific category.

5. What is the mode of a data set?

Answer: The mode is the value that appears most frequently in a given data set. A set can have one mode (unimodal), more than one mode (multimodal), or no mode if no values repeat.

C. Write Answers in Detail

1. Explain the importance of biostatistics in the field of public health. Provide examples of how it is used to inform public health decisions.

Answer:

Importance: Biostatistics provides the quantitative tools necessary to evaluate health trends, assess disease outbreaks, design clinical trials, and determine the safety and efficacy of new vaccines or medicines.

Examples in Public Health Decisions:

Tracking the spread and mortality rates of infectious diseases, such as during pandemics, to allocate healthcare resources and guide public health measures.
Evaluating epidemiological data on smoking rates to formulate public health tobacco control policies.
Analysing clinical trial data to establish safe dietary guidelines or drug dosage recommendations.

2. Discuss the differences between mean, median, and mode. Include examples where each measure is most appropriate to use.

Answer:

Mean: The arithmetic average of a data set. It is best used for relatively symmetric data sets without extreme outliers.

Example: Calculating the average height of students in a class.

Median: The middle value when the data is arranged in order. It is best used for skewed data sets or data sets containing extreme outliers because outliers can distort the mean.

Example: Calculating household income when a few very wealthy households may increase the average considerably.

Mode: The value that occurs most frequently. It is particularly useful for categorical data or for identifying the most popular item.

Example: Determining the most frequently sold shoe size or the most common blood type.

3. Describe the steps involved in creating a bar chart using Excel. Include a discussion on how to customize the chart for better visualization and interpretation of data.

Answer:

Steps in Excel:

Enter the categorical data in one column and the corresponding numerical values in the adjacent column.
Highlight the data table.
Go to the Insert tab on the ribbon.
Click on the Column or Bar Chart option.
Select the standard 2-D Clustered Column Chart.

Customization for Better Visualization:

Add clear axis titles: the x-axis for categories and the y-axis for numerical values.
Give the chart a descriptive title.
Adjust bar colours for good contrast and visual appeal.
Remove distracting gridlines if necessary.
Add data labels directly onto the bars to make the values easier to read.

4. Provide a detailed example of how to calculate the mean, median, and mode of a data set. Use the following data set for your calculations: 12, 15, 22, 8, 19, 25, 15.

Answer:

Given Data Set: 12, 15, 22, 8, 19, 25, 15

Arranging the data in ascending order:

8, 12, 15, 15, 19, 22, 25

Total number of values: (N = 7)

1. Calculation of Mean

Formula:

Mean = Sum of all values ÷ Total number of values

Sum = 8 + 12 + 15 + 15 + 19 + 22 + 25

Sum = 116

Mean = 116 ÷ 7

Mean ≈ 16.57

2. Calculation of Median

Since there are seven values, the median is the middle value, which is the fourth value in the ordered data set.

8, 12, 15, 15, 19, 22, 25

Median = 15

3. Calculation of Mode

The number 15 appears twice, while all other numbers appear only once.

Mode = 15

5. You are given the following data set. Create a bar chart to represent the number of different types of fruits sold at a market in one week. Ensure that the axes are labelled and provide a title for the chart.

Apples: 30
Bananas: 45
Oranges: 20
Grapes: 25
Mangoes: 15

Answer:

Chart Title: Fruit Sales in One Week

X-Axis Label: Fruit Categories

Y-Axis Label: Number of Fruits Sold

Bar Chart (Text Representation)

Fruit Sales in One Week

Fruit Category	Number of Fruits Sold
Apples	30
Bananas	45
Oranges	20
Grapes	25
Mangoes	15

Bar Chart:

Number of Fruits Sold

Apples   | ██████       30
Bananas  | █████████    45
Oranges  | ████         20
Grapes   | █████        25
Mangoes  | ███          15

          Fruit Categories

Exact Values Represented by the Bars:

Apples = 30
Bananas = 45
Oranges = 20
Grapes = 25
Mangoes = 15

The bar chart shows that bananas were the most sold fruit, with 45 sold, while mangoes were the least sold fruit, with 15 sold.

Notes by Sir Dilawar

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