Chapter 11: Biostatistics and Data Handling

Select the correct answer:

1. To which of the following fields of life sciences, biostatistics is not applicable?, and.:

A) health

B) chemical engineering

C) agriculture

D) medicine

Answer: B) chemical engineering

Explanation: Biostatistics is the application of statistics to biological and health-related fields. It is widely used in health, medicine, agriculture, and public health. Chemical engineering is a physical science and engineering discipline, not a life science, so biostatistics is not a primary tool in this field (although statistics is used in chemical engineering, it is not "biostatistics").

2. Biostatistics is involved in:

A) Epidemiological studies

B) Agriculture

C) Economics

D) Public Health

Answer: D) Public Health (Note: Biostatistics is involved in epidemiological studies, agriculture, and public health. Economics is a social science. However, among the options, Public Health is the most directly related to biostatistics. Epidemiological studies are also a major part of biostatistics. If "all of the above" were an option, that would be correct. Given the choices, Public Health is the most encompassing answer related to biology and health.)

3. All of the followings are types of averages except:

A) Arithmetic Mean

B) Median

C) Mode

D) Product of data values

Answer: D) Product of data values

Explanation: Mean, median, and mode are measures of central tendency (averages). The product of data values is not a measure of average.

4. The symbol for mean is:

A) "x̄ " (read as "x bar")

B) "x"̃ (read as "x tilde")

C) "x̂ " (read as x-hat)

D) "μ" (read as highly stable)

Answer: A) "x̄ " (read as "x bar")

Explanation: The symbol for sample mean is x̄ (x-bar). The symbol for population mean is μ (mu).

5. Formula of "Mean" for un-group data is:

A) Σx / n

B) Σx / 2

C) Σf / n

D) n+12

Answer: A) Σx / n

Explanation: The mean for ungrouped data is calculated by summing all the data values (Σx) and dividing by the total number of values (n).

6. Find the mode from this dataset given 46, 49, 55, 58, 62, 66, 64, 65, 66, 67, 68, 70, 72:

A) 46

B) 62

C) 66

D) 72

Answer: C) 66

Explanation: The mode is the value that appears most frequently. In this data set, 66 appears twice, while all other values appear once.

7. The first step in genetic engineering is:

A) Isolation of the gene of interest

B) Insertion of the gene into a vector

C) Transfer of recombinant DNA

D) Expression of the gene

Answer: A) Isolation of the gene of interest

Explanation: The first step in genetic engineering is to isolate the specific gene that is to be transferred or manipulated.

8. Biostatistics is similar to maths because of:

A) Calculations

B) Counting birds

C) Used of symbol pie

D) It is also useful in engineering studies

Answer: A) Calculations

Explanation: Biostatistics is similar to mathematics because it relies heavily on calculations, formulas, and numerical analysis to interpret biological data.

9. If the numbers of diseased persons is greater in 2nd year of study than 1st year then

A) Height of the bar will be greater in 1st year

B) Width of the bar will be greater in 1st year

C) Height of the bar will be smaller in 1st year

D) Width of the bar will be greater in 2nd year

Answer: C) Height of the bar will be smaller in 1st year

Explanation: In a bar chart, the height of the bar represents the frequency or value. If the number of diseased persons is greater in the 2nd year, the bar for the 1st year will be smaller in height.

10. In a bar chart of number of deaths due to hepatitis in Pakistan in last 10 years what will we write at the x-axes of graph?

A) years

B) number of deaths

C) any of the value

D) causes of hepatitis

Answer: A) years

Explanation: The x-axis (horizontal axis) typically represents the independent variable, which in this case is the time period (years). The y-axis would represent the number of deaths.

1. Define mean, median and mode.

Answer:

Mean: The arithmetic average. It is calculated by summing all values in a data set and dividing by the total number of values. Median: The middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values. Mode: The value that appears most frequently in a data set. A data set can have one mode, multiple modes, or no mode.

2. Write down the formulae of mean, median and mode.

Answer:

Mean (Ungrouped Data): x̄ = Σx / n (where Σx is the sum of all values, n is the number of values)

Mean (Grouped Data): x̄ = Σfx / Σf (where f is frequency, x is midpoint)

Median (Ungrouped Data): Arrange data in order. If n is odd, median = (n+12)th value. If n is even, median = average of

(n/2)th and (n/2 + 1)th values.

Median (Grouped Data): Median = L + [n/2 - cff] × h (where L is lower limit of median class, cf is cumulative frequency before median class, f is frequency of median class, h is class width) Mode: The value with the highest frequency.

3. What is importance of mean calculation?

Answer: The mean is important because it is the most commonly used measure of central tendency. It uses all data values in its calculation, making it representative of the entire data set. It is useful for comparing different data sets. It is the basis for many statistical tests, such as t-tests and ANOVA. It is also used to calculate other statistics like variance and standard deviation. However, it can be affected by extreme values (outliers).

4. Why value of mean is not completely reliable to get the correct picture?

Answer: The mean is not completely reliable because it is highly sensitive to extreme values (outliers). A single very high or very low value can significantly skew the mean, making it unrepresentative of the typical data. For example, in a data set of incomes where one person earns billions and others earn thousands, the mean income would be very high and not reflect the typical income. In such cases, the median is a more reliable measure.

5. Write the formula for calculation of Mode.

Answer: For grouped data, the mode can be calculated using the formula:

Mode = L + [f₁ - f₀2f₁ - f₀ - f₂] × h Where:

L = Lower limit of the modal class

f₁ = Frequency of the modal class

f₀ = Frequency of the class preceding the modal class

f₂ = Frequency of the class succeeding the modal class

h = Class width

6. How bar chart is different from pie-chart?

Answer: A bar chart uses rectangular bars to represent data. The height or length of the bar represents the value. Bars can be arranged horizontally or vertically. A pie chart is a circular graph divided into sectors (slices). Each sector represents a proportion of the whole. Bar charts are better for comparing discrete categories, while pie charts are better for showing parts of a whole (percentages). Bar charts can display negative values; pie charts cannot.

7. Write one similarity and one difference between rectangle graph and pie-graph.

Answer:

Similarity: Both are graphical methods used to visually represent data. Difference: A rectangle graph (bar chart) uses rectangular bars to compare quantities across categories. A pie graph uses a circle divided into sectors to show the proportion of each category relative to the whole.

8. How graphical representation of data is important that tabular representation?

Answer: Graphical representation is often more effective than tabular representation because it provides a visual summary of data that is easier to understand and interpret. Graphs can quickly reveal trends, patterns, and outliers that might be missed in a table. They are more engaging and can communicate complex information to a wider audience. Graphs facilitate comparison between

different data sets. However, tables provide precise numerical values, while graphs may approximate.

9. Find the mode from the data set given 84, 91, 72, 68, 87, 78, 86, 82, 83, 84:

Answer: The mode is 84.

Explanation: In the given data set, the number 84 appears twice, while all other numbers appear only once. Therefore, 84 is the mode.

10. Calculate the median of the values given in dataset of question 9 above.

Answer: Data set: 84, 91, 72, 68, 87, 78, 86, 82, 83, 84 Arrange in ascending order: 68, 72, 78, 82, 83, 84, 84, 86, 87, 91

Number of values (n) = 10 (even)

Median = Average of (n/2)th and (n/2 + 1)th values

Median = Average of 5th and 6th values

5th value = 83, 6th value = 84

Median = 83 + 842 = 83.5

1. What are advantages and disadvantages of Median?

Answer:

The median is a measure of central tendency that represents the middle value of a data set.

Advantages of Median:

1. Not Affected by Outliers: The median is not affected by extreme values (outliers). This makes it a more robust measure of central tendency than the mean when the data contains outliers.

2. Easy to Understand: The median is easy to understand and interpret. It is simply the middle value.

3. Can be Used with Open-Ended Data: The median can be calculated even if some data values are open-ended (e.g., "greater than 100").

4. Applicable to Ordinal Data: The median can be used with ordinal data (data that can be ranked but not measured precisely).

Disadvantages of Median:

1. Ignores All Values: The median only considers the middle value(s) and ignores the rest of the data. It does not use all the information available.

2. Not Suitable for Further Statistical Analysis: The median is not amenable to algebraic manipulation. It is not used in many advanced statistical tests.

3. Less Stable for Small Samples: For small samples, the median can be unstable and may not represent the population well.

4. Difficult for Grouped Data: For grouped data, the median is calculated using a formula and may be less intuitive.

In summary, the median is a useful measure of central tendency when data contains outliers or is skewed. However, it ignores much of the data and is less useful for advanced statistical analysis.

2. Complete the following table by filling the values of Cumulative frequency.

Answer:

3. Give details steps to construct the Bar-chart.

Answer: A bar chart is a graphical representation of data using rectangular bars. Steps to construct:

1. Collect and Organize Data: Gather the data and organize it into categories and frequencies.

2. Draw Axes: Draw a horizontal axis (x-axis) and a vertical axis (y-axis).

3. Label Axes: Label the x-axis with the categories. Label the y-axis with the frequency or value. Include units.

4. Choose Scale: Choose an appropriate scale for the y-axis that covers the range of values.

5. Draw Bars: For each category, draw a bar with a height corresponding to its frequency. Bars should be of equal width.

6. Space Bars Equally: Leave equal spaces between bars to distinguish categories.

7. Add Title: Add a clear, descriptive title to the chart.

8. Add Legend (if needed): If multiple data sets are shown, add a legend.

In summary, constructing a bar chart involves organizing data, drawing and labeling axes, choosing a scale, drawing bars, and adding a title.

4. For what the letters l, fm, f1, f2 and h stands in the given formula? For which calculation this formula is used? l + [fm - f12fm - f1 - f2] × h

Answer: The formula is used to calculate the Mode for grouped data.

The letters stand for:

l: Lower limit of the modal class (the class with the highest frequency). fm: Frequency of the modal class. f1: Frequency of the class preceding the modal class.

f2: Frequency of the class succeeding the modal class. h: Class width (size of the class interval).

The formula calculates the mode by adjusting the lower limit of the modal class based on the frequencies of the adjacent classes.

5. Sketch and label the bar-chart by using the data given in the table below about the deaths of vulture birds due to pollution in last five years?

Answer: (Diagram Description)

Title: Vulture Deaths Due to Pollution (2019-2023) X-axis: Years (2019, 2020, 2021, 2022, 2023) Y-axis: Number of Deaths (Scale: 0 to 450) Bars:

2019: Bar height = 250

2020: Bar height = 400

2021: Bar height = 275

2022: Bar height = 350

2023: Bar height = 175

Labels: Clearly label each axis and each bar with its value.

6. Draw a table and then sketch and label the bar-chart by using the data of height (in cm) collected from 200 students of 12th class of your college.

Answer: (This is a practical activity. A sample table and bar chart description is provided.)

Sample Table:

Bar Chart Description:

X-axis: Height Range (cm)

Y-axis: Frequency (No. of Students) Draw bars for each height range with heights corresponding to the frequencies. Title: Height Distribution of 12th Class Students.