Chapter 11: Biostatistics and Data Handling

Select the correct answer:

1. In experiment examining the effects of pH levels on the activity of the enzyme, independent variable will be

A. pH

B. Temperature

C. Substrate

D. Reaction time

Answer: A. pH

Explanation: The independent variable is the one that the researcher manipulates. In this experiment, the researcher changes the pH levels to observe their effect on enzyme activity.

2. The variable that the experimenter changes in the experiment to check its effect during experiment is called.

A. Dependent variable

B. Independent variable

C. Control variable

D. Experimental variable

Answer: B. Independent variable

Explanation: The independent variable is the factor that is deliberately changed or manipulated by the researcher in an experiment.

3. Variables that researcher measure to determine the effect of the independent variable is also known as:

A. Outcome variables

B. Input variables

C. Cause variables

D. Control variable

Answer: A. Outcome variables

Explanation: The dependent variable (also called the outcome variable) is what the researcher measures. It is the outcome that is affected by the independent variable.

4. To which of the following field of life sciences, biostatistics is not applicable?

A. Health

B. Chemical engineering

C. Agriculture

D. Medicine

Answer: B. Chemical engineering

Explanation: Biostatistics applies to biological and health-related fields like health, agriculture, and medicine. Chemical engineering is a physical science and engineering discipline, although statistics can be applied, it is not a field of life science.

5. 25th percentile is the value __ of the data points lie.

A. Above which 25%

B. Below which 25%

C. ¼ th

D. 25

Answer: B. Below which 25%

Explanation: The 25th percentile (also known as the first quartile, Q1) is the value below which 25% of the data points fall.

6. Biostatistics is not involved in:

A. Epidemiological studies

B. Agriculture

C. Petroleum industry

D. Public Health

Answer: C. Petroleum industry

Explanation: Biostatistics is applied to biological and health-related data. Petroleum industry is not a biological field, although statistics can be used in it, it is not biostatistics.

7. The factors that must be kept constant during an experiment across both the experimental and control groups are known as

A. Control variables

B. Outcome variables

C. Input variables

D. Cause variables

Answer: A. Control variables

Explanation: Control variables are factors that are kept constant throughout the experiment to ensure that the results are due to the independent variable and not other factors.

8. All of the following 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.

9. The symbol for mean is:

A. "x̄ " (read as "x bar")

B. "x̄ " (read as "x tilde")

C. "x̄ " (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).

10. 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).

11. Find the mode from the data set 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.

12. 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 into the host organism

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.

13. 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.

14. 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.

15. 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. How Standard Deviation is different from Range?

Answer: Range is the simplest measure of dispersion. It is the difference between the highest and lowest values in a data set. Standard deviation is a more sophisticated measure of dispersion. It measures the average distance of each data point from the mean. Range only considers two extreme values, while standard deviation considers all values in the data set. Standard

deviation is more reliable for describing variability.

2. What are the demerits of relying on range to decide future plans in scientific experiments?

Answer: Relying solely on range to make future plans has demerits:

1. Sensitive to Outliers: Range is greatly affected by extreme values (outliers), which may not represent the typical data.

2. Ignores Distribution: It only uses the maximum and minimum values, ignoring the distribution of data in between.

3. Less Informative: It does not provide information about the spread of most data points around the mean.

4. Unreliable for Prediction: Due to these limitations, range alone is not reliable for predicting future trends or outcomes.

3. Why control group is important for scientific experiments?

Answer: A control group is essential in scientific experiments because it provides a baseline for comparison. The control group is not exposed to the independent variable or treatment being tested. By comparing the experimental group (which receives the treatment) to the control group, researchers can determine if the treatment had a significant effect. Without a control group, it is impossible to know if changes are due to the treatment or other factors. It helps to eliminate alternative explanations.

4. 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.

5. Write down the formulas 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. Mode: The value with the highest frequency.

6. 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).

7. 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.

8. 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

9. 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.

10. 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.

11. 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.

12. Find the mode from the data set given 46, 49, 55, 58, 62, 66, 64, 65, 66, 67, 68, 70, 72:

Answer: The mode is 66.

Explanation: In the given data set, the number 66 appears twice, while all other numbers appear only once. Therefore, 66 is the mode.

13. Calculate the median of the values given in dataset of above question 13.

Answer: (Note: The question refers to the dataset in question 12) Data set: 46, 49, 55, 58, 62, 64, 65, 66, 66, 67, 68, 70, 72

Number of values (n) = 13 (odd)

Median = (n+12)th value = (13+12)th = 7th value

Arranged in order: 46, 49, 55, 58, 62, 64, 65, 66, 66, 67, 68, 70, 72 The 7th value is 65. Therefore, the median is 65.

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. It has several advantages and disadvantages.

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).

5. Easy to Calculate: For ungrouped data, the median is easy to determine by simply arranging the data and finding the middle value.

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. Not Representative of the Whole: The median may not be representative of the entire data set, especially if the data is skewed.

5. 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. Describe detailed procedure to add error bars in the graph.

Answer: Error bars are graphical representations of the variability of data. They are used on graphs to indicate the error or uncertainty in a reported measurement. Adding error bars involves the following procedure:

1. Calculate the Error:

Standard Deviation (SD): Calculate the standard deviation of the data set. This measures the spread of data around the mean. Standard Error of the Mean (SEM): Calculate the SEM, which is SD/[source symbol unavailable]n (where n is the sample size). This measures the precision of the mean. Confidence Interval (CI): Calculate the 95% CI, which is the range in which the true mean is likely to lie.

2. Create the Graph:

Plot the data (e.g., mean values) on a bar chart, line graph, or scatter plot.

3. Add Error Bars:

In Excel: Select the data series, go to "Chart Elements" (+), check "Error Bars," and choose "More Options." Select "Custom" and specify the error amount (e.g., SD, SEM, or CI). In Google Sheets: Select the chart, go to "Customize" > "Series," and check "Error bars." Enter the error value. In GraphPad Prism: Enter data, choose the graph type, and select the error bar option (SD, SEM, CI).

4. Interpret Error Bars:

Small Error Bars: Indicate low variability and high precision. Large Error Bars: Indicate high variability and low precision. Overlapping Error Bars: Suggest no significant difference between groups. Non-Overlapping Error Bars: Suggest a significant difference.

In summary, adding error bars involves calculating the error, plotting the graph, and using software to add the error bars. They provide a visual indication of data variability and help in interpreting results.

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

Answer:

Cumulative frequency for Class 1 = 30

Cumulative frequency for Class 2 = 30 + 50 = 80

Cumulative frequency for Class 3 = 80 + 60 = 140

Cumulative frequency for Class 4 = 140 + 40 = 180

Cumulative frequency for Class 5 = 180 + 30 = 210

4. 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.

5. 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.

6. Sketch and label the Pie-chart by using the data given in the table below about the deaths of vulture birds due to pollution in last five years? Also label the data values in the pie-chart.

Answer: (Diagram Description)

Total deaths = 250 + 400 + 275 + 350 + 175 = 1450 Calculate the angle for each year: (Deaths / Total) × 360°

2019: (2501450) × 360 = 62.07°

2020: (4001450) × 360 = 99.31°

2021: (2751450) × 360 = 68.28°

2022: (3501450) × 360 = 86.90°

2023: (1751450) × 360 = 43.45°

Pie Chart: Draw a circle and divide it into sectors with the calculated angles. Label each sector with the year and the number of deaths (e.g., "2019: 250"). Add a title: "Vulture Deaths Due to Pollution (2019-2023)".

7. 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.

8. Compare and contrast control variables, dependent variables and independent variables.

Answer:

Comparison:

Independent and dependent variables are the primary focus of the experiment. Control variables are kept constant to ensure a fair test. All three are essential for a well-designed experiment.

Contrast:

Independent variable is changed; dependent variable is measured; control variables are kept constant. Independent variable is the cause; dependent variable is the effect.

9. Describe the usage of percentile along with its demerits.

Answer: A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls. For example, the 25th percentile is the value below which 25% of the data lies.

Usage:

Growth Charts: Used to track the growth of children (e.g., height and weight percentiles). Test Scores: Used to rank test scores (e.g., a student scoring in the 90th percentile scored better than 90% of test- takers). Health Indicators: Used in epidemiology to describe the distribution of health-related variables (e.g., BMI percentiles). Income Distribution: Used to describe income inequality (e.g., 90th percentile income).

Demerits:

Misleading if Distribution is Skewed: Percentiles can be misleading if the data is not normally distributed. Ignores Absolute Values: Percentiles only provide relative position, not absolute values. Misinterpretation: Often misinterpreted by the public (e.g., "50th percentile" does not mean average). Requires Large Sample: To be reliable, percentiles require a large sample size.

In summary, percentiles are useful for describing relative position, but they have limitations and can be misinterpreted.

10. Describe stepwise details to make the appropriate chart with proper title, labeled axes, legend, axes units from a fictitious data set.

Answer: Creating an appropriate chart involves several steps. Let's use a fictitious data set of average monthly temperatures for two cities (City A and City B) over a year.

1. Choose the Chart Type: For comparing trends over time, a line graph is appropriate.

2. Prepare the Data: Organize data in a table with months as the independent variable and temperature as the dependent variable for both cities.

3. Draw Axes:

X-axis: Represent months (Jan-Dec). Label as "Month". Y-axis: Represent temperature (°C). Label as "Temperature (°C)".

4. Choose Scale: Select appropriate scales for both axes (e.g., 0-40°C for y-axis).

5. Plot Data: Plot points for City A and connect them with a line. Plot points for City B and connect them with a different colored line.

6. Add Title: "Average Monthly Temperatures for City A and City B".

7. Add Legend: Indicate which line represents City A and which represents City B.

8. Label Axes Units: Ensure axes units are clearly labeled (°C, months).

9. Review and Finalize: Check for clarity, accuracy, and readability.

In summary, creating a chart involves choosing the right type, preparing data, drawing and labeling axes, plotting data, adding a title and legend, and reviewing the final product.