Introduction to Biostatistics: Main Exam, 8 April 2021

Mount Kenya University · Department of Community Health · Diploma in Community Oral Health, Diploma in Dental Technology · DMA1301

Mount Kenya University Introduction to Biostatistics 2020-2021 past paper with model answers for probability, mode, nominal, data presentation, sampling, hypothesis, mean

1. Define the following terms.

  1. a) Probability (2 marks)
    Model answer
    • Probability: The likelihood or chance that a particular event will occur, expressed as a fraction, decimal or percentage between 0 (impossible) and 1 (certain).
  2. b) Mode (2 marks)
    Model answer
    • Mode: The value or class that occurs most frequently in a data set; the most common observation.
  3. c) Nominal (2 marks)
    Model answer
    • Nominal: A level of measurement where data are categorized into mutually exclusive groups without any inherent order (e.g., gender, blood type).

2. Explain how ungrouped data can be presented (5 marks)

Model answer
  • Present raw values in a frequency table showing each observation and its count.
  • List the data in ascending or descending order (a sorted list).
  • Use a stem‑and‑leaf plot to display distribution while retaining original values.
  • Create a dot plot where each dot represents an individual observation.
  • Summarise with a simple bar chart of individual frequencies (one bar per value).

3. State two methods of data collection (5 marks)

Model answer
  • Questionnaire/Survey: Structured set of written questions administered to respondents.
  • Observation: Direct systematic watching and recording of behaviours or events in their natural setting.

4. Explain two types of hypothesis (5 marks)

Model answer
  • Null hypothesis (H₀): A statement of no effect or no difference, which is tested statistically and assumed true until evidence suggests otherwise.
  • Alternative hypothesis (H₁ or Ha): The statement that there is an effect or difference; it is accepted if the null hypothesis is rejected.

5. The exam grades of 7 students are given below. 70, 66, 72, 96, 46, 90, 50 Find

  1. a) the mean (2.5 marks)
    Model answer
    • Sum the grades: 70+66+72+96+46+90+50 = 490
    • Number of students = 7
    • Mean = Total / N = 490 ÷ 7 = 70
  2. b) the sample standard deviation (2.5 marks)
    Model answer
    • Find the mean (from part a) = 70
    • Calculate each deviation from the mean, square it, and sum:
    • (70‑70)²=0, (66‑70)²=16, (72‑70)²=4, (96‑70)²=676, (46‑70)²=576, (90‑70)²=400, (50‑70)²=400 → Σ = 2072
    • Sample variance = Σ/(n‑1) = 2072/6 = 345.33
    • Sample standard deviation = √345.33 ≈ 18.6

6. Explain two types of sampling data (5 marks)

Model answer
  • Cross‑sectional data
  • Collected at one point in time from a sample or population
  • Provides a snapshot of characteristics or outcomes
  • Useful for prevalence studies and comparing groups
  • Longitudinal (time‑series) data
  • Collected from the same subjects repeatedly over time
  • Allows assessment of trends, incidence, and causal relationships
  • Requires more resources and careful follow‑up

7. Describe measures of dispersion (5 marks)

Model answer
  • Range: maximum – minimum; simple but affected by outliers
  • Inter‑quartile range (IQR): Q3 – Q1; shows spread of middle 50 % and resists extremes
  • Variance: average of squared deviations from the mean; basis for other measures
  • Standard deviation: square root of variance; expressed in original units
  • Coefficient of variation (CV): (SD/mean) × 100 %; expresses relative dispersion

SECTION B

1. Discuss two methods of data sampling (15 marks)

Model answer
  • Simple random sampling
  • Every individual has an equal chance of selection
  • Reduces selection bias; easy to analyse statistically
  • Requires a complete sampling frame
  • Stratified sampling
  • Population divided into homogeneous sub‑groups (strata) then random samples taken from each
  • Improves precision for key sub‑populations
  • More complex design and analysis
  • Systematic sampling
  • Select every k‑th element after a random start
  • Simple to implement in field surveys
  • Can introduce bias if there is a hidden periodicity
  • Cluster sampling
  • Whole groups (clusters) are randomly chosen; all members within selected clusters are studied
  • Cost‑effective for dispersed populations
  • Increases sampling error; clusters must be internally heterogeneous
  • Multistage sampling
  • Combines two or more methods (e.g., select districts → schools → students)
  • Flexible and practical for large, diverse populations
  • Requires careful planning to maintain representativeness

2. Critique five measures of central tendency (15 marks)

Model answer
  • Mean
  • Sensitive to extreme values; may not represent skewed data
  • Easy to compute and widely used in parametric tests
  • Median
  • Robust to outliers; better for skewed distributions
  • Less efficient than mean for normal data; not additive
  • Mode
  • Useful for categorical or multimodal data
  • May be absent or multiple; provides limited information on central tendency
  • Geometric mean
  • Appropriate for multiplicative data (e.g., growth rates)
  • Difficult to interpret for data with zeros or negatives
  • Trimmed mean
  • Reduces influence of outliers by discarding a percentage of extreme scores
  • Choice of trimming proportion can be arbitrary; reduces sample size

3. Discuss various methods of presenting data (15 marks)

Model answer
  • Tabular presentation: organizes data in rows and columns for precise values and easy reference.
  • Bar chart: displays categorical data with rectangular bars; height/length proportional to frequency.
  • Histogram: shows distribution of continuous data using adjacent bars; indicates shape, central tendency, spread.
  • Pie chart: represents parts of a whole for categorical percentages; each slice angle equals proportion.
  • Line graph: plots data points connected by lines; ideal for showing trends over time or ordered categories.
  • Stem‑and‑leaf plot: retains original data while showing distribution; useful for small to moderate data sets.
  • Box‑and‑whisker plot: summarizes five‑number summary (minimum, Q1, median, Q3, maximum); highlights skewness and outliers.
  • Scatter plot: displays relationship between two quantitative variables; helps assess correlation.
  • Frequency polygon: line joining mid‑point frequencies of a histogram; useful for comparing multiple distributions.
  • Pareto chart: bar chart ordered by descending frequency with cumulative line; identifies most significant factors.
  • Dot plot: simple representation of individual observations; good for small data sets.
  • Heat map: uses colour intensity to show magnitude across two dimensions; effective for large matrices.
  • Cumulative frequency curve (Ogive): plots cumulative frequencies; assists in determining percentiles.
  • Radar/spider chart: displays multivariate data on axes radiating from a central point; useful for comparing profiles.
  • Control chart: plots process data over time with control limits; monitors stability in quality control.
  • More answers: stacked bar chart, waterfall chart, Gantt chart for time‑based project data.

More Introduction to Biostatistics papers · All dental past papers