Measures of central tendency

Question 1

What are measures of central tendency

Answer 1

Measures of central tendency are statistical tools used to describe the center or typical value of a dataset — they show where most of the data points lie.

In simple terms, they tell you the “average” or “middle” of your data.

Question 2

State The Three Main Measures of Central Tendency.

Answer 2

Mode, Median, Mean

Question 3

Define the following:
1. Mode
2. Median
3. Mean

Answer 3

1. Mean
   *The arithmetic average — sum of all values divided by the number of values.
   → Formula: Mean= ∑f𝑥/𝑛 or ∑f𝑥/𝑛 if given table
2. Median
   *The middle value when data are arranged in order (from smallest to largest).
   If even number of values → average of two middle numbers.

Find position using (150+ 1)/ n, then do a frequency table

3. Mode
   The most frequent value in the dataset.

Question 4

Define measures of dispersion.

Answer 4

Measures of dispersion (also called measures of variability or spread) show how much the data values differ from each other or from the mean.

Question 5

State the measures of dispersion.

Answer 5

Range, IQR, Variance, Standard deviation, Coefficient of Variation (CV)

Question 6

Define relative risk.

Answer 6

Relative risk is the ratio of the probability (risk) of developing disease in the exposed group to the probability of developing disease in the non-exposed group.

It measures how much more (or less) likely exposed individuals are to develop the disease compared to those unexposed.

Question 7

State the formula for calculating relative risk.

Answer 7

RR=Risk in Unexposed/ Risk in Exposed​
=c/(c+d) / a/(a+b)​

Question 8

Describe how relative risk is interpreted.

Answer 8

Interpretation:

RR = 1: No association between exposure and disease

RR > 1: Exposure increases risk (possible risk factor)

RR < 1: Exposure decreases risk (possible protective factor)

Question 9

Define odds ratio

Answer 9

Odds ratio (OR) tells us how much more likely (or less likely) a certain outcome is in one group compared to another.

It compares the odds of disease (or event) in the exposed group to the odds in the unexposed group — mainly used in case–control studies.

Question 10

State the formula for calculating odds ratio.

Answer 10

OR=Odds of disease in unexposed/ Odds of disease in exposed​
OR= ad/bc

Question 11

Describe interpretation of odds ratio.

Answer 11

Interpretation:

OR = 1: No association

OR > 1: Positive association (exposure may increase odds of disease)

OR < 1: Negative association (exposure may be protective)

Question 12

In which studies do we use the following?
I. Relative risk
II. Odds ratio

Answer 12

I. Cohort studies
II. Case control studies

Question 13

What is p value?

Answer 13

The p-value (probability value) is the probability of obtaining the observed results, or results more extreme, if the null hypothesis is true.

In simpler terms, it tells us how likely it is that the results happened by chance.

Question 14

Define the following:
I. Null hypothesis (H₀)
II. Alternative hypothesis (H₁)

Answer 14

Null hypothesis (H₀): There is no difference or no association between the groups or variables.

Alternative hypothesis (H₁): There is a difference or association.

Question 15

Describe interpretation of p value.

Answer 15

1. p < 0.05
   *The result is statistically significant.
   *There is strong evidence against the null hypothesis.
   *We reject H₀ and accept that an association or difference likely exists.
2. p ≥ 0.05
   *The result is not statistically significant.
   *There is insufficient evidence to reject H₀ — the observed difference could be due to chance.

Question 16

Define confidence interval.

Answer 16

A confidence interval (CI) is a range of values that is likely to contain the true population parameter (e.g., mean, proportion, relative risk, odds ratio) with a certain level of confidence — usually 95%.

In simple terms, it tells us how precise our study estimate is and the degree of uncertainty around it.

Question 17

Interpret confidence intervals

Answer 17

1. Does NOT include 1 =The result is statistically significant (the exposure likely affects the outcome).
2. Includes 1= The result is not statistically significant (there may be no real association).

*Narrow CI: The estimate is precise (large sample, less variation).
*Wide CI: The estimate is less precise (small sample, more variation).

How to judge it in practice
*Look at the relative width:

Width ratio=Upper limit/ Lower limit

-If close to 1 → narrow
-If several times larger → wide

Question 18

OR = 0.7
95% CI = (0.4 – 1.3)
p = 0.21

Interpret.

Answer 18

Interpretation:

*OR < 1 → Exposure might be protective.
*CI includes 1 → Not statistically significant.
*p = 0.21 (> 0.05) → Not statistically significant.

➡️ Conclusion: No statistically significant association — the apparent protective effect could be due to chance.

Question 19

RR = 2.5
95% CI = (1.4 – 4.3)
p = 0.02

Interpret

Answer 19

*RR > 1 → Exposure increases risk.
*CI does not include 1 → Statistically significant.
*p = 0.02 (< 0.05) → Statistically significant.

➡️ Conclusion: Exposure is significantly associated with a 2.5-fold increased risk of disease.