Data analysis unit 2

Question 1

What are Measures of Central Tendency?

Answer 1

Think of central tendency as the “gravitational center” of your data.
When you collect a set of observations (for example, the number of hours students sleep), the distribution of values can look messy: some sleep 4 hours, some 9 hours, others 6. Central tendency gives us a single number that best summarizes the typical or most representative value of the group.

From your slides:

They represent the average magnitude of all observed values.

They establish a middle point, a point of balance (center of the distribution).

They are the most used measures in descriptive analysis.

So, in short: Mode (Mo), Median (Mdn), and Mean (M) are three different ways to find that “center.” Each has strengths and weaknesses.

Question 2

Explain The Mode (Mo)

Answer 2

The mode is the value with the greatest frequency in a distribution (the most common score).

Can be nominal, ordinal, or quantitative.

May not exist (if all values occur only once).

Can be bimodal (two modes), trimodal, or even more.

💡 Analogy:
Imagine you walk into a cafeteria. You count how many students chose each dish:

Pasta: 12 students

Salad: 7 students

Pizza: 20 students

Sandwich: 5 students

The mode is Pizza, because it is the most chosen option.
It tells you: “What’s most popular?”

📊 Example from slide:
Gender distribution

Gender 1: 3 (60%)

Gender 2: 2 (40%)
Mode = Gender 1 (because it has the highest frequency).

⚠️ Limitation: The mode doesn’t care about the rest of the data. If in psychology you ask: “How many cigarettes do you smoke a day?” and most people say 0, the mode will be 0 — but this ignores the people who smoke 10–20.
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Question 3

Explain The Median (Mdn)

Answer 3

The middle score when data are ordered from lowest to highest.

Divides the distribution into two equal halves (50% below, 50% above).

Works with ordinal and quantitative variables.

In a normal distribution, it equals the mean and mode.

💡 Analogy:
Imagine lining up 11 students by their exam grades from lowest to highest.
The median is the student standing exactly in the middle — with 5 students having lower grades and 5 students higher.

If the sample size is odd: median is the middle value.

If the sample size is even: median is the average of the two middle values.

📊 Example from slide:
Values: 2, 3, 4, 8, 9 (n = 5, odd).
Median = 4 (middle value).

Values: 2, 3, 4, 8, 9, 11 (n = 6, even).
Median = (4 + 8)/2 = 6.

⚠️ Advantage: robust against outliers.
If one student in a group of 10 earns 1 million euros while others earn 20k–40k, the median income still reflects a “typical” value, while the mean gets distorted.

Question 4

Explain The Mean (M)

Answer 4

The average value, computed as:

x̄ = ∑