🟫 Bivariate Data

Question 1

What is bivariate data?

Answer 1

Data that involves two variables, often used to find relationships between them.

Question 2

What is a scatter plot?

Answer 2

A graph that displays bivariate data using points. Used to identify the correlation between variables.

Question 3

What is correlation and how is it interpreted?

Answer 3

Correlation shows how strongly two variables are related:

Positive = both increase
Negative = one increases, one decreases
None = no pattern

Question 4

What is the purpose of a line of best fit in a scatter plot?

Answer 4

A line of best fit represents the relationship between two variables and helps to predict values within the data range.

Question 5

How do you interpret correlation coefficients?

Answer 5

The correlation coefficient ranges from -1 to +1, where:

+1 indicates a perfect positive correlation

-1 indicates a perfect negative correlation

0 indicates no correlation.

Question 6

A scatter plot shows the relationship between the number of hours studied and test scores for 5 students. The hours studied are: 2, 4, 6, 8, 10, and the corresponding test scores are: 50, 60, 70, 80, 90. Does the data show a positive, negative, or no correlation?

Answer 6

Hours Studied: 2, 4, 6, 8, 10
Test Scores: 50, 60, 70, 80, 90

As the number of hours studied increases, the test scores also increase.

✅ This shows a positive correlation.

Answer: Positive correlation

Question 7

You are given the following bivariate data for two variables, age and height:
Age: 4, 6, 8, 10, 12
Height: 100, 110, 120, 130, 140
Plot a scatter graph and describe the relationship between age and height.

Answer 7

Data:

Age 4 6 8 10 12
Height 100 110 120 130 140
Plot (if drawn): Each point moves up consistently as age increases.

📈 The points form a straight upward-sloping line.

✅ This is a strong positive linear relationship.

Answer: The relationship between age and height is strong, positive, and linear.

Question 8

What is the formula for finding the line of best fit in a bivariate dataset?

Answer 8

The general form for the line of best fit (or linear regression line) is:

y=mx+c

Where:
y = dependent variable (e.g. height, test score)

x = independent variable (e.g. age, hours studied)

m = gradient (rate of change)

c = y-intercept (value when
x = 0)

Answer: y=mx+c
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