# Scatter Plots

## Grade 8 Math Worksheets

In statistics, a **Scatter plot** or a **Scatter diagram** is a **graph** plotted for two variables, taking one variable along the horizontal axis i.e. *X*-axis & the other variable along the vertical axis i.e. the *Y*-axis. Generally, the independent variable is taken along the *X*-axis & the dependent variable is taken along they axis. It helps us to find whether the two variables, say *x* & *y* are correlated or not.

If two variables are correlated, then let’s see how they are related.

- If the pattern of the
**plotted points moves from bottom to top**as we move from left to right on the*X*-axis, then it means the value ofi*y*increases as the value of*x***ncreases**. Hence, there exists a**positive correlation**among the variables*x*&*y*and the graph is seen to be rising above

- If the pattern of the
**plotted points moves from top to bottom**to top as we move from left to right on the*X*axis, then it means the value of. Hence, there exists a*y*decreases as the value of*x*increases**negative correlation**among the variables*x*&*y*and the graph is seen to be falling down.

- If the values of
*y*do not change, as we move from left to right on the*X*axis, then it means the value of. Hence, there exists a*y*is constant as the value of*x*increases**correlation**among the variables*x*&*y*is**constant** - If the pattern of the
**plotted points does not show a recognizable pattern**e.**shows a random behaviour**as we move from left to right on the X axis, then the two variables are**uncorrelated.**

Now, we consider some **examples**.

**Example 1: Draw a scatter plot for the following set of values of x & y and identify if they are correlated. If yes, specify the type of correlation present.**

The scatter plot clearly shows that graph rises down as the values of x are increased i.e. as we move from left to right on the x axis. Hence the **variables x & y are positively correlated.**

Since all the points can be joined by a line, hence the correlation is a **perfect positive** **correlation.**

**Example 2:** **A company keeps a record of the number of electric units consumed in seven days of a week with respect to the average day temperature.**

Construct a scatter plot for the same and check if there exists a relation between the average day temperature & the number of electric units consumed on that day.

The scatter plot clearly shows that graph rises above as the values of x are increased i.e. as we move from left to right on the x axis. Hence the **variables x & y are positively correlated**.

Since all the points can’t be joined exactly by a line, hence the correlation is a **high positive** **correlation**. So, the number of electric units consumed is having a high positive correlation with the average day temperature.

**Example 3:** **Draw a scatter plot for the following set of values of x & y and identify if they are correlated. If yes, specify the type of correlation present.**

The scatter plot clearly shows that graph rises down as the values of x are increased i.e. as we move from left to right on the x axis. Hence the **variables**

**x & y are negatively correlated**. Since all the points can’t be joined exactly by a line, hence the correlation is a **high negative** **correlation**.

From the above example, we see that the scatter plot is a graph plotted between the two variables which give us information, about the correlation between the two variables involved.

**Check Point**

**Construct the scatter plots for the following given set of values & identify the type of correlation (if it exists) .**

##### Answer key

**Perfect Negative correlation**

**High Positive correlation**

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