The question asks to determine the missing data point such that the balance point (or mean) of the given data set is 2.

Step 1: Understand the Balance Point

The balance point or mean of a data set is calculated using the formula: $\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}.$

Here, the mean is given as 2, and we need to find the missing data point.

Step 2: Identify Known Data Points

From the dot plot:

• The known data points are: $1.4, 1.8, 2.2, 2.6, 3.4$.
• There is one missing data point, which we'll call $x$.

Step 3: Use the Formula for the Mean

The mean of the data set is: $\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}.$

Substitute the known values: $2 = \frac{1.4 + 1.8 + 2.2 + 2.6 + 3.4 + x}{6}.$

Step 4: Simplify the Equation

First, calculate the sum of the known data points: $1.4 + 1.8 + 2.2 + 2.6 + 3.4 = 11.4.$

Now substitute this back into the equation: $2 = \frac{11.4 + x}{6}.$

Multiply both sides by 6 to eliminate the denominator: $12 = 11.4 + x.$

Step 5: Solve for $x$

$x = 12 - 11.4 = 0.6.$

Final Answer:

The missing data point is: $\boxed{0.6}.$

Let me know if you want further clarification!

Related Questions:

1. What is the formula for calculating the mean?
2. How does the position of the missing data point affect the balance point of the dot plot?
3. Can there be multiple missing points and still achieve the same mean? Why or why not?
4. How would the calculation change if there were 2 missing points instead of 1?
5. Can the balance point of a dataset be a value not present in the data?

Tip:

When working with means, always check how adding or removing values changes the sum and balance of the dataset!