Question

bubbles blown by each gum chewer
if the mean of the data set is 4 bubbles, find the number of bubbles hannah blew.
\boxed{} bubbles

Explanation:

Step1: Recall the formula for the mean

The mean (average) of a data set is calculated by the sum of all values divided by the number of values. The formula is $\text{Mean} = \frac{\sum_{i = 1}^{n} x_{i}}{n}$, where $x_{i}$ are the individual values and $n$ is the number of values.

Here, we have 4 people (Manueala, Sophia, Jada, Hannah), so $n = 4$. The mean is given as 4. Let the number of bubbles Hannah blew be $x$.

Step2: Find the sum of known values

Manueala blew 4 bubbles, Sophia blew 5 bubbles, Jada blew 6 bubbles. So the sum of the known values is $4 + 5 + 6 = 15$.

Step3: Set up the equation for the mean

Using the mean formula: $\frac{4 + 5 + 6 + x}{4} = 4$.

Step4: Solve for $x$

First, multiply both sides of the equation by 4: $4 + 5 + 6 + x = 4\times4$.

Simplify the right side: $4 + 5 + 6 + x = 16$.

Simplify the left side sum: $15 + x = 16$.

Subtract 15 from both sides: $x = 16 - 15 = 1$.

Answer:

1