Question

1. mr. carlos class is learning about frogs. he took his class to the pond to observe them in their environment. one of the assignments was for each of the 14 students to measure one frog in order to calculate an average length. the average length was 2.35 inches. using the following data, calculate the length of the 14th frog.

frog	length (in.)
2	1.9	9	2.5
3	2.0	10	2.4
4	2.4	11	2.3
5	2.5	12	2.1
6	3.0	13	2.4
7	2.7	14	x

Explanation:

Step1: Recall the average formula

The formula for the average (mean) of a set of numbers is $\text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}}$. Let the length of the 14th frog be $x$. The number of frogs is 14, and the average is 2.35 inches. First, we need to find the sum of the lengths of the first 13 frogs.

Step2: Calculate the sum of the first 13 frogs

We add up the lengths of frogs 1 to 13:

$$
LATEXBLOCK0
$$

Step3: Use the average formula to solve for $x$

The sum of all 14 frogs is $31.1 + x$. The average is 2.35, and the number of frogs is 14. So we set up the equation:

$$ \frac{31.1 + x}{14} = 2.35 $$

Multiply both sides by 14:

$$ 31.1 + x = 2.35 \times 14 $$

Calculate $2.35 \times 14$: $2.35 \times 14 = 32.9$
Then, solve for $x$:

$$ x = 32.9 - 31.1 = 1.8 $$

Answer:

The length of the 14th frog is 1.8 inches.