What is the mean? Round to the nearest tenth if needed.

\begin{tabular}{|l|l|l|l|l|l|}
\hline Value & 1 & 2 & 3 & 4 & 5 \\
\hline Frequency & 7 & 1 & 3 & 2 & 2 \\
\hline
\end{tabular}

A. 3
B. 2.4
C. 7.2
D. 2



Answer :

Certainly! Let's compute the mean of the given values with their respective frequencies, step by step.

Firstly, we have the values and their corresponding frequencies:

Values: [tex]\(1, 2, 3, 4, 5\)[/tex]
Frequencies: [tex]\(7, 1, 3, 2, 2\)[/tex]

To find the mean, we need to follow these steps:

1. Calculate the sum of the products of each value and its frequency:
- For value [tex]\(1\)[/tex] with frequency [tex]\(7\)[/tex]: [tex]\(1 \times 7 = 7\)[/tex]
- For value [tex]\(2\)[/tex] with frequency [tex]\(1\)[/tex]: [tex]\(2 \times 1 = 2\)[/tex]
- For value [tex]\(3\)[/tex] with frequency [tex]\(3\)[/tex]: [tex]\(3 \times 3 = 9\)[/tex]
- For value [tex]\(4\)[/tex] with frequency [tex]\(2\)[/tex]: [tex]\(4 \times 2 = 8\)[/tex]
- For value [tex]\(5\)[/tex] with frequency [tex]\(2\)[/tex]: [tex]\(5 \times 2 = 10\)[/tex]

Adding these products together:
[tex]\[ 7 + 2 + 9 + 8 + 10 = 36 \][/tex]

2. Calculate the total number of observations by summing the frequencies:
[tex]\[ 7 + 1 + 3 + 2 + 2 = 15 \][/tex]

3. Calculate the mean by dividing the sum of the products by the total number of observations:
[tex]\[ \text{Mean} = \frac{36}{15} = 2.4 \][/tex]

Since the mean is already calculated to the nearest tenth, there is no additional rounding needed.

Hence, the mean of the given data is [tex]\(2.4\)[/tex].