To solve this problem, we need to calculate the mean of the given set of data and then round the result to the nearest tenth if necessary. Here are the step-by-step instructions:
1. List the data: The given set of data is:
[tex]\[
110, 101, 42, 120, 111, 122, 110, 100, 70
\][/tex]
2. Sum the data: Add all the numbers together to find the total sum.
[tex]\[
110 + 101 + 42 + 120 + 111 + 122 + 110 + 100 + 70 = 886
\][/tex]
3. Count the numbers: Determine the number of data points in the list.
[tex]\[
\text{There are 9 numbers in the data set.}
\][/tex]
4. Calculate the mean: Divide the total sum by the number of data points to get the mean.
[tex]\[
\text{Mean} = \frac{886}{9} \approx 98.44444444444444
\][/tex]
5. Round the mean to the nearest tenth: Look at the hundredths place to determine how to round the tenths place. Here, the hundredths place digit is 4, so we round down.
[tex]\[
\text{Rounded Mean} = 98.4
\][/tex]
6. Select the correct answer:
From the provided options, the one that matches our calculated rounded mean is:
b) [tex]\(98.4\)[/tex]
Therefore, the mean of the given set of data, rounded to the nearest tenth, is [tex]\( 98.4 \)[/tex].
