Given the following scores, construct a frequency distribution table and find the mean and mode of the…

Question

Given the following scores, construct a frequency distribution table and find the mean and mode of the distribution.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your assignment:

Construct the frequency distribution table for the data.
First, we list all the scores and count their occurrences to find the frequency for each unique score.
The given scores are:
18, 22, 16, 20, 20
20, 20, 24, 20, 20
22, 24, 22, 22, 10
24, 22, 26, 16, 16
16, 24, 18, 22, 20

There are a total of 25 scores.

The frequency distribution table is:
$\begin{array}{|c|c|} \hline \textbf{Score } (x) & \textbf{Frequency } (f) \\ \hline 10 & 1 \\ 16 & 4 \\ 18 & 2 \\ 20 & 7 \\ 22 & 6 \\ 24 & 4 \\ 26 & 1 \\ \hline \textbf{Total} & \textbf{25} \\ \hline \end{array}$
Find the mean of the distribution.
The formula for the mean ( $\bar{x}$ ) of a frequency distribution is $\bar{x} = \frac{\sum fx}{\sum f}$ .
We calculate $fx$ for each score and sum them up.
$\begin{array}{|c|c|c|} \hline \textbf{Score } (x) & \textbf{Frequency } (f) & \textbf{fx} \\ \hline 10 & 1 & 10 \times 1 = 10 \\ 16 & 4 & 16 \times 4 = 64 \\ 18 & 2 & 18 \times 2 = 36 \\ 20 & 7 & 20 \times 7 = 140 \\ 22 & 6 & 22 \times 6 = 132 \\ 24 & 4 & 24 \times 4 = 96 \\ 26 & 1 & 26 \times 1 = 26 \\ \hline \textbf{Total} & \textbf{25} & \sum fx = 504 \\ \hline \end{array}$
Now, we calculate the mean:
$\bar{x} = \frac{\sum fx}{\sum f} = \frac{504}{25} = 20.16$
The mean of the distribution is $\boxed{\textbf{20.16}}$ .
Find the mode of the distribution.
The mode is the score that appears most frequently in the distribution.
From the frequency table in Step 1, the score with the highest frequency is 20, which has a frequency of 7.
The mode of the distribution is $\boxed{\textbf{20}}$ .

Given the following scores, construct a frequency distribution table and find the mean and mode of the distribution.

Answer

Step-by-step solution

Construct the frequency distribution table for the data.

Find the mean of the distribution.

Find the mode of the distribution.

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