A group of friends tracked the number of hours they watched TV in a week. The data set is given. $$ \{8,6,9,6,8,9,8,6,6,8,9,8,9\} $$ Find and interpret the mean and median number of hours of TV watching. Round numbers to the nearest tenth if necessary. Mean $$ = $$ $$ \square $$ Median = $$ \square $$ The values of the mean and median tell us that the data set Write an optional reasoning for your answer: shows a fairly normal distribution is slightly skewed or contains an outlier

Question

UpStudy AI · Accepted Answer

$$
\textbf{Step 1: Compute the Mean}
$$

We have 13 observations:  
$$
\{8,6,9,6,8,9,8,6,6,8,9,8,9\}
$$

Count the frequency:  
- $$6$$ appears 4 times  
- $$8$$ appears 5 times  
- $$9$$ appears 4 times

Now, compute the sum:
$$
\text{Sum} = 4(6) + 5(8) + 4(9) = 24 + 40 + 36 = 100
$$

The mean is:
$$
\text{Mean} = \frac{100}{13} \approx 7.7
$$

$$
\textbf{Step 2: Find the Median}
$$

First, sort the data:
$$
\{6,6,6,6,8,8,8,8,8,9,9,9,9\}
$$

For 13 values, the median is the $$\frac{13+1}{2} = 7^\text{th}$$ number in the ordered list. Counting to the 7th element:
$$
\underbrace{6,6,6,6}_{\text{first 4}},\underbrace{8,8,8}_{\text{5th, 6th, 7th}}, \dots
$$
Thus, the median is:
$$
\text{Median} = 8
$$

$$
\textbf{Step 3: Interpretation}
$$

The mean is approximately $$7.7$$ hours and the median is $$8$$ hours. The fact that the mean is very close to the median indicates that the data is fairly balanced. There is no significant skew or extreme outlier affecting the average.

$$
\textbf{Final Answers:}
$$
$$
\text{Mean} = 7.7 \quad \text{hours}, \quad \text{Median} = 8 \quad \text{hours.}
$$

$$
\textbf{Interpretation:} \text{The values of the mean and median tell us that the data set shows a fairly normal distribution.}
$$
Mean = 7.7 hours Median = 8 hours The data set shows a fairly normal distribution.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Statistics Questions