**Pain:** The General Social Survey asked

830

people how many days they would wait to seek medical treatment if they were suffering pain that interfered with their ability to work. The results are presented in the following table.

Number of DaysFrequency

0

24

1

434

2

261

3

79

4

19

5

13

Total

830

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(a) Compute the mean

μ*X*

. Round the answer to three decimal places as needed.

=μ*X*

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To compute the mean \(\mu_X\) of the number of days people would wait to seek medical treatment, we'll use the formula for the mean of a frequency distribution:

\[
\mu_X = \frac{\sum (x_i \times f_i)}{N}
\]

Where:
- \(x_i\) is the number of days.
- \(f_i\) is the frequency of each \(x_i\).
- \(N\) is the total number of observations.

Given dataTo compute the mean \(\mu_X\) of the number of days people would wait to seek medical treatment, we'll use the formula for the mean of a frequency distribution:

\[
\mu_X = \frac{\sum (x_i \times f_i)}{N}
\]

Where:
- \(x_i\) is the number of days.
- \(f_i\) is the frequency of each \(x_i\).
- \(N\) is the total number of observations.

Given 

\[
\begin{array}{|c|c|}
\hline
\text{Number of Days } (x_i) & \text{Frequency } (f_i) \\
\hline
0 & 24 \\
1 & 434 \\
2 & 261 \\
3 & 79 \\
4 & 19 \\
5 & 13 \\
\hline
\text{Total } (N) & 830 \\
\hline
\end{array}
\]

Now, let's calculate the mean step by step:

1. Multiply each number of days by its frequency:
   \[
   0 \times 24 = 0
   \]
   \[
   1 \times 434 = 434
   \]
   \[
   2 \times 261 = 522
   \]
   \[
   3 \times 79 = 237
   \]
   \[
   4 \times 19 = 76
   \]
   \[
   5 \times 13 = 65
   \]

2. Sum the results:
   \[
   0 + 434 + 522 + 237 + 76 + 65 = 1334
   \]

3. Divide the sum by the total number of observations:
   \[
   \mu_X = \frac{1334}{830} \approx 1.607
   \]

So, the mean \(\mu_X\) is approximately **1.607** days.

Would you like further details or have any questions?

---

Here are 8 related questions for further exploration:

1. What is the median number of days in this dataset?
2. How would the mean change if the frequency for "5 days" was doubled?
3. Can you calculate the variance of the data?
4. What is the standard deviation of the dataset?
5. How would you interpret the mean in the context of this survey?
6. What would be the effect on the mean if we included a "6-day" option with a frequency of 10?
7. How does the distribution shape (skewness) affect the mean?
8. Can you calculate the mode of this dataset?

**Tip:** When dealing with frequency distributions, the mean provides a central value, but understanding the spread and shape of the data is also essential for full interpretation.

Learn how to compute the mean of days people would wait to seek medical treatment using a frequency distribution. This problem involves calculating the mean from a given set of days and their frequencies. Suitable for advanced high school students and anyone interested in statistics.

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