To compute the frequency distribution, sample mean, and sample standard deviation based on the given tuition data (from a pie chart), you need to follow these steps:

1. Frequency Distribution Table:

We will first organize the tuition fees into class intervals, identify the frequency for each interval, and then calculate the midpoint for each class. You have also provided the midpoint of $25,000 or more as $26,249.50.

Typical Structure of the Frequency Distribution Table:

Class Interval	Frequency (f)	Midpoint (x)	$f \times x$
$5,000 - $9,999	f1	m1	f1 \times m1
$10,000 - $14,999	f2	m2	f2 \times m2
$15,000 - $19,999	f3	m3	f3 \times m3
$20,000 - $24,999	f4	m4	f4 \times m4
$25,000 or more	f5	$26,249.50	f5 \times 26,249.50

If you can provide me with the actual frequencies or percentages from the pie chart, I can help you complete this table.

2. Calculate Sample Mean:

The formula for the sample mean is:

$\bar{x} = \frac{\sum (f \times x)}{\sum f}$

Where:

• $\bar{x}$ is the sample mean,
• $f$ is the frequency of each class,
• $x$ is the midpoint of each class,
• $\sum (f \times x)$ is the sum of the product of frequencies and midpoints, and
• $\sum f$ is the total number of observations (total frequency).

3. Calculate Sample Standard Deviation:

The formula for the sample standard deviation $s$ is:

$s = \sqrt{\frac{\sum (f \times (x - \bar{x})^2)}{n - 1}}$

Where:

• $s$ is the sample standard deviation,
• $f$ is the frequency of each class,
• $x$ is the midpoint of each class,
• $\bar{x}$ is the sample mean,
• $n$ is the total frequency (total number of observations).

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Next Steps:

If you provide the frequencies or the actual percentages from the pie chart, I can calculate the sample mean and sample standard deviation for you.

Would you like to continue and input the necessary data from the pie chart?

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Related Questions:

1. What is the total number of institutions in the sample?
2. How were the intervals for tuition charges determined in the sample?
3. How does the sample data compare to national averages for public institutions?
4. What is the significance of using the midpoint for calculations in this case?
5. How do outliers (extreme values) affect the standard deviation in tuition data?

Tip:

Always use the midpoints when calculating the mean and standard deviation for grouped data, as this ensures an accurate approximation of the dataset.