To compute the median, mode, range, and interquartile range (IQR) for this data, I will go step-by-step. The table presents categorical income ranges with their frequencies, so we'll treat it as grouped data.

1. Median:

The median is the value where 50% of the distribution falls below. We need to use cumulative frequencies to find it.

The cumulative frequencies are already given in the last column of the table.

• Total valid responses: 955
• To find the median, look for the cumulative frequency closest to $\frac{955}{2} = 477.5$.

In the table, we see that 54.7% cumulative corresponds to the income range $1,000 to $1,199, meaning this is where the median income lies.

2. Mode:

The mode is the value with the highest frequency.

From the table, the highest frequency occurs in the income range $800 to $999, with 177 responses (3.5%).

Thus, the mode is $800 to $999.

3. Range:

The range is the difference between the highest and lowest values in the dataset.

• Highest value = $\geq 3000$
• Lowest value = $\leq 200$

So, the range is $\geq 3000 - 200 = 2800$.

4. Interquartile Range (IQR):

The IQR is the range between the first quartile (Q1) and the third quartile (Q3).

• Q1: The 25th percentile corresponds to a cumulative frequency of 25%. Looking at the cumulative percentages, Q1 falls in the income range $1,000 to $1,199.

• Q3: The 75th percentile corresponds to a cumulative frequency of 75%. From the cumulative frequencies, Q3 falls in the income range $800 to $999.

So, the IQR is the range between these two values, i.e., $800 to $1,199.

Summary:

• Median: $1,000 to $1,199
• Mode: $800 to $999
• Range: $2800 or more
• IQR: $800 to $1,199

Would you like any more details or further clarification on these calculations? Here are some additional questions to explore:

1. How do you calculate the exact value for the median using interpolation?
2. Why is it important to consider grouped data for these statistics?
3. Can we calculate the mean for this dataset?
4. What insights can we draw from the mode being lower than the median?
5. How does the distribution of income look based on this data?

Tip: The IQR is a robust measure of spread, less sensitive to outliers than the range.