Let's analyze the data from the image. We are given the frequency distribution of 1000 adults based on the type of corrective lenses they wear. The table lists:

• Contacts: 680 people
• Eyeglasses: 50 people
• Contacts and eyeglasses: 130 people
• None: 140 people

You are asked to find the mean, median, and mode of the data.

To calculate each measure:

1. Mean: The mean is calculated as the sum of the products of each category's frequency and its corresponding "lens type" score (if applicable), divided by the total number of people. Since this data isn't numeric, we typically don't calculate a mean for categorical data like this, but the problem asks for one.

   However, if you're referring to the mean frequency, the formula would be:

   $\text{Mean} = \frac{\text{Total sum of frequencies}}{\text{Number of categories}} = \frac{1000}{4} = 250$

   But this does not provide meaningful insight for this context because the categories are qualitative.

2. Median: The median is the value that lies in the middle of the data set when the values are arranged in order. To find it, sum the frequencies cumulatively:

   • Contacts: 680 (cumulative = 680)
   • Eyeglasses: 50 (cumulative = 680 + 50 = 730)
   • Contacts and eyeglasses: 130 (cumulative = 730 + 130 = 860)
   • None: 140 (cumulative = 860 + 140 = 1000)

   The median corresponds to the 500th and 501st values in the ordered dataset, both of which lie within the "Contacts" category, making Contacts the median.

3. Mode: The mode is the value with the highest frequency. Here, Contacts has the highest frequency (680), so the mode is Contacts.

Summary:

• Mean: 250 (if using frequency, though not typically useful here)
• Median: Contacts
• Mode: Contacts

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

1. How would the mean change if an additional category was added?
2. Can a qualitative dataset like this have a mean, and what would it represent if calculated?
3. How would the median change if the frequencies were distributed differently?
4. What if two categories had the same highest frequency? How would that affect the mode?
5. How would you describe the skewness of this dataset based on the mode and median?

Tip: The median is most useful when dealing with ordinal or interval data, but can also be helpful in analyzing frequencies in categorical data.