We should find 401 in the table and look up and across to identify the corresponding headings.

The number 401 lies in the row for people who chose meat and in the column for people who did not add spice. This means that there were 401 people who chose meat chili and did not add spice.

It is not specified whether this group added extra spice or not, so we are looking at all people who chose the vegetarian chili.

Since we are looking at the total number of people who chose vegetarian chili, this is a marginal frequency.

There are 168 people who chose the vegetarian chili.

We can find this total in a variety of ways:

• Add all the joint frequencies
• Add the marginal frequencies for the type of chili
• Add the marginal frequencies whether they added spice or not

Let's add the marginal frequencies for the type of chili.

\text{Meat}+\text{Vegetarian}=732+168=900

There were 900 people who ate chili at Chili Fest.

We can check this by adding up all of the joint frequencies.

331+401+125+43=900

We can first fill in the given information and then subtract joint frequencies from the marginal frequencies to get the missing joint frequencies and subtract marginal frequencies from the total to get the missing marginal frequencies.

Based on the information we have been given, we can already determine:

• Marginal frequency for number that flowered: 1000-136=864
• Joint frequency: 136-30=106

Based on the new calculated information, we can determine:

• Marginal frequency for number planted in peat soil: 394+106=500
• Then the marginal frequency for number planted in peat soil: 1000-500=500
• Joint frequency for plants that flowered in sandy soil: 864-394=470

We can always check by adding across each row and down each column to ensure the marginal frequency is the sum of the joint frequencies.

Keshawn seems to have a misconception around how joint frequencies relate to one another. He has stated that \text{sandy and flowered}+\text{peat and not flowered}=\text{Total} while it should be\text{sandy and flowered}+\text{sandy and not flowered}+\text{peat and flowered}+\text{peat and not flowered}=\\ \text{Total}

We need to consider all possible cases, not just opposite cases.

He should have said that because there were a total of 1000 plants observed and 30 plants that were planted in sandy soil did not flower, this means 1000-30=970 were planted in peat soil or were planted in sandy soil did not flower.