I Need Help With Statistics
2 answers:
<h3>Answer: Choice B</h3>
Explanation:
Check out the attached image below. Figure 1 is the original two-way frequency table. Figure 2 is the answer we want.
Let's start with figure 1. We have 54 people who take Salsa, so this will go at the bottom of the "Salsa" column in the "total" row. Two spots above this, we have 23 which means 23 people take ballet and salsa. Since we have 54 people taking salsa and 23 of those take ballet, this means 54-23 = 31 people taking salsa aren't taking ballet. Which is why 31 is written below the 23.
To further fill out the table, we have 15 people who took ballet but did not take salsa, followed by 10 people who took neither class. Add straight down to get the column total to be 15+10 = 25, so there are 25 people who did not learn salsa.
The row totals are 38 and 41, which are found by adding across the rows. This means 38 people took ballet, while 41 did not.
The grand total is 79 people. You find this by adding either the column totals (54 and 25), or the row totals (38 and 41), or by adding everything that isn't a total (add the four inner values 23, 15, 31, 10)
This wraps up figure 1
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Use figure 1 to help determine figure 2. What we do is divide across the rows. We will divide each value by the row total. In row 1, we have 38 as the row total, so we divide everything in this row by 38.
23/38 = 0.61
15/38 = 0.39
38/38 = 1
We have the values 0.61 and 0.39 and 1 that form the new row1
The same happens with rows 2 and 3
row2: 31/41 = 0.76, 10/41 = 0.24, 41/41 = 1
row3: 54/79 = 0.68, 25/79 = 0.32, 79/79 = 1
So that's how I got the table shown in figure 2. This table matches perfectly with choice B.
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