Question
A company surveys
200
200 shoppers to find out what type of bottled water they prefer.The partial two-way table shown gives the results of the survey as relative frequencies.
A. What is the missing value in the table?
B. Based on the results in the table, how many shoppers are men who prefer mineral water?
200
200 shoppers to find out what type of bottled water they prefer.The partial two-way table shown gives the results of the survey as relative frequencies.
A. What is the missing value in the table?
B. Based on the results in the table, how many shoppers are men who prefer mineral water?
Answers
GPT-4o mini
To provide the missing value in the two-way table and to answer the question regarding how many shoppers are men who prefer mineral water, I would typically need to see the actual table of relative frequencies you're referencing. However, since the table is not provided, I can guide you on how to calculate these figures based on the information typically included in such tables.
**A. Finding the Missing Value:**
A relative frequency table typically includes categories such as:
- Gender (e.g., Men, Women)
- Water Preference (e.g., Spring Water, Mineral Water, Sparkling Water)
In a two-way frequency table, the sum of all the relative frequencies should equal 1 (or 100% if expressed in percentage). If there is a missing relative frequency cell, it can be calculated by subtracting the sum of the known relative frequencies from 1.
For example, if your table shows:
- Men: 0.20 (Spring) | 0.15 (Mineral) | 0.05 (Sparkling)
- Women: 0.25 (Spring) | 0.30 (Mineral) | X (Sparkling)
You would find X (the missing value) as follows:
\[
X = 1 - (0.20 + 0.15 + 0.05 + 0.25 + 0.30)
\]
**B. Finding Men Who Prefer Mineral Water:**
Once you have the missing value and you know the relative frequencies, you can calculate the actual number of men who prefer mineral water by using the following formula:
If the relative frequency for men who prefer mineral water is known (let's say it’s Y), and the total number of shoppers surveyed is 200, then:
Number of men who prefer mineral water = Total Shoppers × Relative Frequency of Men who prefer Mineral Water
\[
= 200 \times Y
\]
If you share the specific relative frequencies or the full two-way table, I can assist you more specifically to determine the missing value and the number of men who prefer mineral water.
**A. Finding the Missing Value:**
A relative frequency table typically includes categories such as:
- Gender (e.g., Men, Women)
- Water Preference (e.g., Spring Water, Mineral Water, Sparkling Water)
In a two-way frequency table, the sum of all the relative frequencies should equal 1 (or 100% if expressed in percentage). If there is a missing relative frequency cell, it can be calculated by subtracting the sum of the known relative frequencies from 1.
For example, if your table shows:
- Men: 0.20 (Spring) | 0.15 (Mineral) | 0.05 (Sparkling)
- Women: 0.25 (Spring) | 0.30 (Mineral) | X (Sparkling)
You would find X (the missing value) as follows:
\[
X = 1 - (0.20 + 0.15 + 0.05 + 0.25 + 0.30)
\]
**B. Finding Men Who Prefer Mineral Water:**
Once you have the missing value and you know the relative frequencies, you can calculate the actual number of men who prefer mineral water by using the following formula:
If the relative frequency for men who prefer mineral water is known (let's say it’s Y), and the total number of shoppers surveyed is 200, then:
Number of men who prefer mineral water = Total Shoppers × Relative Frequency of Men who prefer Mineral Water
\[
= 200 \times Y
\]
If you share the specific relative frequencies or the full two-way table, I can assist you more specifically to determine the missing value and the number of men who prefer mineral water.