Stats: Simple Weighted Means Question

In summary, the conversation is about determining which set of data should be the mean and which should be the weight. In the given example, the weight is the amount of meat/fish consumed and the mean is the average number of grams of fat per ounce. The formula for calculating the weighted mean is [Σ(meat/fish)xfat]/Σ(meat/fish).
  • #1
shawnz1102
26
0
Hey guys, this is for an elementary statistics course. When given a problem, I am having trouble determining which is the data set (X) and which is the weight (W).

For example:

Using the weighted mean, find the average number of grams of fat per ounce of meat or fish that a person would consume over a 5-day period if he ate these:

Meat/Fish
3 oz. fried shrimp
3 oz. veal cutlet
2 oz. roast beef
2.5 oz fried chicken drumbstick
4 oz tuna

Fat (g/oz)
3.33
3.00
2.50
4.40
1.75

Would Meat/Fish be the weight, or would fat (g/oz) be the weight, and why?
 
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  • #2
[Σ(meat/fish)xfat]/Σ(meat/fish) is the answer.
[10+9+5+11+7]/[3+3+2+2.5+4]
 
  • #3
mathman said:
[Σ(meat/fish)xfat]/Σ(meat/fish) is the answer.
[10+9+5+11+7]/[3+3+2+2.5+4]

Yep, but I want to know for future reference how to determine which set of data should be the mean, and which set of data should be the weight.
 
  • #4
I am not sure how to answer your question. In your case "fat" is the function and "meat/fish" is the weight. The mean is the answer.
 
  • #5


As a scientist, it is important to accurately identify and interpret data in order to draw meaningful conclusions. In this case, the data set (X) would be the amount of meat/fish consumed, while the weight (W) would be the corresponding grams of fat per ounce. This is because the weight is being used to calculate the average, or weighted mean, of fat consumption. The weight represents the relative importance or contribution of each data point to the overall average. Therefore, in order to accurately calculate the weighted mean, it is crucial to correctly identify which variable is the data set and which is the weight. I hope this helps clarify the concept for you.
 

1. What is a simple weighted mean?

A simple weighted mean is a type of average that takes into account the importance or weight of each value in a dataset. It is calculated by multiplying each value by its corresponding weight, adding them up, and then dividing by the sum of the weights.

2. How is a simple weighted mean different from a regular mean?

A regular mean, also known as an arithmetic mean, assigns equal weight to each value in a dataset. In contrast, a simple weighted mean assigns different weights to each value based on its importance. This makes the weighted mean a more accurate representation of the data.

3. When should I use a simple weighted mean?

A simple weighted mean should be used when the values in a dataset have different levels of importance or influence on the overall result. This could be the case when analyzing data from a survey where certain responses are more significant than others.

4. How do I calculate a simple weighted mean?

To calculate a simple weighted mean, multiply each value in the dataset by its corresponding weight. Then, add all of these products together and divide by the sum of the weights. The formula for a simple weighted mean is:
Sum of (Value * Weight) / Sum of Weights.

5. What are the limitations of using a simple weighted mean?

One limitation of using a simple weighted mean is that it may not be appropriate for datasets with extreme values or outliers. These values can heavily influence the result and make it less representative of the data. Additionally, the weights assigned to each value are subjective and may vary depending on the person calculating the mean.

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