Using the weighted mean, find the average number of grams of...

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: $\begin{array}{ll}{\text { Meat or fish }} & {\text { Fat }(\mathrm{g} / \mathrm{oz})} \\ \hline 3 \text { oz fried shrimp } & {3.33} \\ {3 \text { oz veal culet (broiled) }} & {3.00} \\ {2 \mathrm{oz} \text { roast beef (lean) }} & {2.50} \\ {2.5 \text { oz fried chicken drumstick }} & {4.40} \\ {4 \text { oz tuna (canned in oil) }} & {1.75}\end{array}$

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:
$\begin{array}{ll}{\text { Meat or fish }} & {\text { Fat }(\mathrm{g} / \mathrm{oz})} \\ \hline 3 \text { oz fried shrimp } & {3.33} \\ {3 \text { oz veal culet (broiled) }} & {3.00} \\ {2 \mathrm{oz} \text { roast beef (lean) }} & {2.50} \\ {2.5 \text { oz fried chicken drumstick }} & {4.40} \\ {4 \text { oz tuna (canned in oil) }} & {1.75}\end{array}$

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Key Concepts

Weighting Factors

Weighting factors are the values that represent how much each data point should influence the weighted mean. In statistical analysis, these factors allow for the adjustment of the impact of each observation depending on its magnitude or frequency. They ensure that items which occur more frequently or have a larger measurement contribute more significantly to the overall calculation.

Weighted Mean

A weighted mean is an average that takes into account the relative importance or frequency of each data point by multiplying each value by a corresponding weight before summing them up. In this method, each data point's contribution to the final average is proportional to its assigned weight, making it especially useful when the data points represent quantities of differing significance.

Transcript

00:01 You already know how to do the mean or average of a dataset.

00:05 So for instance, if your data set is 1, 2, 3, 4, and 5, you know that you need to add them all up, which in this case gives you a total of 15, and then divide by how many you have, which is 1, 2, 3, 4, 5 data points to get an average or mean of 3 for this data set.

00:31 In this data set, the weight for each of these data points is one.

00:37 But when you do a weighted mean, you're giving each data point a different weight than one.

00:43 And so in this problem, you have to weight each type of meat or fish by how many ounces are eaten.

00:50 And then use that weight by multiplying the ounces of each by the fat grams per ounce.

00:56 So, for example, we have the shrimp, veal, roast beef, chicken, and tuna.

01:06 And the ounces eaten are three, three, two, two and a half, and the most that's eaten is tuna at four ounces.

01:18 Then we look at the fat grams.

01:20 Shrimp has 3 .3 fat grams per ounce.

01:26 Veal is leaner at 3 .0.

01:29 Roast beef is even leaner at 2 .5.

01:32 Chicken, a fried chicken drumstick, has the greatest amount of fat grams per ounce at 4 .4.

01:40 And tuna is the leanest at 1 .75.

01:44 This person's actually smart by eating the most amount of tuna...

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