Birth Weights In 2003, babies born after a gestation per iod...

Birth Weights In $2003,$ babies born after a gestation per iod of 32 to 35 weeks had a mean weight of 2600 grams and a standard deviation of 670 grams. In the same year, babies born after a gestation period of 40 weeks had a mean weight of 3500 grams and a standard deviation of 475 grams Suppose a 34 -week gestation period baby weighs 3000 grams and a 40 -week gestation period baby weighs 3900 grams. Which baby weighs less relative to the gestation period?

Birth Weights In $2003,$ babies born after a gestation per iod of 32 to 35 weeks had a mean weight of 2600 grams and a standard deviation of 670 grams. In the same year, babies born after a gestation period of 40 weeks had a mean weight of 3500 grams and a standard deviation of
475 grams Suppose a 34 -week gestation period baby weighs 3000 grams and a 40 -week gestation period baby weighs 3900 grams. Which baby weighs less relative to the gestation period?

Key Concepts

Z-Score

Also known as the standardized score, the z-score indicates how many standard deviations an observation is away from the mean. By computing z-scores for individual babies' weights relative to their gestation group, one can compare their weight relative to the expected weight for that specific gestation period.

Mean

This is the average value of a dataset. In the context of birth weights, it represents the typical weight for babies born at a specific gestation period, providing a central point around which individual weights are distributed.

Standard Deviation

This statistical metric measures the amount of variation or dispersion in a set of values. For birth weights, a higher standard deviation indicates greater variability around the mean weight, while a lower standard deviation suggests that most weights are close to the mean.

Standardization

This process converts different scales into a common scale using the mean and standard deviation. It allows for a fair comparison between different groups (in this case, gestation periods) by adjusting for the variability in each group.

Transcript

00:01 If you happen to do problem 7, you're going to see that this one's very, very similar.

00:06 There's just one slight difference that i'll be sure to point out.

00:10 But we're talking about the weights of babies for those that are born slightly premature between 32 and 35 weeks of a gestation period and babies that are born full term at 40 weeks.

00:24 We're told that the mean weight for the preemie babies is 2 ,600 grams with a standard deviation of 670.

00:31 And the mean weight of full -term babies is 3 ,500 grams with a standard deviation of 475 grams.

00:39 We want to know which baby weighs less relative to the gestation period.

00:44 If a baby that was born at 34 weeks weighed 3 ,000 grams, so it's technically weighing 400 grams more than average than the mean, and then kind of looking at the same thing for a baby that's born full term.

00:59 Again, 400 grams more than the mean 3 ,900 grams.

01:05 But just because you can't answer the question just based off of that and say, well, neither of them weigh less, since they're both 400 grams over the average weight.

01:15 We also can't automatically say that the preemie baby weighs less just because its weight was less.

01:21 I mean, yes, it does, but it doesn't weigh less in relationship to the gestation period.

01:27 We kind of want to know which one is more extreme from the average.

01:32 Now, the one thing that makes us a little different from number seven is these weights are more than the average, which would be a good thing, especially for the preemie baby.

01:41 But we still want to know the idea of being less, you know, again, when kind of compared to their average.

01:49 So we're using the idea of z scores so that we can compare them because they're kind of on two different scales.

01:55 Even though we're talking grams, we've got one average of 2 ,600 versus another average of 3 ,500.

02:02 So we can bring them to the same scale, kind of rescale them, standardize them, by calculating the z score.

02:10 Our z score formula is your observed value minus the mean divided by the standard deviation...

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