Birth Weights In 2003, babies born after a gestation periTod...

Birth Weights In $2003,$ babies born after a gestation periTod 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 2400 grams and a 40 -week gestation period baby weighs 3300 grams. Which baby weighs less relative to the gestation period?

Birth Weights In $2003,$ babies born after a gestation periTod 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 2400 grams and a 40 -week gestation period baby weighs 3300 grams. Which baby weighs less relative to the gestation period?

Key Concepts

Mean

The mean is the average of a set of values, calculated by summing the values and then dividing by the number of values. It represents the central tendency of a dataset, providing a baseline for comparisons.

Standard Deviation

Standard deviation is a measure of spread that quantifies the amount of variation or dispersion in a set of values around the mean. A larger standard deviation indicates that the values are more spread out from the mean.

Z-Score

A z-score is a standardized score that indicates how many standard deviations a data point is away from the mean. It allows for comparing individual values from different distributions on a common scale.

Comparative Standardization

Comparative standardization involves using z-scores to measure how individual data points relate to their respective group distributions. This method enables fair comparisons between groups with different means and standard deviations.

Transcript

00:01 We're told in this question that babies that are born after a 32 to 35 week gestation, gestation period on average weigh 2 ,600 grams with a standard deviation of 670 grams.

00:18 And then babies who are born essentially full term at 40 weeks weigh 3 ,500 grams with a standard deviation of 475 grams.

00:28 So they weigh more, but have less variation.

00:31 In their weights.

00:34 We're told then that we have a baby who was born at 34 weeks, so falls into that first time period, and weighed 2 ,400 grams.

00:43 And then we had a baby who was born at full term weighs 3 ,300 grams.

00:48 So each of them weigh less than their respective average for their time period.

00:53 But we want to know which baby weighs less in putting into perspective the different, again, gestation periods that they had.

01:02 So this is where we want to use the idea of z scores.

01:07 It allows us to take data that comes from, that's represented by different parameters, and compare them to see which baby does technically weigh less.

01:20 Not just in terms of its weight, that's pretty obvious, but in terms of the average for that time period in which it was born.

01:29 So first we'll look at calculating the z score for the baby that was born at 34 weeks.

01:35 Our formula for z score is your observed value minus your mean divided by your standard deviation.

01:45 And so for this particular problem, that's going to mean that we're taking the $2 ,400 grams.

01:53 We're subtracting the mean that corresponds to 34 weeks.

01:58 So that's 2 ,600.

02:01 And we're going to divide that by the standard deviation of 670...

Please give Ace some feedback