Men versus Women The average 20 - to 29 -year-old man is...

Men versus Women The average 20 - to 29 -year-old man is 69.6 inches tall, with a standard deviation of 2.7 inches, while the average 20 - to 29 -year-old woman is 64.1 inches tall, with a standard deviation of 2.6 inches. Who is relatively taller, a 75 -inch man or a 70 -inch woman? (Source: Vital and Health Statistics, Advance Data, Number $347,$ October 27,2004 )

Key Concepts

Mean

The mean, or average, is the sum of all values divided by the number of values. It represents the central or typical value in a dataset and is used as a reference point for comparing individual scores.

Standard Deviation

Standard deviation is a statistic that measures the dispersion or spread of a set of values around the mean. It indicates how much individual values typically deviate from the average, providing insight into the variability within a dataset.

Standard Score (Z-score)

The z-score is a standardized measure that indicates how many standard deviations a particular value is from the mean. It allows for the comparison of values from different distributions by normalizing the values relative to their respective means and standard deviations.

Transcript

00:01 We're looking to compare the heights of a man versus a woman to determine who is taller in relation to their gender.

00:11 We can't just go off of, numerically, yes, we can say that the male is taller if he's 75 inches tall versus a 70 inch female.

00:19 But in relation to their gender, kind of talking about who is more impressive in terms of, you know, extraordinary in terms of what their height is.

00:29 We're given the information that the average male for this age range, 20 to 29 years of age, was between, or excuse me, was 69 .6 inches with a standard deviation of 2 .7 inches.

00:41 And then the average woman for that same age group has a height of 64 .1 inches with a standard deviation of 2 .6 inches.

00:49 So we're looking at, again, a height of a male at 75 inches and a female at 70 inches.

00:56 And we want to know who is more extraordinarily tall for their gender.

01:02 We're going to be so that we can compare these two different genders, because they are different genders, it makes it a little bit difficult to compare.

01:09 We need to standardize the data by calculating the z score.

01:13 So we're going to use our z score formula that's shown there in the upper right corner, taking our observed value minus the mean divided by the standard deviation.

01:23 So for the male, we're going to have a z score.

01:29 That would be 75, that's the observed value, minus the mean for males is 69 .6, and the standard deviation for males is 2 .7.

01:44 So our numerator is going to be 5 .4, and we're dividing that by 2 .7, which is going to be a z score of exactly 2.

01:53 It's not common to get a nice exact z score like that, but it can certainly happen...

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