The researchers realize that the scale was not accurate for...

Name: Problem 25, Chapter 3: Statistics for the Behavioral Sciences
Uploaded: 2019-07-16T23:02:03-08:00
Duration: 7 min 20 s
Channel: Qiao Ruan
Description: The researchers realize that the scale was not accurate for the individual weighing 300 pounds, so they reweigh that individual and record 250 pounds. Will the mean increase or decrease in this situation?

The researchers realize that the scale was not accurate for the individual weighing 300 pounds, so they reweigh that individual and record 250 pounds. Will the mean increase or decrease in this situation?

Key Concepts

Data Correction

Data correction involves re-evaluating and updating measurements or values in a dataset when errors or inaccuracies are discovered. Correcting a measurement ensures that subsequent statistical calculations, such as the mean, better reflect the true values of the observations.

Effect of Changes in Data on the Mean

When a data point in a dataset is altered—especially if the change is substantial—it impacts the calculated mean. In this context, replacing a higher value with a lower one reduces the total sum of the dataset, which in turn decreases the overall mean.

Arithmetic Mean

The arithmetic mean is a measure of central tendency calculated by summing all values in a dataset and then dividing by the number of values. It provides a summary statistic that represents the average, and any change in one of the data points will affect the overall mean accordingly.

Transcript

00:01 Here are the problem 141.

00:02 We're going to calculate for the approximate percent increase.

00:07 So given that the mass of the person is equal to 155 pounds, and converting pounds to grams, each pound is 453 .5 .9 grams.

00:26 So this is equal to 7 .03 times 10 to the fourth.

00:31 Grams.

00:33 And the density is about 1 grams per centimeter cube.

00:40 So the volume of the person is going to be mass divided by density.

00:47 And that is 7 .03 times 10 to the 4th gram divided by 1 gram per centimeter cube.

00:54 And that is 7 .03 times 10 to the 4 centimeter cube.

01:01 So we know the height of the person is equal to four feet and converting feet to centimeter that is 30 .48 centimeter per feet.

01:17 So we get the person's height in centimeter is one to one point nine two centimeter and we know that for assume that a person is a cylinder.

01:32 The volume is equal to pi r square xx0.

01:42 So the volume 7 .03 times 10 to the 4th is equal to pi r square times 121 .92.

01:55 So to find out the value of r we have r square equal to the volume divided by pi times h.

02:14 7 .03 times 10 to the 4th.

02:20 Kx times pi times 1 .1 .92 centimeter.

02:28 So r is equal to the square root of 7 .03 times 10 to 4 centimeter square because we cancelled 1 centimeter divided by pi times 1 .92.

02:46 And we've got this number is about 13 .55 centimeters.

02:52 So a person can be modeled by a cylinder, so the waist of the person is equal to the circumference of the circle, which is in the center of the cylinder.

03:04 So the waist is about 2 pi r, so 2 times pi times 13 .55 centimeter, and we get the number about 85 .1 centimeter.

03:22 So after gaining 40 pounds of fat, the body density now is going to be .918 gram per centimeter cube...

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