Question

Response Questions PartA To B A. In theMean and Median applet, place three observations on the line by clicking below it: two a) Pull the single rightmost observation out to the right (place the cursor on the point, hold down close together near the center of the line, and one somewhat to theright of these two a mouse button, and drag the point). How the mean behave? How does the median behave? Exp lain briefly why each measure acts as it does Now drag the single rightmost point to the left as far as you can. What happens to the mean? What happens to the median as you drag this point past the other two (watch carefully)? Figure 1.8 isa histogram of the distribution of ageat onset of anorexia for 691 Canadian girls diagnosed with the disorder. If you round the age to whole number of years, the first bar of the histogram (thefirst class) would include all girls diagnosed during their 11h year. With a little care, you can find the median and the quartiles from the histogram. What are these numbers? How did you find them? b) B. 200 150 100 50 112 13 14 15 16 1718 Age (years) at onset of anorexia FIGURE 1.8 Histogram of age at onset (in years of age girs diagnosed with the disorder, for Exercise 1.8. The first class includes 11-year-old girls b excludes 12-year-olds.

Answer 1

ANSWER:

Response Questions PartA To B A. In theMean and Median applet, place three observations on the line by clicking below it: two a) Pull the single rightmost observation out to the right (place the cursor on the point, hold down close together near the center of the line, and one somewhat to theright of these two a mouse button, and drag the point). How the mean behave? How does the median behave? Exp lain briefly why each measure acts as it does Now drag the single rightmost point to the left as far as you can. What happens to the mean? What happens to the median as you drag this point past the other two (watch carefully)? Figure 1.8 isa histogram of the distribution of ageat onset of anorexia for 691 Canadian girls diagnosed with the disorder. If you round the age to whole number of years, the first bar of the histogram (thefirst class) would include all girls diagnosed during their 11h year. With a little care, you can find the median and the quartiles from the histogram. What are these numbers? How did you find them? b) B. 200 150 100 50 112 13 14 15 16 1718 Age (years) at onset of anorexia FIGURE 1.8 Histogram of age at onset (in years of age girs diagnosed with the disorder, for Exercise 1.8. The first class includes 11-year-old girls b excludes 12-year-olds.

a
1. Mean is the sum of the three values divided by three.
Median is the middle value.

In this case 2 points are close to each other at the center and third is away, hence the mean is greater than the mid point of the total line. If the 3rd point was close to the other two points, the mean would be roughly near the median value.

The median value is the middle point in the dataset and it is unaffected by the extreme points.

2.

On dragging the right most point to the left median changes to to 4.8, which is the value of the first point. This is because now the first point become the middle value.

The mean decrease below the mid value of the line. As the left most point is almost equal to zero.

3.

The median value is the 345th observation which lies in 14 year bar. Hence the median value is 14 year

Quartile -
The first quartile is the 25th percentile value which lies at 173 th observation which fall in the 13 year bar. Hence the first quartile is 13 year
The fourth quartile is the 75th percentile value which lies at the 517th observation which fall in the 15 years bar. Hence the third quartile is 15 years.
The second quartile is 14 years.