Question

the moon illusion refers, roughly speaking, to the common experience that the moon appears larger (and closer to us) when it is near the horizon than when it is at its zenith. to investigate, we have designed an experiment in which participants must adjust the diameter of a variable circular light placed at eye level to match the diameter of a fixed circular light placed well above eye level. (see, for example, kaufman, l & rock, i. (1989), \the moon illusion thirty years later,\ chapter 8 in m. hershenson (ed.) the moon illusion, hillsdale, nj: l. earlbaum.) we have tested 25 participants and recorded for each participant her experimental \adjustable/ fixed ratio.\ our data are summarized in the following histogram. based on the histogram, draw the ogive (the cumulative relative frequency polygon) for our data.

Explanation:

Step1: Calculate cumulative frequency

First, find the cumulative frequency for each class. The frequencies are 3, 6, 9, 5, 2. Cumulative frequencies: 3, 3+6=9, 9+9=18, 18+5=23, 23+2=25.

Step2: Calculate cumulative relative frequency

Total number of participants \( n = 25 \). Cumulative relative frequencies: \( \frac{3}{25}=0.12 \), \( \frac{9}{25}=0.36 \), \( \frac{18}{25}=0.72 \), \( \frac{23}{25}=0.92 \), \( \frac{25}{25}=1 \).

Step3: Plot the ogive

Plot the points at the upper class boundaries (0, 0.2, 0.4, 0.6, 0.8, 1.0) with cumulative relative frequencies (0, 0.12, 0.36, 0.72, 0.92, 1). Connect the points with line segments.

Answer:

To draw the ogive:

1. Upper Class Boundaries: 0, 0.2, 0.4, 0.6, 0.8, 1.0
2. Cumulative Relative Frequencies: 0, \( \frac{3}{25}=0.12 \), \( \frac{9}{25}=0.36 \), \( \frac{18}{25}=0.72 \), \( \frac{23}{25}=0.92 \), 1
3. Plot Points: (0, 0), (0.2, 0.12), (0.4, 0.36), (0.6, 0.72), (0.8, 0.92), (1.0, 1)
4. Connect Points with straight lines to form the cumulative relative frequency polygon (ogive).