Q1.
Discuss how well both the groups fared at this activity. Describe and compare the variability in data and their central tendency. [Group A: Mean = 58.21, Median = 60. Group B: Mean = 59.28, Median = 59.5.]
Answer
Both groups did well, and Group B did slightly better — its mean and median are both closer to the target of 60 seconds and closer to each other.
| Group A | Group B | |
|---|---|---|
| Mean | 58.21 s | 59.28 s |
| Median | 60 s | 59.5 s |
| Distance of mean from 60 s | 1.79 s | 0.72 s |
| Gap between mean and median | 1.79 s | 0.22 s |
| Spread of the dots | about 42 s to 70 s | about 44 s to 71 s |
Central tendency. Group A's median is exactly 60 — half the children in Group A opened their eyes at or after the full minute. Group B's mean is nearer 60, so as a whole Group B was closer.
Variability. In both groups the dots pile up between about 55 and 65 seconds, with a few children well short (in the low 40s) and a few well over (around 70). Group B's dots are more tightly stacked just under 60; Group A has a longer tail of early openers, which is exactly why its mean (58.21) falls below its median (60).
Why it happens: mean < median for Group A tells us, without counting a single dot, that the low values in Group A are further from the middle than the high values are. The children who opened too early were further out than the children who waited too long.
The strongest thing you can say: most children in both groups can judge a minute to within about 5 seconds, and the typical estimate is a little under a minute rather than over. But with only two groups you cannot claim that children in general underestimate a minute — that would need far more data.