Question 1

We will analyze how well two groups estimated one minute using dot plots.

Step 1 — Analyzing Group A's Estimates

The dots show each child's estimate in seconds. For Group A, the mean estimate is 58.21 seconds. The median estimate for Group A is 60 seconds. The median is exactly 1 minute. The mean is slightly below 1 minute. The lowest estimate in Group A is 42 seconds. The highest estimate in Group A is 69 seconds. Let us find the range of estimates. The range is the highest value minus the lowest value.

$= 69 - 42$

$\boxed{27 \text{ seconds}}$

The estimates for Group A are quite spread out. Some children estimated much shorter times.

Step 2 — Analyzing Group B's Estimates

For Group B, the mean estimate is 59.28 seconds. The median estimate for Group B is 59.5 seconds. Both the mean and median are very close to 1 minute. This shows good accuracy for Group B. The lowest estimate in Group B is 45 seconds. The highest estimate in Group B is 71 seconds. Let us find the range of estimates. The range is the highest value minus the lowest value.

$= 71 - 45$

$\boxed{26 \text{ seconds}}$

The estimates for Group B are more clustered. Most estimates are close to 60 seconds.

Step 3 — Comparing Both Groups' Performance

Let us compare the central tendency first. Group A's median is exactly 60 seconds. Group B's mean is 59.28 seconds. Group B's median is 59.5 seconds. Both groups show good accuracy. Group B's mean is closer to 60 seconds. Group A's median is perfectly 60 seconds. So, both groups fared well on average.

Now, let us compare the variability. Group A has a range of 27 seconds. Group B has a range of 26 seconds. The ranges are very similar. However, Group B's estimates are more concentrated. Many children in Group B estimated very close to 1 minute. Group A has more estimates further away from 60 seconds. This means Group B was slightly more consistent.

Answer

Both groups fared well in estimating 1 minute. For central tendency, Group A's median was exactly 60 seconds, while Group B's mean (59.28 seconds) and median (59.5 seconds) were very close to 60 seconds. This shows both groups were accurate on average. For variability, Group A had a range of 27 seconds (from 42 to 69 seconds). Group B had a range of 26 seconds (from 45 to 71 seconds). While the ranges are similar, Group B's estimates were more clustered around 60 seconds, indicating slightly better consistency than Group A.