Question

what is true of the data in the dot plot? check all that apply.
number of minutes shelly spent waiting for the bus each morning
dot plot with dots at 10 (2 dots), 11 (4 dots), 12 (0 dots), 13 (3 dots), 14 (6 dots), 15 (1 dot)
the center is 13.
the center is 14.
the peak is at 14.
it has two clusters.

Explanation:

Step1: Analyze the dot plot's peak

Look at the number of dots at each value. At 14, there are the most dots (6 dots), so the peak is at 14.

Step2: Analyze clusters

We can see groups of dots: around 10 - 11, 13 - 14, and a single dot at 15. But the main clusters are around 10 - 11, 13 - 14 (and 15 is an outlier). Wait, actually, the dots are at 10 (2), 11 (4), 13 (3), 14 (6), 15 (1). So the clusters are 10 - 11, 13 - 14 (since 12 has no dots, separating them). So it has two clusters.

Step3: Analyze the center (median)

First, list the data points: 10,10,11,11,11,11,13,13,13,14,14,14,14,14,14,15. There are 16 data points. The median is the average of the 8th and 9th terms. 8th term:13, 9th term:13? Wait no, let's count again. Wait 10:2, 11:4 (total 6), 13:3 (total 9), 14:6 (total 15), 15:1 (total 16). So positions 1 - 2:10, 3 - 6:11, 7 - 9:13, 10 - 15:14, 16:15. So 8th term:13, 9th term:13? Wait no, 7th term is 13 (since 2 + 4 = 6, so 7th is first 13), 8th:13, 9th:13, 10th:14. Wait, median is (8th + 9th)/2? Wait no, for even number of terms, median is average of n/2 and (n/2 + 1)th terms. n = 16, so 8th and 9th. 8th term: let's list all: [10,10,11,11,11,11,13,13,13,14,14,14,14,14,14,15]. So 8th term:13, 9th term:13. Wait, but maybe the center (mean) or median? Wait the options say center is 13 or 14. Wait the median here: 8th and 9th are 13 and 13? Wait no, wait 10:2, 11:4 (total 6), so next 3 are 13 (positions 7,8,9), then 6 are 14 (positions 10 - 15), then 15 (position 16). So 8th term:13, 9th term:13. So median is 13? But wait the peak is at 14 (most dots). And it has two clusters (10 - 11 and 13 - 14, with 12 empty). So the true statements are: The peak is at 14, It has two clusters, and wait what about the center? Wait maybe I made a mistake. Wait the number of data points: 2 (10) + 4 (11) + 3 (13) + 6 (14) + 1 (15) = 16. So median is average of 8th and 9th. 8th term: let's count: 10 (2), 11 (4) → 6, then 13 (3) → 9. So 8th term is 13 (since 6 + 2 = 8? Wait no, 10:2 (1,2), 11:4 (3,4,5,6), 13:3 (7,8,9), 14:6 (10 - 15), 15:1 (16). So 7th:13, 8th:13, 9th:13. So median is 13. But wait the peak is at 14 (most dots). And it has two clusters (10 - 11 and 13 - 14, separated by 12 with no dots). So the true options are: The peak is at 14, It has two clusters, and The center is 13? Wait but let's check the options given (the checkboxes):

Options:

- The center is 13.

- The center is 14.

- The peak is at 14.

- It has two clusters.

So from analysis:

Peak: 14 has 6 dots, most, so peak at 14: true.

Clusters: 10 - 11 (dots) and 13 - 14 (dots), with 12 no dots: two clusters: true.

Center (median): as above, median is 13: so "The center is 13" is true? Wait but when I listed the data, 8th and 9th are 13, so median is 13. So "The center is 13" is true? Wait but let's check mean: (2*10 + 4*11 + 3*13 + 6*14 + 1*15)/(2 + 4 + 3 + 6 + 1) = (20 + 44 + 39 + 84 + 15)/16 = (20+44=64; 64+39=103; 103+84=187; 187+15=202)/16 ≈ 12.625, close to 13. So center (median or mean) is around 13. So "The center is 13" is true, "The peak is at 14" is true, "It has two clusters" is true. Wait but maybe the options are presented as checkboxes, so we need to check which are true.

Wait the original problem says "Check all that apply". So let's re - evaluate:

1. The center is 13: median is 13, mean ~12.6, so center (median) is 13: true.

2. The center is 14: mean ~12.6, median 13, so false.

3. The peak is at 14: 14 has 6 dots, more than others: true.

4. It has two clusters: dots at 10 - 11 and 13 - 14, with 12 empty: two clusters: true.

But maybe the user's options are as given, so the true ones are "The center is 13", "The peak is at 14", "It has two clusters". But let's check the dot plot again. Wait 11 has 4 dots, 14 has 6 dots (peak at 14). The clusters: 10 - 11 (group), then 13 - 14 (group), with 12 in between with no dots: so two clusters. The center (median) is 13 (as calculated). So the true statements are: The center is 13, The peak is at 14, It has two clusters. But maybe the options are presented with checkboxes, so we need to identify which are correct.

Answer:

The center is 13, The peak is at 14, It has two clusters (assuming the options are checkboxes, so the correct ones are: "The center is 13", "The peak is at 14", "It has two clusters" – but based on the given options in the problem, we check the applicable ones. If we have to list the options as per the problem's checkboxes:

• The center is 13: True

• The center is 14: False

• The peak is at 14: True

• It has two clusters: True

So the answer would be the checkboxes for "The center is 13", "The peak is at 14", and "It has two clusters" (depending on the original options' formatting, but as per the problem, we check all that apply, so the correct ones are "The center is 13", "The peak is at 14", "It has two clusters").