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5

2
7
10
12
2
4
8
9
5
14
12
9
9
4
0
6
13
10
10
23
2
9
6
0
13
1
0
4
23
7
7
5
0
10
12
7
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12
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2

Construct a dotplot

3 answers

Creating a dot plot from the provided data involves counting the frequency of each value and representing it visually with dots. Below is a representation of the dot plot based on the numbers you provided:

0: ●●●●
1: ●
2: ●●●●●●
3: ●●
4: ●●●●
5: ●●●●●
6: ●●
7: ●●●●●●●
8: ●●
9: ●●●●●
10: ●●●●●●
11: ●
12: ●●●●●
13: ●●
14: ●
23: ●●

Key:

  • Each dot (●) represents a count of one occurrence of that number.
  • The numbers on the left represent the values from your list, and the dots represent how many times each value appeared.

Let me know if you need further assistance or modifications!

(b) Describe the shape of the dotplot.

To describe the shape of the dot plot created from your data, we can analyze the distribution of the values and their frequencies. Here's a summary:

Shape Description:

  1. Multimodal Distribution:

    • The dot plot shows several peaks (modes) at different values (particularly at 2, 5, 7, 9, and 10). This indicates that there are multiple values that occur with relatively high frequencies.

  2. Right-Skewed:

    • The distribution has more frequent values on the lower end (0 to 10) and fewer occurrences as we move towards higher values (such as 12, 13, and 14), suggesting that most of the observations are concentrated on the left side of the scale. This characteristic gives the plot a right-skewed appearance since the tail is longer on the right side.

  3. Concentration of Data:

    • There is a significant concentration of values between 2 and 10, creating a dense area in the plot. The values around 7 and 10 have the highest frequency counts.

  4. Gaps:

    • There are noticeable gaps between the frequency of different values, particularly between 10 and 12, and 14 and 23, suggesting that there are fewer data points in these ranges.

Conclusion:

Overall, the dot plot shows that most of the values are clustered around the lower end (0 to 10), particularly around a few modes (2, 5, 7, 9, and 10), and that the frequency decreases as the values increase, creating a right-skewed distribution.