Answer
The observations made are:
1. The data is left-skewed
2. The data has one mode at 5 but also has a smaller peak at 8.
3. 0 is the only outlier in the dataset
SOLUTION
Problem Statement
We are given a dot plot illustrating the number of movies seen by 26 students in a class. We are asked to comment on the overall patterns in the data set and any striking deviations.
Solution
Below are the observations made on the data.
1. The data is left-skewed because there are is a greater concentration of data points at the right side of the graph.
2. The Data set has 1 mode of 5 (Since it occurs most) but also has a smaller peak of 8.
3. The data set has an outlier of 0. We can confirm this using the following calculation:
[tex]\begin{gathered} \text{Upper outlier}>Q_3+1.5(IQR) \\ \text{Lower outlier}
We can write out the numbers as follows:
0, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10.
Q1 and Q3 are gotten as follows:
(0, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6), (6, 6, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10)
The middle number of the first bracket gives Q1
(0, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6) --> 5 is the center of this bracket.
Thus, Q1 = 5
The middle number of the second bracket gives Q3.
(6, 6, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10) --> 8 is the middle number in this bracket.
Q3 = 8
Thus, we can say that:
[tex]\begin{gathered} \text{IQR}=8-5=3 \\ \\ \text{Upper outlier}>Q_3+1.5(IQR) \\ \text{Upper outlier}>8+1.5(3) \\ \\ \therefore\text{Upper outlier}>12.5 \\ \\ \text{ Since all numbers are lower than 12.5, then there is NO upper outlier} \\ \\ \\ \text{Lower Outlier }
Thus, we can conlude that 0 is an outlier in the dataset
Final Answer
The observations made are:
1. The data is left-skewed
2. The data has one mode at 5 but also has a smaller peak at 8.
3. 0 is the only outlier in the dataset