Question
Identify the five important values from this box-and-whisker plot. Explain how you got your answers.
40 42 46 48 50 52 54 56 58 60 62 64 66 68
40 42 46 48 50 52 54 56 58 60 62 64 66 68
Answers
GPT 3.5
To identify the five important values from this box-and-whisker plot, we need to understand how to interpret the plot. A box-and-whisker plot displays the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values of a dataset.
In this case, we need the dataset values provided to draw the box-and-whisker plot. Once we have that information, we can organize the data in ascending order:
40 42 46 48 50 52 54 56 58 60 62 64 66 68
Next, we calculate the median (Q2) which lies in the middle of the dataset, dividing it into two halves. In this case, there are an even number of values, so we will take the average of the two middle values: (54 + 56) / 2 = 55.
Now, we need to find the first quartile (Q1), which represents the median of the lower half of the dataset. Since there are 14 values, the median of the lower half is the 7th value, which is 52.
Similarly, we find the third quartile (Q3), which represents the median of the upper half of the dataset. Again, since there are 14 values, the median of the upper half is the 7th value from the end, which is 62.
Finally, we identify the minimum and maximum values of the dataset, which are 40 and 68, respectively.
Summary of values:
Minimum: 40
First Quartile (Q1): 52
Median (Q2): 55
Third Quartile (Q3): 62
Maximum: 68
Therefore, the five important values from this box-and-whisker plot are 40, 52, 55, 62, and 68.
In this case, we need the dataset values provided to draw the box-and-whisker plot. Once we have that information, we can organize the data in ascending order:
40 42 46 48 50 52 54 56 58 60 62 64 66 68
Next, we calculate the median (Q2) which lies in the middle of the dataset, dividing it into two halves. In this case, there are an even number of values, so we will take the average of the two middle values: (54 + 56) / 2 = 55.
Now, we need to find the first quartile (Q1), which represents the median of the lower half of the dataset. Since there are 14 values, the median of the lower half is the 7th value, which is 52.
Similarly, we find the third quartile (Q3), which represents the median of the upper half of the dataset. Again, since there are 14 values, the median of the upper half is the 7th value from the end, which is 62.
Finally, we identify the minimum and maximum values of the dataset, which are 40 and 68, respectively.
Summary of values:
Minimum: 40
First Quartile (Q1): 52
Median (Q2): 55
Third Quartile (Q3): 62
Maximum: 68
Therefore, the five important values from this box-and-whisker plot are 40, 52, 55, 62, and 68.