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
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.
To identify the five important values from this box-and-whisker plot, we can follow the standard steps:
1. Find the minimum value: The minimum value is the smallest data point. From the given data, the minimum value is 40.
2. Find the lower quartile (Q1): The lower quartile is the median of the lower half of the data. To find it, we divide the data into two equal halves. Since we have 14 data points, the lower half will have 7 points. The middle value of this lower half is the lower quartile. In this case, the lower quartile is 50.
3. Find the median (Q2): The median is the middle value of the data. Similar to the calculation of Q1, the median will also be 50 since we have an even number of data points.
4. Find the upper quartile (Q3): The upper quartile is the median of the upper half of the data. Similar to the calculation of Q1, the upper quartile will also be 58.
5. Find the maximum value: The maximum value is the largest data point. From the given data, the maximum value is 68.
So, the five important values from this box-and-whisker plot are: 40, 50, 50, 58, and 68.