Which Box-and-Whisker-Plot shows the scores of 10 students on an exam? 89, 78, 93, 90, 75, 81, 91, 80, 89, 79.
There is a bunch of options but i cant post links. I dont understand how to do it. Please help.
Arrange score in order of value. That allows you to find the median and quartiles.
In a box and whisker plot: the ends of the box are the upper and lower quartiles, so the box spans the interquartile range. the median is marked by a vertical line inside the box. the whiskers are the two lines outside the box that extend to the highest and lowest observations.
To create a box-and-whisker plot for the given scores, follow these steps:
Step 1: Arrange the data in ascending order:
75, 78, 79, 80, 81, 89, 89, 90, 91, 93.
Step 2: Find the median (middle value) of the data set. Since there are 10 data points, the median will be the average of the 5th and 6th terms:
Median = (81 + 89) / 2 = 85.
Step 3: Determine the lower quartile (25th percentile). This is the median of the lower half of the data, which includes the 1st, 2nd, 3rd, and 4th terms:
Lower Quartile = (78 + 79) / 2 = 78.5
Step 4: Determine the upper quartile (75th percentile). This is the median of the upper half of the data, which includes the 7th, 8th, 9th, and 10th terms:
Upper Quartile = (90 + 91) / 2 = 90.5
Step 5: Calculate the interquartile range (IQR), which is the difference between the upper quartile and lower quartile:
IQR = Upper Quartile - Lower Quartile = 90.5 - 78.5 = 12.
Step 6: Identify any outliers. Outliers are data points that are exceptionally high or low compared to the rest of the data. In this case, there are no evident outliers.
Now that we have the necessary information, let's construct the box-and-whisker plot:
- Draw a number line with a vertical axis.
- Mark the minimum score (75) on the left side and the maximum score (93) on the right side of the number line.
- Draw a box from the lower quartile (78.5) to the upper quartile (90.5).
- Draw a solid line inside the box to represent the median (85).
- Draw a line (whisker) from the left side of the box to the minimum score (75).
- Draw another line (whisker) from the right side of the box to the maximum score (93).
The resulting box-and-whisker plot should visually represent the distribution of scores for the 10 students on the exam.
Unfortunately, as you mentioned you cannot post links, so I am unable to see the options you mentioned in your question. However, you can follow these steps to create the box-and-whisker plot yourself and compare it to the given options to choose the correct one.
To create a box-and-whisker plot for the given data, follow these steps:
1. Arrange the data in ascending order: 75, 78, 79, 80, 81, 89, 89, 90, 91, 93.
2. Find the median, which is the middle value of the data set. In this case, there are 10 data points, so the median is the average of the 5th and 6th values. Therefore, the median is (81 + 89) / 2 = 85.
3. Find the lower quartile (Q1), which is the median of the lower half of the data set. In this case, the lower half is the first five values: 75, 78, 79, 80, 81. The median of this set is (78 + 79) / 2 = 78.5.
4. Find the upper quartile (Q3), which is the median of the upper half of the data set. In this case, the upper half is the last five values: 89, 89, 90, 91, 93. The median of this set is (89 + 90) / 2 = 89.5.
5. Calculate the interquartile range (IQR), which is the difference between Q3 and Q1. In this case, IQR = 89.5 - 78.5 = 11.
6. Identify any outliers in the data set. Outliers are values that are significantly higher or lower than the rest of the data. To determine if there are outliers, consider any values that are more than 1.5 times the IQR away from the quartiles. No outliers are present in this data set.
7. Lastly, draw a number line and plot the five key values: the minimum (75), Q1 (78.5), median (85), Q3 (89.5), and the maximum (93) to create a box-and-whisker plot.
Based on the given data, the box-and-whisker plot will have a box that spans from Q1 to Q3, with a line inside representing the median. The minimum and maximum will be the endpoints of the whiskers.