A sample of 50 values produced the following summary statistics: Q1 = 10, Q2 = 14.6, Q3 = 16.7 and x = 15.3. Based on this information, the left and right ends of the box in a box and whisker plot are, respectively,
a. 10 and 14.6
b. 14.6 and 16.7
c. 10 and 16.7
d. 5.3 and 32.0
e. none of these
10 and 16.7
To determine the left and right ends of the box in a box and whisker plot, we need to find the minimum (lower whisker) and maximum (upper whisker) values in the data set.
In this case, the lower whisker is represented by Q1 (the first quartile), and the upper whisker is represented by Q3 (the third quartile). Therefore, the left and right ends of the box in the box and whisker plot are Q1 and Q3, respectively.
From the given information, Q1 = 10 and Q3 = 16.7. So, the left and right ends of the box in the box and whisker plot are 10 and 16.7, respectively.
Therefore, the correct answer is c. 10 and 16.7.
To answer this question, you need to understand what the summary statistics and the box and whisker plot represent.
Summary statistics provide information about the distribution of a dataset. In this case, we have the first quartile (Q1), second quartile (Q2, also known as the median), third quartile (Q3), and the mean (x).
The box and whisker plot, on the other hand, is a graphical representation of the summary statistics. It consists of a box, which represents the interquartile range (IQR), and two lines (whiskers), which represent the minimum and maximum values within a certain range.
To determine the left and right ends of the box, you need to find the minimum and maximum values within the dataset. Unfortunately, the given summary statistics do not provide this information directly. However, you can make an estimation of the minimum and maximum values based on the given information.
Since Q1 is 10 and Q2 is 14.6, it can be assumed that the minimum value is slightly less than 10, as Q1 is the lowest quartile. Likewise, since Q3 is 16.7 and x (mean) is 15.3, it can be assumed that the maximum value is slightly greater than 16.7.
Therefore, the left and right ends of the box in the box and whisker plot would be somewhere between 10 and 14.6, and somewhere between 14.6 and 16.7, respectively.
Based on this estimation, the correct answer is e. none of these, as none of the given options match the estimation made.