Answer: To construct a box plot from the given data, we need to first find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
The minimum value is 47.
To find the quartiles, we first need to put the data in order from smallest to largest:
47, 49, 49, 52, 58, 59, 68, 71, 90, 91
There are 10 data points, so the median (Q2) is the average of the fifth and sixth values:
Q2 = (58 + 59)/2 = 58.5
To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively. The lower half of the data is:
47, 49, 49, 52, 58
So the median (Q1) of this half is:
Q1 = (49 + 49)/2 = 49
The upper half of the data is:
68, 71, 90, 91
So the median (Q3) of this half is:
Q3 = (71 + 90)/2 = 80.5
Now that we have found the minimum, Q1, Q2, Q3, and maximum values, we can construct the box plot:
| *
| * |
|-----|-----|-----|-----|-----|-----
40 50 60 70 80 90 100
The line inside the box represents the median (Q2), the box goes from Q1 to Q3, and the whiskers extend from the box to the minimum and maximum values. The asterisk (*) represents an outlier, which is any data point more than 1.5 times the interquartile range (IQR) away from the nearest quartile. In this case, there are no outliers.
Explanation: