Read stem-and-leaf plots and box plots incl. the five-number summary.
Free, timed SHSAT practice sets on stem-and-leaf & box plots— every question includes a full worked explanation, and there's no account required.
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Stem-and-leaf plot: each leaf is one data value. The row 3 | 1 4 7 means 31, 34 and 37. Write out the values in order (they are already sorted), count them, then find what is asked. With 12 values, the median is the average of the 6th and 7th values.
Box plot: it shows the five-number summary: minimum, Q1, median, Q3, maximum.
Common traps: using the range when the IQR is asked (or the other way around), calling Q1 or Q3 the median, and forgetting to divide by 2 when the median falls between two values.
| Stem | Leaves |
|---|---|
| 1 | 3 3 5 9 |
| 2 | 7 8 |
| 3 | 4 4 |
| 4 | 1 3 3 4 |
Reading off the leaves gives the sorted scores: 13, 13, 15, 19, 27, 28, 34, 34, 41, 43, 43, 44. With 12 scores, the median is the average of the two middle scores: (28 + 34) \(\div\) 2 = 31. (Reporting the mean (\(354 \div 12\)) gives 29.5. Adding the two middle scores but not dividing by 2 (\(28 + 34\)) gives 62. Using only the lower of the two middle scores gives 28.) The median score is 31.
The five values 40, 50, 60, 75, 80 split the data into four parts with about 25% of the data in each. Values greater than 75 fill 1 of those parts, so about 1 \(\times\) 25% = 25%. (Finding the percent less than 75 gives 75%. Treating 75 as the median (half the data is on each side of the median) gives 50%. Judging by length (the part from 75 to 80 is 5 of the 40 units the plot covers) gives about 13%.)
Class 1: median 50, IQR 55 \(-\) 45 = 10, range 65 \(-\) 40 = 25. Class 2: median 45, IQR 50 \(-\) 35 = 15, range 55 \(-\) 20 = 35. So the true statement is: Class 2 has the greater range.