茎叶图 - 用茎叶图表示数据分布
保留原始数据：茎叶图能完整保留所有原始数据值。
显示分布形状：能直观显示数据的分布形状和集中趋势。
便于比较：特别适合比较两组数据的分布。
茎（Stem）：表示数据的十位或更高位数。
叶（Leaf）：表示数据的个位数。
键（Key）：说明如何解读茎叶值。
用于比较两组数据，茎在中间，两组数据的叶分别向左右延伸。
The ages of 20 people at a party are: 23, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 45, 47, 49
Draw a stem and leaf diagram for these data.
茎叶图：
| 2 | 3 5 7 8 9 |
| 3 | 1 2 3 4 5 6 7 8 9 |
| 4 | 1 2 3 5 7 9 |
键：2|3 表示23岁
The test scores of two classes are shown in a back-to-back stem and leaf diagram.
Class A: 45, 52, 58, 61, 63, 65, 67, 68, 70, 72, 74, 76, 78, 80, 82, 85, 87, 89, 91, 93
Class B: 48, 55, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96
a) Draw a back-to-back stem and leaf diagram.
b) Compare the distributions of the two classes.
a) 背靠背茎叶图：
| Class A | Stem | Class B |
| 5 8 | 4 | 8 |
| 1 3 5 7 8 | 5 | 5 |
| 0 2 4 6 8 | 6 | 2 4 6 8 |
| 0 2 4 6 8 | 7 | 0 2 4 6 8 |
| 0 2 5 7 9 | 8 | 0 2 4 6 8 |
| 1 3 | 9 | 0 2 4 6 |
b) 比较：
Thirty college students were asked how many movies they had in their collection. The results are as follows:
12, 25, 34, 17, 12, 18, 29, 34, 45, 6, 15, 9, 25, 3, 29, 22, 20, 32, 15, 15, 19, 12, 26, 27, 27, 32, 35, 42, 26, 25
Draw a stem and leaf diagram to represent these data.
a) Find the median.
b) Find the lower quartile.
c) Find the upper quartile.
d) Find the interquartile range.
答题区域：
The stem and leaf diagram shows the ages of people at a wedding:
| 1 | 8 9 |
| 2 | 0 1 3 4 5 6 7 8 9 |
| 3 | 0 1 2 3 4 5 6 7 8 9 |
| 4 | 1 2 3 5 6 8 |
| 5 | 2 4 6 8 |
| 6 | 5 |
Key: 2|3 represents 23 years old
a) How many people attended the wedding?
b) What is the age of the youngest person?
c) What is the age of the oldest person?
d) Find the median age.
e) Find the range of ages.
答题区域：
The back-to-back stem and leaf diagram shows the test scores of two groups of students:
| Group A | Stem | Group B |
| 5 8 | 4 | 8 |
| 1 3 5 7 8 | 5 | 5 |
| 0 2 4 6 8 | 6 | 2 4 6 8 |
| 0 2 4 6 8 | 7 | 0 2 4 6 8 |
| 0 2 5 7 9 | 8 | 0 2 4 6 8 |
| 1 3 | 9 | 0 2 4 6 |
Key: 4|5 represents 45 marks
a) How many students are in each group?
b) Find the median score for each group.
c) Compare the performance of the two groups.
d) Which group has a higher average score?
答题区域：
The heights of 25 students (in cm) are: 152, 155, 158, 160, 163, 165, 167, 169, 170, 172, 174, 176, 178, 180, 182, 185, 187, 189, 190, 193, 196, 198, 200, 203, 205
a) Draw the stem and leaf diagram.
b) Find the median height.
c) Find the range of heights.
d) How many students are taller than 170 cm?
e) Find the interquartile range.
答题区域：
解答过程：
茎叶图：
| 0 | 3 6 9 |
| 1 | 2 2 2 5 5 5 7 8 9 |
| 2 | 0 2 5 5 5 6 6 7 7 |
| 3 | 2 2 4 4 5 |
| 4 | 2 5 |
a) 中位数：第15、16项平均值 = \( \frac{22+25}{2} = 23.5 \)
b) 下四分位数：第8项 = 15
c) 上四分位数：第23项 = 32
d) 四分位距：32 - 15 = 17
解答过程：
a) 总人数：数叶子总数 = 2+9+10+6+4+1 = 32人
b) 最年轻：茎叶图最小值 = 18岁
c) 最年长：茎叶图最大值 = 65岁
d) 中位数：第16、17项平均值 = \( \frac{32+33}{2} = 32.5 \)岁
e) 极差：65 - 18 = 47岁
解答过程：
a) Group A：20人；Group B：20人
b) Group A中位数：第10、11项平均值 = 75
Group B中位数：第10、11项平均值 = 78
c) Group B的分数分布更集中，整体表现更好
d) Group B的平均分更高
解答过程：
a) 茎叶图：
| 15 | 2 5 8 |
| 16 | 0 3 5 7 9 |
| 17 | 0 2 4 6 8 |
| 18 | 0 2 5 7 9 |
| 19 | 0 3 6 8 |
| 20 | 0 3 5 |
b) 中位数：第13项 = 178 cm
c) 极差：205 - 152 = 53 cm
d) 超过170 cm的人数：数叶子 = 15人
e) 四分位距：Q₃ - Q₁ = 190 - 165 = 25 cm