Using the following stem \& leaf plot, find the five number summary for the data by hand. $$ 1 \mid 35 $$ $$ 2 \mid 236 $$ $$ 3 \mid 23 $$ $$ 4 \mid 1257 $$ $$ 5 \mid 34567 $$ $$ 6 \mid 02 $$ Min $$ = $$ Q1 $$ =\square $$ Med $$ =\square $$ Q3 $$ =\square $$ Max $$ =\square $$ Question Help: Submit Question Message instructor

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To find the five-number summary (minimum, first quartile $$Q1$$, median, third quartile $$Q3$$, and maximum) from the given stem-and-leaf plot, we first need to extract the data points represented in the plot.

### Step 1: Extract the Data
From the stem-and-leaf plot, we can interpret the data as follows:

- $$1 \mid 35$$ represents the values: 13, 15
- $$2 \mid 236$$ represents the values: 22, 23, 26
- $$3 \mid 23$$ represents the values: 32, 33
- $$4 \mid 1257$$ represents the values: 41, 42, 45, 47
- $$5 \mid 34567$$ represents the values: 53, 54, 55, 56, 57
- $$6 \mid 02$$ represents the values: 60, 62

### Step 2: List All Data Points
Now, we can list all the data points in ascending order:

- 13, 15, 22, 23, 26, 32, 33, 41, 42, 45, 47, 53, 54, 55, 56, 57, 60, 62

### Step 3: Find the Minimum and Maximum
- **Minimum (Min)**: The smallest value in the dataset is $$13$$.
- **Maximum (Max)**: The largest value in the dataset is $$62$$.

### Step 4: Find the Median
To find the median, we need to determine the middle value of the ordered dataset. Since there are 18 data points (an even number), the median will be the average of the 9th and 10th values.

- The 9th value is $$41$$.
- The 10th value is $$42$$.

Calculating the median:
$$
\text{Median} = \frac{41 + 42}{2} = \frac{83}{2} = 41.5
$$

### Step 5: Find the First Quartile $$Q1$$
The first quartile $$Q1$$ is the median of the first half of the data (the first 9 values):
- First half: 13, 15, 22, 23, 26, 32, 33, 41, 42

Since there are 9 values, the median (or $$Q1$$) is the 5th value:
- $$Q1 = 26$$

### Step 6: Find the Third Quartile $$Q3$$
The third quartile $$Q3$$ is the median of the second half of the data (the last 9 values):
- Second half: 42, 45, 47, 53, 54, 55, 56, 57, 60, 62

Since there are 9 values, the median (or $$Q3$$) is the 5th value:
- $$Q3 = 54$$

### Summary of Results
Now we can summarize the five-number summary:
- Min $$ = 13 $$
- $$Q1 = 26$$
- Med $$ = 41.5$$
- $$Q3 = 54$$
- Max $$ = 62$$

Thus, the five-number summary is:
- Min $$ = 13 $$
- $$Q1 = 26$$
- Med $$ = 41.5$$
- $$Q3 = 54$$
- Max $$ = 62$$
- **Minimum (Min)**: 13 - **First Quartile ($$Q1$$)**: 26 - **Median**: 41.5 - **Third Quartile ($$Q3$$)**: 54 - **Maximum (Max)**: 62

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