Ages of golfers participating in a golf toumament were ,
32 , and 74 . Homework Help
a. Create a stem-and-leaf plot for this data.
b. Use the stem-and-leaf plot to create a histogram.
c. Describe the shape and spread of the data. Are there any apparent outliers?
d. Use the appropriate measure of center to describe the “typical” age of golfers at the toumament.

Ask by West Graham. in the United States

Mar 24,2025

Question

Ages of golfers participating in a golf toumament were ,
32 , and 74 . Homework Help
a. Create a stem-and-leaf plot for this data.
b. Use the stem-and-leaf plot to create a histogram.
c. Describe the shape and spread of the data. Are there any apparent outliers?
d. Use the appropriate measure of center to describe the “typical” age of golfers at the toumament.

Ask by West Graham. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

**(a) Stem‐and‐Leaf Plot**

We first list the ages in order from smallest to largest:

$$
25,\;28,\;29,\;30,\;32,\;33,\;34,\;34,\;35,\;35,\;37,\;38,\;40,\;42,\;43,\;43,\;43,\;44,\;44,\;45,\;45,\;46,\;47,\;48,\;50,\;51,\;57,\;60,\;61,\;74 
$$

Next, we form the stem‐and‐leaf plot using the tens digit as the stem and the ones digit as the leaf. We create bins for the 20’s, 30’s, 40’s, etc.

- **Stem 2** (ages in the 20s):  
  Ages: 25, 28, 29  
  $$
  2 \;|\; 5\;8\;9
  $$

- **Stem 3** (ages in the 30s):  
  Ages: 30, 32, 33, 34, 34, 35, 35, 37, 38  
  $$
  3 \;|\; 0\;2\;3\;4\;4\;5\;5\;7\;8
  $$

- **Stem 4** (ages in the 40s):  
  Ages: 40, 42, 43, 43, 43, 44, 44, 45, 45, 46, 47, 48  
  $$
  4 \;|\; 0\;2\;3\;3\;3\;4\;4\;5\;5\;6\;7\;8
  $$

- **Stem 5** (ages in the 50s):  
  Ages: 50, 51, 57  
  $$
  5 \;|\; 0\;1\;7
  $$

- **Stem 6** (ages in the 60s):  
  Ages: 60, 61  
  $$
  6 \;|\; 0\;1
  $$

- **Stem 7** (ages in the 70s):  
  Age: 74  
  $$
  7 \;|\; 4
  $$

---

**(b) Histogram**

We form the histogram by grouping the ages into bins corresponding to the stems used above. Count the numbers in each bin:

- **20–29:** 3 golfers  
- **30–39:** 9 golfers  
- **40–49:** 12 golfers  
- **50–59:** 3 golfers  
- **60–69:** 2 golfers  
- **70–79:** 1 golfer

A rough sketch of the histogram is as follows:

```
Frequency
   12 |         *****
   11 |         *****
   10 |         *****
    9 |         *****      <-- 30–39 has 9
    8 |         *****
    7 |         *****
    6 |         *****
    5 |         *****
    4 | *****   *****
    3 | *****   *****   *****         <-- 20–29: 3, 50–59: 3
    2 | *****   *****   *****              <-- 60–69: 2
    1 | *****   *****   *****         ***** <-- 70–79: 1
      -------------------------------
         20s    30s    40s    50s   60s    70s
```

*Note:* The stars (*****) represent frequency bars for each interval. The exact appearance may vary when drawn by hand or with graphing software.

---

**(c) Shape and Spread of the Data**

- **Shape:**  
  The data are concentrated in the 30s and 40s. The stem-and-leaf plot and histogram show a roughly unimodal distribution with the highest frequency in the 40–49 bin. There is a slight right skew because a few higher ages (especially 74) extend the tail to the right.

- **Spread:**  
  The ages range from $$25$$ to $$74$$, giving a broad spread in the data. Most golfers are clustered between the ages of $$30$$ and $$50$$.

- **Outliers:**  
  The age $$74$$ appears isolated, as it is much higher than the next highest ages (the next being $$61$$). This makes $$74$$ an apparent outlier.

---

**(d) Measure of Center**

Because the data contain an outlier (age $$74$$), the median is the more appropriate measure of center than the mean.

With $$30$$ data points, the median is the average of the $$15^{th}$$ and $$16^{th}$$ values in the ordered list.

The sorted data are:

$$
25,\,28,\,29,\,30,\,32,\,33,\,34,\,34,\,35,\,35,\,37,\,38,\,40,\,42,\,\mathbf{43},\,\mathbf{43},\,43,\,44,\,44,\,45,\,45,\,46,\,47,\,48,\,50,\,51,\,57,\,60,\,61,\,74
$$

The $$15^{th}$$ and $$16^{th}$$ values are both $$43$$. Thus, the median is

$$
\text{Median} = \frac{43 + 43}{2} = 43.
$$

The "typical" age of golfers at the tournament is therefore $$43$$ years.
**(a) Stem-and-Leaf Plot** - **Stem 2:** 25, 28, 29 - **Stem 3:** 30, 32, 33, 34, 34, 35, 35, 37, 38 - **Stem 4:** 40, 42, 43, 43, 43, 44, 44, 45, 45, 46, 47, 48 - **Stem 5:** 50, 51, 57 - **Stem 6:** 60, 61 - **Stem 7:** 74 **(b) Histogram** - **20–29:** 3 golfers - **30–39:** 9 golfers - **40–49:** 12 golfers - **50–59:** 3 golfers - **60–69:** 2 golfers - **70–79:** 1 golfer **(c) Shape and Spread** - **Shape:** The data is roughly unimodal with a slight right skew, centered around the 40s. - **Spread:** Ages range from 25 to 74, with most golfers between 30 and 50. - **Outliers:** Age 74 is an apparent outlier. **(d) Typical Age** The median age is 43, indicating that the typical age of golfers at the tournament is 43 years.

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