Ages of golfers participating in a golf tournament 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 tournament.

Ask by Huang Coles. in the United States

Mar 24,2025

Question

Ages of golfers participating in a golf tournament 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 tournament.

Ask by Huang Coles. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

Let's tackle the problem step by step.

### a. Create a stem-and-leaf plot for the data.

To create a stem-and-leaf plot, we will separate each age into a "stem" (the leading digit or digits) and a "leaf" (the last digit).

The ages provided are:
$$ 44, 48, 40, 25, 28, 37, 29, 34, 45, 51, 43, 35, 38, 57, 50, 35, 47, 30, 61, 43, 44, 60, 46, 43, 33, 45, 42, 34, 32, 74 $$

**Stems and Leaves:**
- 20s: 2 | 5 8 9
- 30s: 3 | 0 3 4 5 5 7 8
- 40s: 4 | 0 2 3 3 4 4 5 5 6 7 8
- 50s: 5 | 0 1 7
- 60s: 6 | 1 0
- 70s: 7 | 4

The stem-and-leaf plot can be represented as follows:

```
Stem | Leaf
------------
  2  | 5 8 9
  3  | 0 3 4 5 5 7 8
  4  | 0 2 3 3 4 4 5 5 6 7 8
  5  | 0 1 7
  6  | 1 0
  7  | 4
```

### b. Use the stem-and-leaf plot to create a histogram.

To create a histogram, we will count the number of occurrences of ages within specific ranges (bins).

**Bins:**
- 20-29: 3
- 30-39: 7
- 40-49: 11
- 50-59: 3
- 60-69: 2
- 70-79: 1

The histogram can be represented as follows:

```
Age Range | Frequency
----------------------
  20-29   | *****
  30-39   | ***********
  40-49   | ***************
  50-59   | *****
  60-69   | **
  70-79   | *
```

### c. Describe the shape and spread of the data. Are there any apparent outliers?

**Shape:** 
The histogram shows that the distribution of ages is somewhat right-skewed, with a higher frequency of golfers in their 40s and 30s, and fewer in the 20s and 50s.

**Spread:**
The ages range from 25 to 74, indicating a spread of 49 years.

**Outliers:**
The age of 74 appears to be an outlier, as it is significantly higher than the other ages.

### d. Use the appropriate measure of center to describe the "typical" age of golfers at the tournament.

To find the typical age, we can calculate the mean and median.

1. **Mean:**
   $$
   \text{Mean} = \frac{\text{Sum of all ages}}{\text{Number of ages}} = \frac{44 + 48 + 40 + 25 + 28 + 37 + 29 + 34 + 45 + 51 + 43 + 35 + 38 + 57 + 50 + 35 + 47 + 30 + 61 + 43 + 44 + 60 + 46 + 43 + 33 + 45 + 42 + 34 + 32 + 74}{30}
   $$

2. **Median:**
   To find the median, we need to arrange the ages in ascending order and find the middle value.

Let's calculate the mean and median.

### Calculating Mean and Median

**Sum of Ages:**
$$
\text{Sum} = 44 + 48 + 40 + 25 + 28 + 37 + 29 + 34 + 45 + 51 + 43 + 35 + 38 + 57 + 50 + 35 + 47 + 30 + 61 + 43 + 44 + 60 + 46 + 43 + 33 + 45 + 42 + 34 + 32 + 74
$$

**Number of Ages:**
$$
\text{Count} = 30
$$

Now, I will calculate the sum and then the mean.
Calculate the value by following steps:
- step0: Calculate:
  $$44+48+40+25+28+37+29+34+45+51+43+35+38+57+50+35+47+30+61+43+44+60+46+43+33+45+42+34+32+74$$
- step1: Write as a multiplication:
  $$44+48+40+25+28+37+29+34+45+51+43\times 3+35+38+57+50+35+47+30+61+44+60+46+33+45+42+34+32+74$$
- step2: Multiply the numbers:
  $$44+48+40+25+28+37+29+34+45+51+129+35+38+57+50+35+47+30+61+44+60+46+33+45+42+34+32+74$$
- step3: Add the numbers:
  $$1273$$
Calculate or simplify the expression $$ 1273 / 30 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1273}{30}$$
The sum of the ages is $$ 1273 $$.

Now, let's calculate the mean:
$$
\text{Mean} = \frac{1273}{30} \approx 42.43
$$

### Median Calculation
To find the median, we need to arrange the ages in ascending order:
$$ 25, 28, 29, 30, 32, 33, 34, 34, 35, 35, 37, 38, 40, 43, 43, 43, 44, 44, 45, 45, 46, 47, 48, 50, 51, 57, 60, 61, 74 $$

Since there are 30 ages (an even number), the median will be the average of the 15th and 16th values:
- 15th value: 43
- 16th value: 43

Thus, the median is:
$$
\text{Median} = \frac{43 + 43}{2} = 43
$$

### Summary of Results
- **Mean Age:** Approximately $$ 42.43 $$
- **Median Age:** $$ 43 $$

### Conclusion
The typical age of golfers at the tournament can be described using the median, which is $$ 43 $$. The data is right-skewed with an outlier at age $$ 74 $$.
- **Stem-and-Leaf Plot:** ``` Stem | Leaf 2 | 5 8 9 3 | 0 3 4 5 5 7 8 4 | 0 2 3 3 4 4 5 5 6 7 8 5 | 0 1 7 6 | 1 0 7 | 4 ``` - **Histogram:** ``` Age Range | Frequency 20-29 | ***** 30-39 | *********** 40-49 | *************** 50-59 | ***** 60-69 | ** 70-79 | * ``` - **Shape and Spread:** - **Shape:** Right-skewed with a higher frequency in the 40s and 30s. - **Spread:** Ages range from 25 to 74. - **Outliers:** Age 74 is an outlier. - **Typical Age:** - **Median:** 43 - **Mean:** Approximately 42.43 **Conclusion:** The typical age of golfers is 43, with the data showing a right-skewed distribution and an outlier at age 74.

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Solución

a. Create a stem-and-leaf plot for the 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 tournament.

Calculating Mean and Median

Median Calculation

Summary of Results

Conclusion

Bonus Knowledge

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