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Part 1
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers.
32  63  58  79  51  36  30  60  62  54  
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Part 1
What is the​ mean? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.
A.
The mean is 
  
52.5. ​(Round to one decimal place as​ needed.)
Your answer is correct.B.
There is no mean.
Part 2
What is the​ median? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.
A.
The median is 
  
56.​ (Round to one decimal place as​ needed.)
Your answer is correct.B.
There is no median.
Part 3
What​ is(are) the​ mode(s)? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.
A.
The​ mode(s) is(are) 
  
enter your response here. ​(Round to one decimal place as needed. Use a comma to separate answers as​ needed.)
B.
There is no mode.

Let's work through each part of the question to find the mean, median, and mode for the data set:  
\[ 32, 63, 58, 79, 51, 36, 30, 60, 62, 54 \]

### Part 1: Mean
To calculate the mean (average), we sum all the numbers and divide by the total number of values.

\[
\text{Sum} = 32 + 63 + 58 + 79 + 51 + 36 + 30 + 60 + 62 + 54 = 525
\]
The number of values is 10.

\[
\text{Mean} = \frac{525}{10} = 52.5
\]
So, the mean is **52.5** (Answer A).

### Part 2: Median
To find the median, we need to arrange the data in ascending order:
\[ 30, 32, 36, 51, 54, 58, 60, 62, 63, 79 \]

The median is the middle value in an ordered data set. Since there are 10 values (an even number), the median is the average of the 5th and 6th values:

\[
\text{Median} = \frac{54 + 58}{2} = \frac{112}{2} = 56
\]
So, the median is **56** (Answer A).

### Part 3: Mode
The mode is the number that appears most frequently. Since each value in the data set occurs only once, there is no mode.

So, the mode is **there is no mode** (Answer B).

### Summary:
- **Mean**: 52.5 (Part 1, Answer A)
- **Median**: 56 (Part 2, Answer A)
- **Mode**: There is no mode (Part 3, Answer B)

Would you like any further details or explanations?

Here are 5 related questions you might find interesting:
1. How is the median affected if an additional value is added to the data set?
2. What happens to the mean if you increase one value significantly?
3. Can a data set have more than one mode? If yes, how is it determined?
4. How do you calculate the range of a data set?
5. What is the effect of an outlier on the mean and median?

**Tip**: The median is less sensitive to extreme values (outliers) than the mean, which can be greatly affected by them.

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers. 32, 63, 58, 79, 51, 36, 30, 60, 62, 54. What is the mean, median, and mode?

Calculate the mean, median, and mode of a data set representing word counts from dictionary pages. This problem covers statistical concepts and central tendency measures, including detailed solutions for the mean (52.5), median (56), and mode (none). Ideal for students in Grades 6-8.

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