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Let's solve the questions based on the provided data set: 

**Data Set:** 54, 53, 44, 44, 38, 31, 55, 47

### (a) What is the median of this data set?

To find the **median**, we must first arrange the numbers in **ascending order**:

31, 38, 44, 44, 47, 53, 54, 55

Since the data set has 8 numbers (even), the median will be the average of the 4th and 5th numbers:
\[
\text{Median} = \frac{44 + 47}{2} = \frac{91}{2} = 45.5
\]

Thus, the **median** is **45.5**.

### (b) What is the mean of this data set?

The **mean** is calculated by summing all the numbers and dividing by the number of values:
\[
\text{Sum} = 54 + 53 + 44 + 44 + 38 + 31 + 55 + 47 = 366
\]
\[
\text{Mean} = \frac{366}{8} = 45.75
\]

Thus, the **mean** is **45.8** (rounded to one decimal place).

### (c) How many modes does the data set have, and what are their values?

The **mode** is the number that appears most frequently. From the data set:

31, 38, 44, 44, 47, 53, 54, 55

The number **44** appears twice, while the others appear only once. Therefore, the data set has **one mode**, which is **44**.

### Summary:
- (a) Median: **45.5**
- (b) Mean: **45.8**
- (c) Mode: **44**

Do you have any questions or would you like more details on the calculations?

Here are 5 additional related questions:
1. What is the range of this data set?
2. How would the mean change if we added another number, say 50, to the data set?
3. What would the new median be if the number 50 was added to the data set?
4. What is the difference between mean and median in skewed data distributions?
5. How can we calculate the variance and standard deviation for this data set?

**Tip:** The median is a good measure of central tendency for skewed data because it is not affected by extreme values like the mean is.

A tour company in a major city has a daily sightseeing trip. Each day, tour officials record the number of people making the trip. The data for a selection of summer days is as follows: 54, 53, 44, 44, 38, 31, 55, 47. (a) What is the median of this data set? (b) What is the mean of this data set? (c) How many modes does the data set have, and what are their values?

Learn how to find the median, mean, and mode for a data set of sightseeing trips in a major city. This problem includes a data set of 54, 53, 44, 44, 38, 31, 55, 47 and guides through calculating the central tendencies: median (45.5), mean (45.8), and mode (44).

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