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Part 1

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the data and then​ (e) answer the given questions.

Listed below are selling prices​ (dollars) of TVs that are 60 inches or larger and rated as a​ "best buy" by a popular magazine. Are the resulting statistics representative of the population of all TVs that are 60 inches and​ larger? If you decide to buy one of these​ TVs, what statistic is most​ relevant, other than the measures of central​ tendency?

17001700   

18001800   

18501850   

18001800   

19501950   

12501250   

18001800   

16001600   

12501250   

13001300   

18001800   

15501550**** 
  
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Part 1

**a.** Find the mean. 

The mean is 

​$1637.51637.5.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

Part 2

**b.** Find the median.

The median is 

​$enter your response here.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

Let's solve each part of the problem one step at a time.

### Part 1: Data
The given data set (selling prices of TVs) is:

1700, 1800, 1850, 1800, 1950, 1250, 1800, 1600, 1250, 1300, 1800, 1550

---

### (a) Find the Mean
To find the mean, sum up all the values and divide by the number of data points.

\[
\text{Mean} = \frac{\sum \text{values}}{\text{number of values}}
\]

Values:  
1700, 1800, 1850, 1800, 1950, 1250, 1800, 1600, 1250, 1300, 1800, 1550

Sum of values:

\[
1700 + 1800 + 1850 + 1800 + 1950 + 1250 + 1800 + 1600 + 1250 + 1300 + 1800 + 1550
\]

Let's calculate that:

\[
\text{Sum} = 20650
\]

There are 12 values.

\[
\text{Mean} = \frac{20650}{12} = 1720.83
\]

### (b) Find the Median
To find the median, arrange the numbers in ascending order:

\[
1250, 1250, 1300, 1550, 1600, 1700, 1800, 1800, 1800, 1800, 1850, 1950
\]

The median is the middle value. Since there are 12 values (an even number), the median is the average of the 6th and 7th values.

6th value = 1700  
7th value = 1800

\[
\text{Median} = \frac{1700 + 1800}{2} = 1750
\]

### Summary so far:
- Mean: $1720.8
- Median: $1750

Would you like to continue with the mode, midrange, and other parts of the question? Let me know if you'd like further details or clarification. Here are 5 related questions to think about:

1. How does the mode differ from the mean and median in a data set?
2. What does the midrange represent in a data set?
3. In which scenarios is the median more informative than the mean?
4. What factors affect whether the mean or median is a better representation of central tendency?
5. How would outliers impact the mean and median in this example?

**Tip**: When calculating the mean, rounding can introduce slight inaccuracies. Always consider rounding rules when precision is needed!

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given questions. Listed below are selling prices (dollars) of TVs that are 60 inches or larger and rated as a 'best buy' by a popular magazine. Are the resulting statistics representative of the population of all TVs that are 60 inches and larger? If you decide to buy one of these TVs, what statistic is most relevant, other than the measures of central tendency?

1700, 1800, 1850, 1800, 1950, 1250, 1800, 1600, 1250, 1300, 1800, 1550

Find the mean, median, mode, and midrange for a data set of selling prices for 60-inch TVs. This problem involves calculating central tendency measures and is suitable for high school students. Learn how to analyze whether the statistics represent the larger population of TVs.

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