Math Problem Statement

The length​ (in words) of seven articles from a particular newspaper are listed below. Find the​ mean, median, and mode of the​ data, if possible. If any of these measures cannot be found or a measure does not represent the center of the​ data, explain why. 1230 1127 1371 1275 1274 817 1155

Question content area bottom Part 1 Find the mean word count. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The mean word count is    enter your response here. ​(Round to one decimal place as​ needed.) B. There is no mean word count. Part 2 Does the mean represent the center of the​ data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is not a data value. D. The mean does not represent the center because it is the largest data value. E. There is no mean word count. Part 3 Find the median word count. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The median word count is    enter your response here. ​(Round to one decimal place as​ needed.) B. There is no median word count. Part 4 Does the median represent the center of the​ data? A. The median represents the center. B. The median does not represent the center because it is not a data value. C. The median does not represent the center because it is the largest data value. D. The median does not represent the center because it is the smallest data value. E. There is no median word count. Part 5 Find the mode of the word counts. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The​ mode(s) of the word counts 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. Part 6 Does​ (Do) the​ mode(s) represent the center of the​ data? A. The​ mode(s) represent(s) the center. B. The​ mode(s) does​ (do) not represent the center because it​ (one) is the largest data value. C. The​ mode(s) does​ (do) not represent the center because it​ (one) is the smallest data value. D. The​ mode(s) does​ (do) not represent the center because it​ (they) is​ (are) not a data value. E. There is no mode. If any of these measures cannot be found or a measure does not represent the center of the data, explain why.Select the correct choice below and, if necessary, fill in the answer box to complete your choice.Does the mean represent the center of the data?input field 2Select the correct choice below and, if necessary, fill in the answer box to complete your choice.Does the median represent the center of the data?input field 3Select the correct choice below and, if necessary, fill in the answer box to complete your choice.Does (Do) the mode(s) represent the center of the data?

Solution

Let's go through the steps to find the mean, median, and mode of the word counts, and then determine if they represent the center of the data.

Part 1: Find the mean word count

To find the mean, add all the word counts together and divide by the number of values.

Word counts:
1230, 1127, 1371, 1275, 1274, 817, 1155

Sum of the word counts:
1230+1127+1371+1275+1274+817+1155=92491230 + 1127 + 1371 + 1275 + 1274 + 817 + 1155 = 9249

Number of articles: 7

Mean:
Mean=92497≈1321.3\text{Mean} = \frac{9249}{7} \approx 1321.3

Thus, the mean word count is 1321.3.

Choice:
A. The mean word count is 1321.3.

Part 2: Does the mean represent the center of the data?

The mean represents the arithmetic average, which generally reflects the center, but sometimes it can be skewed by outliers (very high or low values).

In this case, the mean is not one of the data values, but it does give a reasonable estimate of the center. So:

Choice:
C. The mean does not represent the center because it is not a data value.

Part 3: Find the median word count

To find the median, first arrange the word counts in ascending order:
817, 1127, 1155, 1230, 1274, 1275, 1371

Since there are 7 values, the median is the middle value (the 4th one):
The median is 1230.

Choice:
A. The median word count is 1230.

Part 4: Does the median represent the center of the data?

The median is the middle value, so it always represents the center of the data. Since 1230 is a data value:

Choice:
A. The median represents the center.

Part 5: Find the mode of the word counts

The mode is the value that appears most frequently. In this case, each word count appears exactly once, so there is no mode.

Choice:
B. There is no mode.

Part 6: Does the mode represent the center of the data?

Since there is no mode, it cannot represent the center.

Choice:
E. There is no mode.

Conclusion

  • Mean: 1321.3
  • Median: 1230
  • Mode: There is no mode.

Questions for deeper understanding:

  1. How does the presence of outliers affect the mean and median?
  2. Why might the median sometimes be a better measure of central tendency than the mean?
  3. What does it mean when there is no mode in a data set?
  4. How would the results change if there were more articles or different word counts?
  5. In which scenarios is the mode a useful measure of central tendency?

Tip:

The median is a more robust measure of central tendency than the mean when your data set has outliers or is skewed.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency

Formulas

Mean = (Sum of values) / (Number of values)
Median = Middle value of ordered data
Mode = Most frequent value in data set

Theorems

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Suitable Grade Level

Grades 8-10

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