Math  /  Data & Statistics

QuestionThe 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 doe not represent the center of the data, explain why.
818 1278 1153 1126 1369 1230 1274 E. There is no median word count.
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) \square . (Round to one decimal place as needed. Use a comma to separate answers as needed.) B. There is no mode.
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.

Studdy Solution

STEP 1

1. The data set consists of the following word counts: 818,1278,1153,1126,1369,1230,1274 818, 1278, 1153, 1126, 1369, 1230, 1274 .
2. The mean is the average of the data points.
3. The median is the middle value when the data points are ordered.
4. The mode is the most frequently occurring value in the data set.

STEP 2

1. Calculate the mean of the data.
2. Determine the median of the data.
3. Identify the mode of the data.
4. Assess if the mode represents the center of the data.

STEP 3

Calculate the mean by summing all the data points and dividing by the number of data points.
Sum=818+1278+1153+1126+1369+1230+1274=8248\text{Sum} = 818 + 1278 + 1153 + 1126 + 1369 + 1230 + 1274 = 8248
Mean=824871178.29\text{Mean} = \frac{8248}{7} \approx 1178.29

STEP 4

Order the data points to find the median:
818,1126,1153,1230,1274,1278,1369 818, 1126, 1153, 1230, 1274, 1278, 1369
Since there are 7 data points, the median is the 4th value:
Median=1230 \text{Median} = 1230

STEP 5

Identify the mode by finding the most frequently occurring value. Since all values are unique, there is no mode.

STEP 6

Assess if the mode represents the center of the data. Since there is no mode, it cannot represent the center.
Solution Summary: - Mean: 1178.29 \approx 1178.29 - Median: 1230 1230 - Mode: There is no mode.
The correct choice for the mode is: B. There is no mode.

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