Question 1197349: The duration (minutes) of 26 electric power outages in the community of Sonando Heights over the past five years are shown below.
35 48 25 65 25 9 57 11 51 5 15 46 41
101 32 17 13 50 23 5 18 26 89 28 13 19
a) Find the mean, median, and mode. (Round your answer to 2 decimal places.)
b) Are the mean and median about the same?
c) Is the mode a good measure of center for this data set?
d) is the distribution skewed?
Answer by onyulee(41)   (Show Source):
You can put this solution on YOUR website!
**1. Calculate the Mean**
* Sum of all durations: 35 + 48 + 25 + 65 + 25 + 9 + 57 + 11 + 51 + 5 + 15 + 46 + 41 + 101 + 32 + 17 + 13 + 50 + 23 + 5 + 18 + 26 + 89 + 28 + 13 + 19 = 744
* Mean = Sum of durations / Number of observations = 744 / 26 = 28.62 minutes
**2. Calculate the Median**
* Arrange the data in ascending order:
5, 5, 9, 11, 13, 13, 15, 17, 18, 19, 23, 25, 25, 26, 28, 32, 35, 41, 46, 48, 50, 51, 57, 65, 89, 101
* Since there are 26 observations (even number), the median is the average of the 13th and 14th values.
* Median = (25 + 26) / 2 = 25.5 minutes
**3. Determine the Mode**
* The mode is the most frequent value.
* In this case, the mode is 13 minutes (it appears twice).
**a) Results:**
* Mean: 28.62 minutes
* Median: 25.5 minutes
* Mode: 13 minutes
**b) Are the mean and median about the same?**
* No, the mean (28.62) is significantly higher than the median (25.5).
**c) Is the mode a good measure of center for this data set?**
* No, the mode (13) is not a good measure of center for this data set.
* It is significantly lower than both the mean and median.
* The distribution has several other values that appear more than once.
**d) Is the distribution skewed?**
* Yes, the distribution is likely skewed to the right (positively skewed).
* The mean is greater than the median, which is a typical characteristic of right-skewed distributions.
* The presence of some very high values (like 89 and 101) also suggests right-skewness.
**In summary:**
* The mean and median are different, indicating potential skewness.
* The mode is not a representative measure of center for this data.
* The distribution is likely right-skewed.
**a) Find the mean, median, and mode.**
* **Mean:**
* Sum of all values / Number of values
* Mean = (35 + 48 + 25 + 65 + 25 + 9 + 57 + 11 + 51 + 5 + 15 + 46 + 41 + 101 + 32 + 17 + 13 + 50 + 23 + 5 + 18 + 26 + 89 + 28 + 13 + 19) / 26
* Mean ≈ 30.73 minutes
* **Median:**
* Arrange the data in ascending order:
5, 5, 9, 11, 13, 13, 13, 15, 17, 18, 19, 23, 25, 25, 26, 28, 32, 35, 41, 46, 48, 50, 51, 57, 65, 89, 101
* Median (middle value) = (26th value + 27th value) / 2 = (26 + 28) / 2 = 27 minutes
* **Mode:**
* The most frequent value is 13 minutes.
**b) Are the mean and median about the same?**
* No, the mean (30.73 minutes) is significantly higher than the median (27 minutes).
**c) Is the mode a good measure of center for this data set?**
* No, the mode (13 minutes) is not a good measure of center for this data set. It doesn't represent the typical outage duration well, as there are many values that are much higher.
**d) Is the distribution skewed?**
* **Yes, the distribution is likely skewed to the right (positively skewed).**
* The presence of some very high values (outliers like 89 and 101) pulls the mean to the right, while the median is less affected by these extreme values.
* This suggests that most outages are relatively short, but there are a few very long outages that skew the data.
**In summary:**
* The mean is 30.73 minutes.
* The median is 27 minutes.
* The mode is 13 minutes.
* The mean and median are not the same.
* The mode is not a good measure of center.
* The distribution is likely skewed to the right.
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