Question 1197349

**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.