1) Find the mean Median and mode. Descriptive Statistics Data Mean ? Median ? Mode ? 2. Are the mean and median about the same? The mean is ? Yes or no The Median is ? greater or less 3. Is the mode a good measur of center for this data set ? yes or no ? 4. Is the distribution skewed? Yes, the istribution is skewed right. Yes, the distribution is skewed left. No, the distribution is symmetric.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The durations (Minutes) of 26 electric outages in the commuity of Sonando Height over the ast five years are shown below.
33 47 25 68 25 9 58 9 50 4 16 48 41
100 31 20 20 13 48 23 3 17 26 88 29 14 18
(1) Find the
Mean ?
Median ?
Mode ?
2. Are the mean and median about the same?
The mean is
? Yes or no
The Median is
? greater or less
3. Is the mode a good measur of center for this data set ?
yes or no ?
4. Is the distribution skewed?
Yes, the istribution is skewed right.
Yes, the distribution is skewed left.
No, the distribution is symmetric.
Note: It is given that there are 26 electric outages. but there are 27 observations. Here, we are finding measures of center for given 27 values. if needed for correct observation, kindly repost the question.
a.
Let X be the duration.
The given data is 33, 47, 25, 68, 25, 9, 58, 9, 50, 4, 16, 48, 41, 100, 31, 20, 20, 13, 48, 23, 3, 17, 26, 88, 29, 14, 18.
Mean:
Median:
Arrange the data in an ascending order
| 3 | 4 | 9 | 9 | 13 | 14 | 16 | 17 | 18 | 20 | 20 | 23 | 25 | 25 | 26 |
| 29 | 31 | 33 | 41 | 47 | 48 | 48 | 50 | 58 | 68 | 88 | 100 |
Since the sample size n=27 is even. The median is the average of the two values in the positions (n+1/2).
The value in the 14th position is 25.
Mode:
Mode is the most frequently obtained value in the data set.
From the given data set it can be observed that the observations 9,20, 25 and 48 obtained more number of times than the other observations. The number of times both the observations obtained is 2.
Thus, the mode values are 9,20, 25 and 48.
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