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The following set of data is from sample of
a. Compute the mean, median, and mode.
b. Compute the
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.
a.
Find the mean, median and mode of the data.
Answer to Problem 1PS
The mean is 6, median is 7, and there is no mode.
Explanation of Solution
A sample of data of size
The formula to calculate sample mean is,
Here n is the sample size,
Substitute the given values of the variable X in the formula. So, the mean is calculated as,
Thus, the mean of the sample is 6.
The median is the
This means that by Rule 1, the median is the value associated with third-ranked value. So, arrange the values from the smallest to the largest and give ranks. So, the given data is ranked as,
So, the median is 7.
The mode is the value which appears most frequently. In the given data set, none of the data are repeated. So, there is no mode for the data.
Therefore, the mean is 6, median is 7, and there is no mode for the data.
b.
Find the range, variance, standard deviation, coefficient of variation.
Answer to Problem 1PS
The range is
Explanation of Solution
The formula for range is defined as,
In the given data, the largest value is 9, and the smallest value is 2. So, the range is calculated as,
Thus, the range is 7.
The formula for sample variance is defined as,
The sample mean of the data is obtained as 6 in part (a). So,
Thus, the variance is
The standard deviation is the square root of the variance. So, the sample standard deviation is calculated as,
Thus, the standard deviation is
The formula for coefficient of variation is defined as,
Substitute the obtained values of
Thus, the coefficient of variation is
Therefore, the range is
c.
Find the Z scores and determine if there are any outliers.
Answer to Problem 1PS
The Z scores are,
There are no outliers in the data set.
Explanation of Solution
The formula for Z score is defined as,
Use this formula and the obtained values
The largest Z score is
d.
Explain the shape of the data set.
Answer to Problem 1PS
The distribution of data is negative or left-skewed.
Explanation of Solution
The mean is obtained as
Here the mean value (6) is less than the median value (7). So, the data distribution is negative or left-skewed distribution.
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