Answer :
For the given data set we can calculate the mean and other properties of it:
- The mean = 47.11
- The Median = 45.25
- The mode = 45
- The range = 29.6
- The variance = 72.3
- The standard deviation = 8.49
What is Mean?
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given a data set 45.5, 47.0, 34.0, 42.0, 54.0, 43.5, 53.6, 56.9, 58.0, 45.0, 54.5, 54.0, 43.6, 45.0, 53.9, 41.8, 33.0, 43.1, 52.4, 37.9, 34.5, 40.1, 33.0, 59.9, 62.6, 54.1, 45.7, 40.7, 45.0, 59.0
The general formula for mean:
[tex]\text{mean} = \overline{x} = \dfrac{\sum_{i=1}^{n}x_i}{n}[/tex]
In our case,
Mean = 1413.3/30
Thus, Mean = 47.11
Since The median x˜ is the data value separating the upper half of a data set from the lower half.
- Arrange data values from lowest to the highest value
- The median is the data value in the middle of the set
- If there are 2 data values in the middle the median is the mean of those 2 values.
Thus, median = 45.25
Since Mode is the value or values in the data set that occurs most frequently.
Thus, in our case, as we can observe the mode = 45.0
Since Interquartile Range,
IQR = Q3 - Q1
In our case,
IQR = 29.6
For variance and standard deviation,
[tex]s^{2} = \dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n - 1}\\s^{2} = \dfrac{SS}{n - 1}\\s^{2} = \dfrac{2091.767}{30 - 1}\\s^{2} = 72.129897[/tex]
Thus,
Variance s² = 72.13
Standard Deviation s = 8.49
Learn more about Mean here:
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