The most appropriate measure of center is Median. As the data has a large value (290) at the end, it is the better choice to choose the median for finding the center because the mean or average is appropriate to represent the general level if there are not too large or too small values in the set. The median for the given bowling scores for 6 people is 117.5.
Definitions:
- Mean, the average value of the set of values. It is given by the ratio of the sum of all the values in the set to the total number of values in the set
- Median, the mid-point or middle value of the set of values. It is calculated by arranging the values of the set in ascending order and taking the middle value or center value
- Standard deviation, shows the variation in data. If the data is close together so it will be small or if the data is spread out then it will be large. Standard deviation is the square root of the variance.
- Range, the mathematical distance between the lowest and highest values in the data set. It is calculated by taking the difference between the highest value and the lowest value in the set
Since the standard deviation and range gives the variability of the given data, the mean and median are used for calculating the center.
Calculating mean and median:
Given data values are,
112, 114, 115, 120, 122, 290
Mean of the given data values,
Mean = Sum of all values / number of values
Sum of values = 112 + 114 + 115 + 120 + 122 + 290 = 873
Number of values = 6
∴ Mean = [tex]\frac{873}{6}[/tex]
= 145.5
Median of the given data values,
Arranging the data values in the ascending order - 112, 114, 115, 120, 122, 290
Number of values = 6 (even)
So, the median is the average between the two centers
∴ Median = [tex]\frac{115+120}{2}[/tex]
= 117.5
Since the last value in the set is larger than all the values (a sudden change or rise in the value), the most appropriate measure of center is the median and it is 117.5.
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