Points scored
85. 78. 90
52. 81. 79
The table shows the Points a basketball team scored in different games. When the outlier is removed from the data set, what happens to the mean Points scored by the basketball team?
To determine the outlier, we need to find the number that is clearly outside the range of the other numbers. From the data, we can see that 52 is significantly lower than the rest of the numbers, so it is likely the outlier.
To remove the outlier, we will recalculate the mean by adding up the remaining scores and dividing by the number of scores minus one (since we are removing one score):
New mean = (85 + 78 + 90 + 81 + 79) / 4 = 82.6
So when the outlier is removed, the mean points scored by the basketball team increases from 73 to 82.6.
To find the mean points scored by the basketball team, we need to add all the points and divide by the number of games. However, we need to remove the outlier first.
The given data set is:
85, 78, 90, 52, 81, 79
To find the outlier, we can examine the data values and see if any of them are significantly different from the other values. Let's calculate the mean of the data first:
(85 + 78 + 90 + 52 + 81 + 79) / 6 = 83.33
Now, let's calculate the absolute deviations from the mean for each data point:
|85 - 83.33| = 1.67
|78 - 83.33| = 5.33
|90 - 83.33| = 6.67
|52 - 83.33| = 31.33
|81 - 83.33| = 2.33
|79 - 83.33| = 4.33
From the absolute deviations, we can see that 52 has the highest deviation, making it the outlier.
To find the mean without the outlier, we can recalculate the mean without considering the outlier:
(85 + 78 + 90 + 81 + 79) / 5 = 82.6
Therefore, when the outlier (52) is removed from the data set, the mean points scored by the basketball team decreases from 83.33 to 82.6.