Given the data 14, 26, 23, 19, 24, 46, 15, 21:
What is the outlier in the data?
What is the mean with the outlier?
What is the mean without the outlier?
A. 14; 20.3; 23.5
B. 14; 23.5; 20.3
C. 46; 20.3; 23.5
D. 46; 23.5; 20.3
The outlier in the data is 46.
To find the mean with the outlier, we add all the numbers and divide by the total number of values: (14+26+23+19+24+46+15+21)/8 = 23.5
To find the mean without the outlier, we first need to remove it from the dataset: 14, 26, 23, 19, 24, 15, 21
Then we add those numbers and divide by the total number of values: (14+26+23+19+24+15+21)/7 = 20.3
Therefore, the answer is B. 14; 23.5; 20.3
To find the outlier in the data, we can calculate the z-score for each data point. The z-score measures how many standard deviations a data point is from the mean.
Calculating the z-score for each data point:
z-score = (data point - mean) / standard deviation
Given data: 14, 26, 23, 19, 24, 46, 15, 21
First, let's calculate the mean:
mean = (14 + 26 + 23 + 19 + 24 + 46 + 15 + 21) / 8 = 20.3
Next, let's calculate the standard deviation:
To do this, we will calculate the sum of squared differences from the mean and then divide it by the number of data points and take the square root of the result.
sum of squared differences = (14 - 20.3)^2 + (26 - 20.3)^2 + (23 - 20.3)^2 + (19 - 20.3)^2 + (24 - 20.3)^2 + (46 - 20.3)^2 + (15 - 20.3)^2 + (21 - 20.3)^2
= 29.2 + 29.2 + 6.13 + 2.9 + 13.69 + 411.15 + 29.2 + 0.49
= 521.98
standard deviation = sqrt(521.98/8) = 8.63
Now, let's calculate the z-score for each data point:
z-score for 14 = (14 - 20.3) / 8.63 = -0.73
z-score for 26 = (26 - 20.3) / 8.63 = 0.66
z-score for 23 = (23 - 20.3) / 8.63 = 0.31
z-score for 19 = (19 - 20.3) / 8.63 = -0.15
z-score for 24 = (24 - 20.3) / 8.63 = 0.43
z-score for 46 = (46 - 20.3) / 8.63 = 2.98
z-score for 15 = (15 - 20.3) / 8.63 = -0.61
z-score for 21 = (21 - 20.3) / 8.63 = 0.08
Looking at the z-scores, we can see that the 46 is the outlier because its z-score is 2.98, which is significantly higher than the other z-scores.
Now, let's calculate the mean with the outlier:
mean with the outlier = (14 + 26 + 23 + 19 + 24 + 46 + 15 + 21) / 8 = 20.3
Next, let's calculate the mean without the outlier:
mean without the outlier = (14 + 26 + 23 + 19 + 24 + 15 + 21) / 7 = 23.5
Therefore, the answer is:
A. 14; 20.3; 23.5