Given the data 12, 39, 21, 18, 24, 17, 12, 25
a. What is the outlier in the data?
b. What is the mean with the outlier?
c. What is the mean without the outlier?
A. 12; 21; 18.4
B. 12; 18.4; 21
C. 39; 21; 18.4
D. 39; 18.4; 21
I would like some help because i cant figure this out please
I think it's C Ím not sure Sorry
First, do you know how to figure out which on the outlier is?
To find the outlier in a given set of data, you need to identify the value that is significantly different from the other values.
To calculate the mean (average), you add up all the values and divide the sum by the number of values.
Let's go through each question step by step:
a. What is the outlier in the data?
To identify the outlier, you can calculate the interquartile range (IQR) of the data. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Any value that falls below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is considered an outlier.
To find Q1 and Q3, you need to arrange the data in ascending order:
12, 12, 17, 18, 21, 24, 25, 39
Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data. In this case, Q1 is 17 and Q3 is 25.
Next, calculate the IQR: IQR = Q3 - Q1 = 25 - 17 = 8.
Now, calculate the lower and upper bounds for outliers:
Lower bound = Q1 - 1.5 * IQR = 17 - 1.5 * 8 = 17 - 12 = 5.
Upper bound = Q3 + 1.5 * IQR = 25 + 1.5 * 8 = 25 + 12 = 37.
Comparing the values in the data to the bounds, we see that the value 39 is greater than the upper bound of 37. Therefore, 39 is the outlier in the data.
b. What is the mean with the outlier?
To find the mean with the outlier, sum up all the values and divide by the total count.
Mean = (12 + 39 + 21 + 18 + 24 + 17 + 12 + 25) / 8 = 168 / 8 = 21.
Therefore, the mean with the outlier is 21.
c. What is the mean without the outlier?
To calculate the mean without the outlier, you need to exclude the outlier and recalculate the mean.
Mean (without outlier) = (12 + 21 + 18 + 24 + 17 + 12 + 25) / 7 = 129 / 7 ≈ 18.43.
Therefore, the mean without the outlier is approximately 18.43.
Based on the above calculations, the correct choice is:
B. 12; 18.4; 21.