If the outliers are not included, what is the mean of the data set?
72, 82, 3, 55, 62, 73, 90, 80, 151, 59, 46, 31
59
65
67
73
is it b
Yes. B.
To calculate the mean of a data set without including the outliers, you need to identify the outliers and exclude them from the calculation.
To determine the outliers, you can use a method like the 1.5*IQR rule, where any data point greater than (Q3 + 1.5*IQR) or less than (Q1 - 1.5*IQR) is considered an outlier.
Let's find the outliers first:
Arrange the data set in ascending order:
3, 31, 46, 55, 59, 62, 72, 73, 80, 82, 90, 151
Calculate the middle two values to find the quartiles:
Q1 = (55 + 59) / 2 = 57
Q3 = (82 + 90) / 2 = 86
Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 86 - 57 = 29
Based on the 1.5*IQR rule, any data point greater than (Q3 + 1.5*IQR) or less than (Q1 - 1.5*IQR) is considered an outlier.
(Q3 + 1.5*IQR) = 86 + (1.5 * 29) = 86 + 43.5 = 129.5
(Q1 - 1.5*IQR) = 57 - (1.5 * 29) = 57 - 43.5 = 13.5
Since the data set does not contain any values greater than 129.5 or less than 13.5, there are no outliers in this data set.
Therefore, you can calculate the mean by summing all the values and dividing by the number of data points:
Mean = (3 + 31 + 46 + 55 + 59 + 62 + 72 + 73 + 80 + 82 + 90 + 151) / 12
Mean ≈ 65.42
So, the mean of the data set without including the outliers is approximately 65.42, which is closest to option b) 65.
To find the mean of a data set, you need to sum up all the values in the data set and then divide by the total number of values. However, in this case, you mentioned that outliers are not included.
To calculate the mean without outliers, follow these steps:
1. Arrange the data set in ascending order: 3, 31, 46, 55, 59, 62, 72, 73, 80, 82, 90, 151.
2. Identify any outliers. Outliers are extreme values that deviate significantly from the other values in the data set. In this case, based on the data set, it seems that 151 may be an outlier.
3. Remove the outliers from the data set. After excluding 151, the modified data set becomes: 3, 31, 46, 55, 59, 62, 72, 73, 80, 82, 90.
4. Calculate the sum of the remaining values: 3 + 31 + 46 + 55 + 59 + 62 + 72 + 73 + 80 + 82 + 90 = 663.
5. Count the total number of values in the modified data set: 11.
6. Calculate the mean by dividing the sum by the total count: 663 / 11 = 60.27 (rounded to two decimal places).
Therefore, the mean of the data set, excluding the outlier, is approximately 60.27. The closest option in your choices is 59, which is the correct answer.