Question

What is the outlier in this set of numbers:

88, 85, 90, 35, 75, 99, 100, 77, 76, 92, 82
a. 81.7
b. 11.6
c. 86.4
d. 7.4

Answer 1

To identify the outlier in the given set of numbers, we use the interquartile range (IQR) method. The outlier in this set of numbers is 35.

Step-by-step explanation:

In order to identify the outlier in the given set of numbers: 88, 85, 90, 35, 75, 99, 100, 77, 76, 92, 82, we need to find the value that is significantly different from the other values.

To do this, we can use the interquartile range (IQR) method. The IQR is the range between the 25th percentile (Q1) and the 75th percentile (Q3).

Calculating the IQR:

1. Sort the numbers in ascending order: 35, 75, 76, 77, 82, 85, 88, 90, 92, 99, 100
2. Find Q1 and Q3: Q1 = 77 and Q3 = 92
3. Calculate the IQR: IQR = Q3 - Q1 = 92 - 77 = 15

Next, we can determine if any number in the set is an outlier. Any value that is more than 1.5 times the IQR away from Q1 or Q3 is considered an outlier.

Calculating the lower and upper bounds:

1. Lower bound = Q1 - 1.5 * IQR = 77 - 1.5 * 15 = 55.5
2. Upper bound = Q3 + 1.5 * IQR = 92 + 1.5 * 15 = 113.5

Now, we can check each number in the set to see if it falls within the lower and upper bounds. In this case, the number 35 is less than the lower bound, so it is considered an outlier.

Therefore, the outlier in the given set of numbers is 35.