What is the outlier here
30,54,47,45,42,50,54,49
a.47
b.30
c.49
d.54****
Please check this
Nope. Look again.
Yes, B. It's 12 less than the next highest number.
54 is only 5 units higher than the second last highest of 49
while 30 is 12 units lower than the 2nd lowest of 42
Draw your conclusion from this observation.
Thank you
To identify the outlier in a set of numbers, you need to find the number that is significantly different from the other numbers. One way to identify the outlier is by calculating the interquartile range (IQR). Here are the steps to find the outlier in the given set of numbers:
1. Arrange the numbers in ascending order: 30, 42, 45, 47, 49, 50, 54, 54.
2. Calculate the IQR by finding the difference between the third quartile (Q3) and the first quartile (Q1). To find Q1 and Q3, you need to divide the dataset into two halves: lower half and upper half.
- Lower half: 30, 42, 45, 47
- Upper half: 49, 50, 54, 54
Q1: The median of the lower half is 43.5 (average of 42 and 45).
Q3: The median of the upper half is 51.5 (average of 50 and 54).
IQR = Q3 - Q1
= 51.5 - 43.5
= 8
3. Calculate the lower and upper boundaries. The lower boundary is Q1 - 1.5 * IQR, and the upper boundary is Q3 + 1.5 * IQR.
Lower boundary = 43.5 - (1.5 * 8)
= 43.5 - 12
= 31.5
Upper boundary = 51.5 + (1.5 * 8)
= 51.5 + 12
= 63.5
4. Any number below the lower boundary or above the upper boundary is considered an outlier. In this case, the number 30 is below the lower boundary (31.5), so it is identified as the outlier.
Therefore, the correct answer is b.30.