Math  /  Data & Statistics

QuestionCalculate the interquartile range of the skewed dataset 0,2,6,7,7,7,8,8,8,8,8,9,9,9,100,2,6,7,7,7,8,8,8,8,8,9,9,9,10 (1 point)
The interquartile range= \square
Check answer Remaining Attempts : 3

Studdy Solution

STEP 1

1. The dataset is: 0,2,6,7,7,7,8,8,8,8,8,9,9,9,100, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10.
2. The interquartile range (IQR) is the difference between the third quartile (Q3Q3) and the first quartile (Q1Q1).

STEP 2

1. Order the dataset.
2. Determine the first quartile (Q1Q1).
3. Determine the third quartile (Q3Q3).
4. Calculate the interquartile range (IQR).

STEP 3

Order the dataset (it is already ordered):
0,2,6,7,7,7,8,8,8,8,8,9,9,9,10 0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10

STEP 4

Find the first quartile (Q1Q1), which is the median of the first half of the dataset. The first half is:
0,2,6,7,7,7,8 0, 2, 6, 7, 7, 7, 8
The median of this subset is the 4th value:
Q1=7 Q1 = 7

STEP 5

Find the third quartile (Q3Q3), which is the median of the second half of the dataset. The second half is:
8,8,8,8,9,9,9,10 8, 8, 8, 8, 9, 9, 9, 10
The median of this subset is the 4th value:
Q3=9 Q3 = 9

STEP 6

Calculate the interquartile range (IQR):
IQR=Q3Q1=97=2 \text{IQR} = Q3 - Q1 = 9 - 7 = 2
The interquartile range is:
2 \boxed{2}

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