Solved on Feb 29, 2024

Find the outlier in a data set with 25th percentile 13.5 and 75th percentile 18.2. Options: a) 24.78, b) 6.54, c) $6.42$ , d) 20.17, e) None.

STEP 1

Assumptions
1. The 25th percentile (Q1) of the data set is 13.5.
2. The 75th percentile (Q3) of the data set is 18.2.
3. An outlier is typically defined as a data point that lies outside the interquartile range (IQR), more specifically, below $Q1 - 1.5 \times IQR$ or above $Q3 + 1.5 \times IQR$ .

STEP 2

First, we need to calculate the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile.
$IQR = Q3 - Q1$

STEP 3

Now, plug in the given values for Q3 and Q1 to calculate the IQR.
$IQR = 18.2 - 13.5$

STEP 4

Calculate the IQR.
$IQR = 18.2 - 13.5 = 4.7$

STEP 5

Next, we need to calculate the lower bound for an outlier, which is $Q1 - 1.5 \times IQR$ .
$Lower\, bound = Q1 - 1.5 \times IQR$

STEP 6

Plug in the values for Q1 and IQR to calculate the lower bound.
$Lower\, bound = 13.5 - 1.5 \times 4.7$

STEP 7

Calculate the lower bound.
$Lower\, bound = 13.5 - 1.5 \times 4.7 = 13.5 - 7.05 = 6.45$

STEP 8

Now, we need to calculate the upper bound for an outlier, which is $Q3 + 1.5 \times IQR$ .
$Upper\, bound = Q3 + 1.5 \times IQR$

STEP 9

Plug in the values for Q3 and IQR to calculate the upper bound.
$Upper\, bound = 18.2 + 1.5 \times 4.7$

STEP 10

Calculate the upper bound.
$Upper\, bound = 18.2 + 1.5 \times 4.7 = 18.2 + 7.05 = 25.25$

STEP 11

With the lower and upper bounds calculated, we can now determine which data value is considered an outlier. Any data value below 6.45 or above 25.25 is considered an outlier.

STEP 12

Examine each data value to see if it falls outside the calculated bounds.
a) 24.78 is less than 25.25, so it is not an outlier. b) 6.54 is greater than 6.45, so it is not an outlier. c) $* * * * 6.42$ is less than 6.45, so it is an outlier. d) 20.17 is less than 25.25, so it is not an outlier. e) "None of the above is outlier" is not correct because we found an outlier in option c).

STEP 13

The data value considered an outlier is $* * * * 6.42$ (option c).
The solution is option c) $* * * * 6.42$ .

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Find the outlier in a data set with 25th percentile 13.5 and 75th percentile 18.2. Options: a) 24.78, b) 6.54, c) $6.42$ , d) 20.17, e) None.

STEP 1

Assumptions
1. The 25th percentile (Q1) of the data set is 13.5.
2. The 75th percentile (Q3) of the data set is 18.2.
3. An outlier is typically defined as a data point that lies outside the interquartile range (IQR), more specifically, below $Q1 - 1.5 \times IQR$ or above $Q3 + 1.5 \times IQR$ .

STEP 2

First, we need to calculate the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile.
$IQR = Q3 - Q1$

STEP 3

Now, plug in the given values for Q3 and Q1 to calculate the IQR.
$IQR = 18.2 - 13.5$

STEP 4

Calculate the IQR.
$IQR = 18.2 - 13.5 = 4.7$

STEP 5

Next, we need to calculate the lower bound for an outlier, which is $Q1 - 1.5 \times IQR$ .
$Lower\, bound = Q1 - 1.5 \times IQR$

STEP 6

Plug in the values for Q1 and IQR to calculate the lower bound.
$Lower\, bound = 13.5 - 1.5 \times 4.7$

STEP 7

Calculate the lower bound.
$Lower\, bound = 13.5 - 1.5 \times 4.7 = 13.5 - 7.05 = 6.45$

STEP 8

Now, we need to calculate the upper bound for an outlier, which is $Q3 + 1.5 \times IQR$ .
$Upper\, bound = Q3 + 1.5 \times IQR$

STEP 9

Plug in the values for Q3 and IQR to calculate the upper bound.
$Upper\, bound = 18.2 + 1.5 \times 4.7$

STEP 10

Calculate the upper bound.
$Upper\, bound = 18.2 + 1.5 \times 4.7 = 18.2 + 7.05 = 25.25$

STEP 11

With the lower and upper bounds calculated, we can now determine which data value is considered an outlier. Any data value below 6.45 or above 25.25 is considered an outlier.

STEP 12

STEP 13

The data value considered an outlier is $* * * * 6.42$ (option c).
The solution is option c) $* * * * 6.42$ .

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Find the outlier in a data set with 25th percentile 13.5 and 75th percentile 18.2. Options: a) 24.78, b) 6.54, c) 6.426.426.42, d) 20.17, e) None.

STEP 1

STEP 2

First, we need to calculate the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile.IQR=Q3−Q1IQR = Q3 - Q1IQR=Q3−Q1

STEP 3

Now, plug in the given values for Q3 and Q1 to calculate the IQR.IQR=18.2−13.5IQR = 18.2 - 13.5IQR=18.2−13.5

STEP 4

Calculate the IQR.IQR=18.2−13.5=4.7IQR = 18.2 - 13.5 = 4.7IQR=18.2−13.5=4.7

STEP 5

Next, we need to calculate the lower bound for an outlier, which is Q1−1.5×IQR Q1 - 1.5 \times IQR Q1−1.5×IQR.Lower bound=Q1−1.5×IQRLower\, bound = Q1 - 1.5 \times IQRLowerbound=Q1−1.5×IQR

STEP 6

Plug in the values for Q1 and IQR to calculate the lower bound.Lower bound=13.5−1.5×4.7Lower\, bound = 13.5 - 1.5 \times 4.7Lowerbound=13.5−1.5×4.7

STEP 7

Calculate the lower bound.Lower bound=13.5−1.5×4.7=13.5−7.05=6.45Lower\, bound = 13.5 - 1.5 \times 4.7 = 13.5 - 7.05 = 6.45Lowerbound=13.5−1.5×4.7=13.5−7.05=6.45

STEP 8

Now, we need to calculate the upper bound for an outlier, which is Q3+1.5×IQR Q3 + 1.5 \times IQR Q3+1.5×IQR.Upper bound=Q3+1.5×IQRUpper\, bound = Q3 + 1.5 \times IQRUpperbound=Q3+1.5×IQR

STEP 9

Plug in the values for Q3 and IQR to calculate the upper bound.Upper bound=18.2+1.5×4.7Upper\, bound = 18.2 + 1.5 \times 4.7Upperbound=18.2+1.5×4.7

STEP 10

Calculate the upper bound.Upper bound=18.2+1.5×4.7=18.2+7.05=25.25Upper\, bound = 18.2 + 1.5 \times 4.7 = 18.2 + 7.05 = 25.25Upperbound=18.2+1.5×4.7=18.2+7.05=25.25

STEP 11

With the lower and upper bounds calculated, we can now determine which data value is considered an outlier. Any data value below 6.45 or above 25.25 is considered an outlier.

STEP 12

STEP 13

The data value considered an outlier is ∗∗∗∗6.42* * * * 6.42∗∗∗∗6.42 (option c).The solution is option c) ∗∗∗∗6.42* * * * 6.42∗∗∗∗6.42.

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Find the outlier in a data set with 25th percentile 13.5 and 75th percentile 18.2. Options: a) 24.78, b) 6.54, c) $6.42$ , d) 20.17, e) None.

First, we need to calculate the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile.
$IQR = Q3 - Q1$

Now, plug in the given values for Q3 and Q1 to calculate the IQR.
$IQR = 18.2 - 13.5$

Calculate the IQR.
$IQR = 18.2 - 13.5 = 4.7$

Next, we need to calculate the lower bound for an outlier, which is $Q1 - 1.5 \times IQR$ .
$Lower\, bound = Q1 - 1.5 \times IQR$

Plug in the values for Q1 and IQR to calculate the lower bound.
$Lower\, bound = 13.5 - 1.5 \times 4.7$

Calculate the lower bound.
$Lower\, bound = 13.5 - 1.5 \times 4.7 = 13.5 - 7.05 = 6.45$

Now, we need to calculate the upper bound for an outlier, which is $Q3 + 1.5 \times IQR$ .
$Upper\, bound = Q3 + 1.5 \times IQR$

Plug in the values for Q3 and IQR to calculate the upper bound.
$Upper\, bound = 18.2 + 1.5 \times 4.7$

Calculate the upper bound.
$Upper\, bound = 18.2 + 1.5 \times 4.7 = 18.2 + 7.05 = 25.25$

The data value considered an outlier is $* * * * 6.42$ (option c).
The solution is option c) $* * * * 6.42$ .