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    identify the outlier for the given data 34,23,43,28,56,125,52,40,26,24,37,25

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    Finding Outliers

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    10th -

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    10th - 12th Finding Outliers

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    13 Qs

    Find the outlier in the set of data:

    Show Answers See Preview 1. Multiple-choice 3 minutes 5 pts Q.

    4, 11.6, 50, 23, 20.1, 19, 29, 12.7, 8, 23, 57.5

    answer choices 57.5 50, 57.5 4, 50, 57.5 2. Multiple-choice 3 minutes 5 pts Q.

    Your math grades are 90, 85, 0, 90, 80, 100, and 90.  Which grade is the outlier?

    Identify the outlier for the given data?

    answer choices 90 0 3. Multiple-choice 3 minutes 5 pts Q.

    23, 34, 27, 7, 30, 26, 28, 31, 34

    answer choices 7 23 31 34 4. Multiple-choice 3 minutes 5 pts

    Q.

    What is the outlier in the following data?

    11, 19, 17, 8, 37, 11, 19, 16, 22

    answer choices 37 8 11 22 5. Multiple-choice 3 minutes 5 pts Q.

    Which of the following numbers is the outlier?34, 75, 82, 95, 100, 100

    At Dominique's Donuts the number of donut holes in a bag can vary. Help Dominique find the mode.

    answer choices 75 34 95 100 6. Multiple-choice 3 minutes 5 pts Q.

    12,10,10,10,13,12,11,13,10

    answer choices 13 12 11 10 7. Multiple-choice 3 minutes 5 pts Q.

    A value that is much higher or much lower than the other values in a set of data.

    Find the range.

    answer choices Outlier Box Plot Range Histogram 8. Multiple-choice 3 minutes 5 pts Q. 7, 1, 1, 7, 1, 4, 1 answer choices 6 5 7 3 9. Multiple-choice 5 minutes 5 pts Q.

    Find the median, first quartile, third quartile, and interquartile range of the data.

    23, 33, 25, 16, 27, 43, 29, 40, 35

    answer choices Median: 29 First Quartile: 24

    Third Quartile: 37.5

    IQR: 13.5 Median: 27 First Quartile: 25 Third Quartile: 35 IQR: 10 Median: 29 First Quartile: 25

    Third Quartile: 37.5

    IQR: 12.5 Median: 27 First Quartile: 24 Third Quartile: 35 IQR: 11 10. Multiple-choice 5 minutes 5 pts Q.

    Use the interquartile range to identify any outliers in the following data.

    32, 53, 72, 66, 47, 54, 49, 67, 71

    The data set below has an outlier of 42.

    answer choices No outliers. 32 is an outlier. 11. Multiple-choice 1 minute 5 pts Q.

    2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42

    What effect does removing the outlier have on the distribution of the data?

    answer choices

    The mean will decrease

    The median will decrease

    The mean will increase

    The median will increase

    Gabriella’s quiz grades are shown below.

    12. Multiple-choice 1 minute 5 pts Q. 88, 92, 92, 96, 98

    Gabriella scored a 20 on her sixth quiz. What effect does this score have?

    answer choices

    The low score causes the median to increase.

    The low score causes the median to decrease.

    The low score causes the mean to increase.

    The low score causes the mean to decrease.

    If 20 is added to the data set below, which statement will be true?

    13. Multiple-choice 3 minutes 5 pts Q. 50, 55, 55, 60, 62 answer choices

    The median will be 20

    The mode will increase

    The mean will increase

    The mean will decrease

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    स्रोत : quizizz.com

    Identifying outliers with the 1.5xIQR rule (article)

    Box and whisker plots

    Identifying outliers with the 1.5xIQR rule

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    An outlier is a data point that lies outside the overall pattern in a distribution.

    The distribution below shows the scores on a driver's test for

    19 19 19

    applicants. How many outliers do you see?

    0 0 5 5 10 10 15 15 20 20 25 25 Scores

    Some people may say there are

    5 5 5

    outliers, but someone else might disagree and say there are

    3 3 3 or 4 4 4

    outliers. Statisticians have developed many ways to identify what should and shouldn't be called an outlier.

    A commonly used rule says that a data point is an outlier if it is more than

    1.5\cdot \text{IQR} 1.5⋅IQR

    1, point, 5, dot, start text, I, Q, R, end text

    above the third quartile or below the first quartile. Said differently, low outliers are below

    \text{Q}_1-1.5\cdot\text{IQR}

    Q 1 ​ −1.5⋅IQR

    start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text

    and high outliers are above

    \text{Q}_3+1.5\cdot\text{IQR}

    Q 3 ​ +1.5⋅IQR

    start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text

    .

    Let's try it out on the distribution from above.

    Step 1) Find the median, quartiles, and interquartile range

    Here are the 19 19 19 scores listed out. 5 5 5 , 7 7 7 , 10 10 10 , 15 15 15 , 19 19 19 , 21 21 21 , 21 21 21 , 22 22 22 , 22 22 22 , 23 23 23 , 23 23 23 , 23 23 23 , 23 23 23 , 23 23 23 , 24 24 24 , 24 24 24 , 24 24 24 , 24 24 24 , 25 25 25

    What is the median?

    \text{median}= median=

    start text, m, e, d, i, a, n, end text, equals

    What is the first quartile?

    \text{Q}_1= Q 1 ​ =

    start text, Q, end text, start subscript, 1, end subscript, equals

    What is the third quartile?

    \text{Q}_3= Q 3 ​ =

    start text, Q, end text, start subscript, 3, end subscript, equals

    What is the interquartile range?

    \text{IQR}= IQR=

    start text, I, Q, R, end text, equals

    Step 2) Calculate

    1.5\cdot\text{IQR} 1.5⋅IQR

    1, point, 5, dot, start text, I, Q, R, end text

    below the first quartile and check for low outliers.

    Calculate

    PROBLEM A

    \text{Q}_1-1.5\cdot\text{IQR}

    Q 1 ​ −1.5⋅IQR

    start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text

    \text{Q}_1-1.5\cdot\text{IQR}=

    Q 1 ​ −1.5⋅IQR=

    start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text, equals

    PROBLEM B

    How many data points can we say are low outliers?Step 3) Calculate

    0 0 5 5 10 10 15 15 20 20 25 25 Scores Choose 1 answer: Choose 1 answer: 1.5\cdot\text{IQR} 1.5⋅IQR

    1, point, 5, dot, start text, I, Q, R, end text

    above the third quartile and check for high outliers.

    Calculate

    PROBLEM A

    \text{Q}_3+1.5\cdot\text{IQR}

    Q 3 ​ +1.5⋅IQR

    start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text

    \text{Q}_3+1.5\cdot\text{IQR}=

    Q 3 ​ +1.5⋅IQR=

    start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text, equals

    PROBLEM B

    How many data points can we say are high outliers?

    0 0 5 5 10 10 15 15 20 20 25 25 Scores Choose 1 answer: Choose 1 answer:

    Bonus learning: Showing outliers in box and whisker plots

    Box and whisker plots will often show outliers as dots that are separate from the rest of the plot.

    Here's a box and whisker plot of the distribution from above that does not show outliers.

    Scores 0 0 5 5 10 10 15 15 20 20 25 25

    Here's a box and whisker plot of the same distribution that does show outliers.

    Scores 0 0 5 5 10 10 15 15 20 20 25 25

    Notice how the outliers are shown as dots, and the whisker had to change. The whisker extends to the farthest point in the data set that wasn't an outlier, which was

    15 15 15 .

    Here's the original data set again for comparison.

    0

    स्रोत : www.khanacademy.org

    What Is Outlier Formula? Examples

    The extreme values in the data are called outliers. Understand the outlier formula with examples and FAQs.

    Outlier Formula 

    The extreme values in the data are called outliers. The outlier formula helps us to find outliers in a data set. The outlier in the literary world refers to the best and the brightest people. There is a non-fiction book 'Outliers' written by Malcolm Gladwell that debuted as the number one on the best seller books of the New York Times. Here, Malcolm describes outliers as people with exceptional intelligence, large fortunes, and who are different from the usual set of people.  In this lesson, we shall explore the outlier formula,by finding answers to questions like what is an outlier, how to find outliers using the turkey method, and solving examples at the end.

    What Is Outlier Formula?

    The extreme values in the data are called outliers.

    Example: For a data set containing  2, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 84

    In the above number line, we can observe the numbers 2 and 84 are at the extremes and are thus the outliers. The outliers are a part of the group but are far away from the other members of the group. The problem with outliers: Outliers create an imbalance in the data-set and hence are generally removed from the data. Also, sometimes the outlier occurs in the data-set, due to an error.

    Consider the data:  70, 73, 77, 71, 7, 73, 72, and 78

    Let's calculate the mean to understand how the outlier affects the results.

    Here, the datapoint 7, is an outlier.

    Mean (with outlier) = (70 + 73 + 77 + 71 + 7 + 73 + 72 + 78)/8  =  521/8  = 65.1

    Mean (without an outlier) = (70 + 73 + 77 + 71 + 73 + 72 + 78)/7  = 514/7  = 73.4

    We can now observe how the outlier creates a variation in the mean value of the data.

    Before we learn about finding the outlier, let's know about the quartiles and interquartile range.

    First Quartile Q1: The mid-value of the first half of the data represents the first quartile.

    Second Quartile Q2: The mid-value or the median of the data represents the second quartile

    Third Quartile Q3: The mid-value of the second half of the data represents the third quartile

    Outlier Formula (Turkey Method)

    Turkey's method is a mathematical method to find outliers. As per the Turkey method, the outliers are the points lying beyond the upper boundary of  Q3  +1.5 IQR and the lower boundary of Q1  - 1.5 IQR. These boundaries are referred to as outlier fences.

    Upper~Fence = Q3  +1.5 IQR

    Lower~Fence = Q1  - 1.5 IQR

    The data points beyond the upper and the lower fence in this box plot are referred to as outliers.

    The data points beyond the upper and the lower fence in this box plot are referred to as outliers.

    How Does Removing the Outlier Affect the Mean?

    Removing an outlier changes the value of the mean. Let us understand this with sample data of 10, 11, 14, 15, and 55

    Mean = (10 + 11 + 14 + 15 + 55)/5 = 105/5 = 21

    Mean (without the outlier) = (10 + 11 + 14 + 15)/4 = 50/4 = 12.5

    Here, on removing the outlier 55 from the sample data the mean changes from 21 to 12.5

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    Solved Examples Using Outlier Formula

    Example 1: Sam has got a set of multiples of the numbers 4, 8, 12, 16, 20, 22, 24, 28, 32, 36, 40, 44, 48, and 52. Help Sam to find the first quartile and the third quartile along with the outlier(s) of this data. Solve this by using the outlier formula.Solution:  The given data is 4, 8, 12, 16, 20, 22, 24, 28, 32, 36, 40, 44, 48, and 52

    Median = 28

    The first half of the data is 4, 8, 12, 16, 20, 22, 24, 28 and its mid-value is 16

    Q1 = 16

    The second half of the data is 28, 32, 36, 40, 44, 48, 52 and the mid-value is 40

    Q3 = 40

    Interquartile range IQR = Q3 - Q1 = 40 - 16 = 24

    1.5 IQR = 1.5 × 24 = 36

    Upper Boundary = Q3  +1.5 IQR = 40 + 36 = 76

    Lower Boundary = Q1  - 1.5 IQR = 16 - 36 = -20

    The outlier boundaries are -20 and 76, and no number lies beyond the upper and lower boundaries.

    Answer: The first quartile is 16 and the third quartile is 40. There are no outliers.Example 2: John has made a note of the scores of his classmates in a drawing assignment as 12, 19, 36, 33, 27, 19, 9, 66, 55, 44, 42, 71, 37, 39, 28, and 25.  Help John find the interquartile range and oulier(s) for this set of marks. Solve this by using the outlier formula.Solution:

    The given data is 12, 19, 36, 33, 27, 19, 9,  66, 55, 44, 42, 71, 37, 39, 28, and 25

    Arranging the data in an ascending order, we will have: 9, 12, 19, 19, 25, 27, 28, 33, 36,  37, 39, 42, 44, 55, 66, and 71

    Median = 33

    The first half of the data is  9, 12, 19, 19, 25, 27, 28, 33

    Q1 = (19 + 25)/2 = 44/2 = 22

    The second half of the data is 36, 37, 39, 42, 44, 55, 66, 71

    Q3 = (42 + 44)/2 = 86/2 = 43

    Interquartile Range IQR = Q3 - Q1 = 43 - 22 = 21

    स्रोत : www.cuemath.com

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