# Using the IQR to Find Outliers in a Data Set## Problem StatementThe last 11 calls to a customer support line had the following lengths (in minutes):52, 53, 53, 54, 56, 60, 62, 63, 64, 99Complete the parts below to identify any outliers.### Steps to Follow#### (a) Quartiles1. **Find the Lower Quartile (\(Q_1\))** and the Upper Quartile (\(Q_3\)) of the data set. Enter the values for \(Q_1\) and \(Q_3\). | Quartile | Value | |----------|-------| | \(Q_1\) | | | \(Q_3\) | |#### (b) Interquartile Range (IQR)2. **Find the Interquartile Range (IQR)** of the data set. \(\text{IQR} = Q_3 - Q_1\) IQR: [Enter value]#### (c) Calculate Boundaries3. **Calculate a Lower Boundary** using \(Q_1 - 1.5 \times \text{IQR}\).4. **Calculate an Upper Boundary** using \(Q_3 + 1.5 \times \text{IQR}\) (Note that 1.5-IQR means 1.5 times the IQR). | Boundary | Value | |----------------|-------| | Lower boundary | | | Upper boundary | |#### (d) Identify Outliers5. **Identify outliers**: Any values less than the lower boundary or greater than the upper boundary are considered outliers. List all outliers of the data set. If there is more than one outlier, separate them with commas. If there are no outliers, select "None". Outliers: [Enter values]### Interface Controls- **Check Button:** Verify your answers.- **Explanation Button:** View an explanation of the process.- **None Box:** Select if there are no outliers. The task is to apply the steps to calculate quartiles, IQR, boundaries, and determine the outliers. Enter the computed values in the corresponding fields.---This educational tool helps in understanding how to systematically identify out

observations in accending order52,53,53,54,55,56,60,62,63,64,99

Answered: O DESCRIPTIVE STATISTICS Using the IQR…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Questions 28 through 31
Are there any outliers? Show work. Min: 6. The following gives the time it takes to run 100M with 10 friends. Use the table to find the 5 number summary and IQR. Name AI Time (sec) 11.3 Beth Cindy David Emily Frank Gary 12.9 11.9 10.3 11.1 18.6 10.8 Find the 5 number summary: Q1: 5 10:3 103 10 0 11-15/01/3 Is 18.6 an outlier? Show work. 3-1.5 Median: Q3: Max: Helen Ida 10.5 12.0 Jay 10.9 IQR:
Are cigarettes bad for people? Cigarette smoking involves tar, carbon monoxide, and nicotine (measured in milligrams). The first two are definitely not good for a person's health, and the last ingredient can cause addiction. Use the data in the table above to make a stem-and-leaf display for milligrams of tar per cigarette smoked. (Enter NONE in any unused answer blanks.) Are there any outliers? A. Yes, 1.0 may be an outlier. B. No, there are no outliers. C. Yes, 29.8 may be an outlier.
The 11 members of the swim team completed the following numbers of laps at today's practice. 29, 78, 78, 79, 81, 83, 86, 87, 90, 91, 157 Complete the parts below to identify any outliers. (a) Let Q₁ be the lower quartile and Q3 be the upper quartile of the data set. Find 2₁ and 23 for the data set. 21₁=0 Q3 = (b) Find the interquartile range (IQR) of the data set. IQR Lower boundary: Upper boundary: X (c) Calculate a lower boundary using Q₁-1.5-IQR. Calculate an upper boundary using 23 +1.5-IQR. (Note that 1.5-IQR means 1.5 times the IQR.) Outliers: Explanation Check i X X (d) Any values less than the lower boundary or greater than the upper boundary are considered outliers. Identify all the outliers of the data set. If there is more than one outlier, separate them with commas. If there are no outliers, click "None". S X J None S McGraw Hill LLC. All Rights Reserved. Terms of Use | F
Use the following data set to answer Questions #12 and #13. 65 55 65 54 60 57 55 58 63 58 57 65 57 58 84 Are there any outliers? There exists at least one outlier in the data set at 84. There exists outliers in the data set at 55 and 84. O There are no outliers in the data set.
The outlier(s) in the data set 10, 17, 20, 21, 27, 22, 25, 24, 40 is (are) O a. 27 and 40 O b. 10 and 40 O c. 10 and 17 O d. 10 Ое. 40
5. The table below shows the temperature for each month in St. Pete, Florida. Use the table to find the 5 number summary and IQR. Min: Month Jan Feb Mar Apr May Jun 64 68 Temp 63 74 80 Min: 16 4 (3756 10 Find the 5 number summary: Are there any outliers? Show work. ( 18 Name Al Time (sec) Q1: 11.3 Q1: Median: Find the 5 number summary: 16. Median: Is 18.6 an outlier? Show work. 6. The following gives the time it takes to run 100M with 10 friends. Use the table to find the 5 number summary and IQR. 5 10 3 10 00 0-8-1-57 5 (12) 84 86, 86 Q3: 10.3 July Aug Sept 84 Beth Cindy David Emily Frank Gary Helen Ida 12.9 11.9 11.1 10.8 10.5 12.0 154 Q3: Max: 18.6 1500 Oct Nov Dec 70 78 48 IOR: Max: Jay 10.9 IQR:
The 5 numbers are 1, 6, 9, 11.25, and 28. Draw a Box Plot for this data. (Hint: Remember how to determine and show outliers in a box plot. See Fig. 4.3.3 on p. 184 in the textbook for an example.) Hints: The box extends from Q 1 to Q3 Draw a line through the box at the median Use the IQR method to determine outliers Outliers are any values less than Q1 - (1.5 x IQR) or greater than Q 3 - (1.5 x IQR) Show any outliers with Draw a whisker from the left side of the box to the lowest value that is NOT an outlier Draw a whisker from the right side of the box to the highest value that is NOT and outlier. 10
5 20 22 27 30 17 12 15 16 9 9 18 13 12 28 19 3. Compute the five-number summary and the interquartile range. Any outliers? 12 in the
For a set of observations, Q1 80 and Q3 = 130. Values greater than and less than are possible outliers.
The following stem-and-leaf plot is constructed using data collected from the speed (km/h) of cars passing through an intersection. Data values were rounded to one decimal place. Leaf Steam 50 51 52 53 54 55 9 0 1 1 0 1 7 5 2 1 2 7 5 5 1 3 Key: 50 | 9 = 50.9 km/h 7 6 2 7 7 5 a. How many cars were sampled? b. How many cars traveled through the intersection at 52.5 km/h? C. What is the highest speed (km/h) recorded? d. Is the distribution skewed positively or negatively? 9 6 6
Here are the scores of 10 students in an introductory statistics course: 55 74 75 81 83 85 92 93 93 97 Find the interquartile range and use the 1.5 x IQR rule to check for outliers. How low would the lowest score need to be for it to be an outlier according to the rule?

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