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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Box and Whisker Plots, Identifying Outliers

Grade: 1400-a Lesson: S4-L6

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the interquartile range(IQR) 8, 12, 13, 19, 22, 25, 7, 14, 5, and 16.
2	Step	Given the data set: 8, 12, 13, 19, 22, 25, 7, 14, 5, and 16.
3	Step	First, we have to find the first quartile and third quartile ranges Q1 and Q3. → Q1 is the median of the lower half of the data: (5, 7, 8, 12, and 13) = 8. → Q3 is the median of the upper half of the data:(14, 16, 19, 22, and 25) = 23.
4	Formula:	Inter Quartile Range(IQR) = Q3 - Q1.
5	Step	Now, we can calculate the interquartile range (IQR) using the formula → IQR = Q3 − Q1. → IQR = 19 - 8 = 11.
6	Step	Therefore the quartile range(IQR) for the given dataset is 11.
7	Choice.A	This option is correct because 11 is the accurate inter-quartile range for the given dataset	11
8	Choice.B	This option is incorrect. Although 13 is close to the actual IQR value, it is higher than the actual IQR value	13
9	Choice.C	This option is incorrect because 9 is not accurate when compared to the actual value of IQR	9
10	Choice.D	This option is incorrect because 17 is very much higher than the actual IQR value for a given dataset	17
11	Answer	Option	A
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the interquartile range(IQR)
8, 12, 13, 19, 22, 25, 7, 14, 5, and 16.

Step

Given the data set: 8, 12, 13, 19, 22, 25, 7, 14, 5, and 16.

Step

First, we have to find the first quartile and third quartile ranges Q1 and Q3.
→ Q1 is the median of the lower half of the data: (5, 7, 8, 12, and 13) = 8.
→ Q3 is the median of the upper half of the data:(14, 16, 19, 22, and 25) = 23.

Formula:

Inter Quartile Range(IQR) = Q3 - Q1.

Step

Now, we can calculate the interquartile range (IQR) using the formula
→ IQR = Q3 − Q1.
→ IQR = 19 - 8 = 11.

Step

Therefore the quartile range(IQR) for the given dataset is 11.

Choice.A

This option is correct because 11 is the accurate inter-quartile range for the given dataset

Choice.B

This option is incorrect. Although 13 is close to the actual IQR value, it is higher than the actual IQR value

Choice.C

This option is incorrect because 9 is not accurate when compared to the actual value of IQR

Choice.D

This option is incorrect because 17 is very much higher than the actual IQR value for a given dataset

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?