Question

The box plots compare the number of students in Mr. Ishimoto’s classes and in Ms. Castillo’s classes over the last two semesters.
Which statement is true about the box plots? Check all that apply.
-Both box plots show the same range.
-Both box plots show the same interquartile range.
-The data for Mr. Ishimoto has an outlier.
-Mr. Ishimoto had the class with the greatest number of students.
-The smallest class size was 24 students.

Answer 1

-Both box plots show the same interquartile range.
 >Interquartile range (IQR) is computed by Q3-Q1. 
For Mr. Ishimoto's class, Q3 is 35 and Q1 is 31. 35-31 = 4.
For Ms. Castillo's class, Q3 is 34 and Q1 is 30. 34-30 = 4.

-Mr. Ishimoto had the class with the greatest number of students.
 >Mr. Ishimoto had 40 students, represented by the last data point of the whiskers.

-The smallest class size was 24 students.
 >Which was Ms. Castillo's class.

Answer 2

Answer:

Step-by-step explanation:

In case of Mr. Ishimoto's class

Minimum :

$Q_0 = 28$

Lower Quartile :

$Q_1 = 31$

Median :

$Q_2 = 33$

Upper Quartile

$Q_3 = 35$

Maximum :

$Q_4 = 40$

In Case of Ms. Castilllo's class

Minimum :

$Q_0 = 24$

Lower Quartile :

$Q_1 = 30$

Median :

$Q_2 = 31$

Upper Quartile

$Q_3 = 34$

Maximum :

$Q_4 = 38$

Now range : $Q_4 - Q_0$

Range of Mr. Ishimoto's class : $40-28 =12$

Range of Ms. Castilllo's class: $38-24 =14$

Thus option A is incorrect since the range of the both box plots are not same

Inter quartile range :  $Q_3 - Q_1$

Inter quartile range(IQR) of Mr. Ishimoto's class : $35-31=4$

Inter quartile range (IQR)of Ms. Castilllo's class: $34-30=4$

Thus Option B is correct : Both box plots show the same interquartile range.

Now for the outlier of Mr. Ishimoto's class:

$Q_1 - 1.5*IQR$

$31-1.5*4$

$31-6$

$25$

$Q_3+1.5*IQR$

$35+1.5*4$

$35+6$

$41$

Thus the interval for outlier is(25,41)

Since all the values of the box plot lies within this interval .

So,The data for Mr. Ishimoto has no outlier.

Thus Option C is incorrect.

Mr. Ishimoto had 40 students, represented by the last data point of the whiskers.

So, Mr. Ishimoto's class  have greatest number of students.

Thus option D is correct.

The smallest class size was 24 students.

Which was Ms. Castillo's class.

So, Option E is true for Ms. Castillo's class.