Question

The students in Mr. McIntyre’s class and in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results.
Mr. McIntyre’s Class
A dot plot titled Mister McIntyre's Class. A number line going from 0 to 5 is labeled Number of Pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Mrs. Ramos’s Class
A dot plot titled Misses Ramos's Class. A number line going from 0 to 5 is labeled Number of Pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
Which statement correctly compares the measures of center of the data in the dot plots?
The median is greater for Mr. McIntyre’s class.
The median is the same for both classes.
The mode is greater for Mrs. Ramos’s class.
The mode is the same for both classes.

Answer 1

Therefore, The median is the same for both classes.

Given:

In Mr. McIntyre’s Class

A dot plot titled Mister McIntyre's Class.

A number line going from 0 to 5 is labeled Number of Pets.

There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.

In Mrs. Ramos’s Class

A dot plot titled Misses Ramos's Class.

A number line going from 0 to 5 is labeled Number of Pets.

There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, and 3 above 5.

To Find:

Correct Comparison of measurement of center of the data in the dot plots.

Solution:

We can simply solve this numerical problem by using the following process.

Given that

In Mr. McIntyre’s Class

Number of dots above 0 = 5

Number of dots above 1 = 5

Number of dots above 2 = 4

Number of dots above 3 = 1

Number of dots above 4 = 0

Number of dots above 5 = 0

Representation of above data in the form of data set Mc = { 5, 5, 4, 1, 0, 0 }

In Mrs. Ramos’s Class

Number of dots above 0 = 1

Number of dots above 1 = 2

Number of dots above 2 = 2

Number of dots above 3 = 4

Number of dots above 4 = 3

Number of dots above 5 = 3

Representation of above data in the form of data set Rc = { 1, 2, 2, 4, 3, 3 }

Finding the Median for both the data sets,

Median of Mr. McIntyre’s Class,

Writing the elements in Mc in ascending order

⇒ { 0,0,1,4,5,5 }

Median = Average of middle most two elements ( because the data set consists of even numbers ) = ( 1 + 4 )/2

⇒ Median of Mr. McIntyre’s Class Mc = 2.5

Mode = Most often repeated value in the Data set

⇒ Mode of Mr. McIntyre’s Class Mc = 0 and 5

Similarly writing the elements in ascending order of Mrs. Ramos’s Class

⇒ { 0,2,2,3,3,4 }

Median of Mrs. Ramos’s Class Rc = ( 2+3 )/2

⇒ Median of Mrs. Ramos’s Class Rc = 2.5

⇒  Mode of Mrs. Ramos’s Class Rc = 2 and 3

Hence, Median of Mc = Median of Rc

Therefore, The median is the same for both classes.

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