Question

The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.

Answer 1

1) What is the mean of the data set:

The best plot is the dot plot. Sum the values of each dot and divide by the number of dots.

2) What is the median of the data set:

Use the box plot. The median is the value in the middle of the rectangle. That is 8.

3) What is the interquartile range:

Use the box plot.  The interquartile range is the length of the rectangle. That is 10 - 6 = 4

4) How many members use the facility 10 days a month:

Use the box plot. The answer count how many dots are over the number 10. That is 2.

Answer 2

Answer: Mean = 8

Median = 8

Interquartile range= 4

The number of member use facility 10 days a month = 2

Step-by-step explanation:

From the given dot plot, the mean of the data is given by :-

$\text{Mean}=\dfrac{\sum\ fx}{\sum f}$

, where f is represents the number of dots for each value and x represent the value on number line

$\\\\\\\Rightarrow\text{Mean}=\dfrac{6\cdot2+7\cdot1+8\cdot3+9\cdot1+2\cdot10+11\cdot1+12\cdot1+14\cdot1}{15}\\\\=\dfrac{120}{15}=8$

The number of dots in the dot plot = 15 (odd)

Then, the term of median value = value of middle most dot = 8

Using the given box plot, the interquartile range of the data is given by :-

$IQ=Q_3-Q_1\\\\\Rightarrow\ IQ=10-6=4$

From dot , plot the number of member use facility 10 days a month = 2