Data 1
0 2
4
7
Data 2
0
2
Part(a)
In complete sentences, explain why each statement is false.
(1) Data 1 has more data values above 2 than Data 2 has above 2.
In a box plot, only the medians can be viewed, not how many data values there actually are.
In Data 1, the data value 2 is the lower quartile, and in Data 2, the data value 2 is the median.
In a box plot, only the percentages can be viewed above a given data value, not how many data values there actually are.
The whisker is longer for Data 2 than for Data 1, so Data 2 has more data values above 2.
Incorrect. Quartiles and medians do not tell us how many data values are above those numbers.
(i) The data sets cannot have the same mode.
The boxes overlap the same values on the scale, so the data sets can have the same mode.
O Two data sets with different values can still have the same average.
O Only the median in two data sets cannot be the same.
O The mode of a data set is not evident in a box plot.
x
Incorrect. The box describes where half of the data values lie, but does not tell what the specific values are.
(iii) For Data 1, there are more data values below 4 than there are above 4.
The box plot is more compact above 4 than below 4, so there are more values close together.
O The mode of the data set is 4, which indicates that half of the values are below 4 and half of the values are above 4.
The top half of the box is more compact than the bottom half, so there are more values close together.
O The median of the data set is 4, which indicates that half of the values are below 4 and half of the values are above 4.