Interpreting Mode from Graphical Displays

1) What is the mode of the number of books read?

3

5

6

4

The mode is the number that appears most frequently in a data set. According to the dot plot, 4 is the most frequently occurring number, so the mode is 4.

Explanation

The mode is the number that appears most frequently in a data set. According to the dot plot, 4 is the most frequently occurring number, so the mode is 4.

2) Which statement best explains the mode in this context?

More students read 4 books than any other number.

Most students read between 5 and 6 books.

The average student read 4 books.

Half of the students read 4 books.

The mode represents the value that appears most frequently in the data set, which is 4. So, the correct explanation is that more students read 4 books than any other number.

Explanation

The mode represents the value that appears most frequently in the data set, which is 4. So, the correct explanation is that more students read 4 books than any other number.

3) If one more student who read 4 books is added to the data, how does the mode change?

The mode decreases.

The mode increases.

The mode stays the same.

Since 4 is already the mode and adding one more student who read 4 books increases the frequency of 4, the mode will stay the same.

Explanation

Since 4 is already the mode and adding one more student who read 4 books increases the frequency of 4, the mode will stay the same.

4) If all students who read 6 books are removed, what is the mode?

4

5

6

3

If the students who read 6 books are removed, the most frequent value left in the data set would be 4, which remains the mode.

Explanation

If the students who read 6 books are removed, the most frequent value left in the data set would be 4, which remains the mode.

5) If one additional dot is added at 8, what happens to the mode?

The mode becomes 8.

The mode becomes 5.

The distribution becomes bimodal at 4 and 8.

The mode remains 4.

Adding a dot at 8 does not make it the most frequent number, as 4 is still the mode. The distribution would become bimodal at 4 and 8 because both numbers would have the same frequency.

Explanation

Adding a dot at 8 does not make it the most frequent number, as 4 is still the mode. The distribution would become bimodal at 4 and 8 because both numbers would have the same frequency.

6) If the dot at 8 is moved to 4, which statement becomes true?

The mode becomes 5.

The mode at 4 becomes even more frequent.

The distribution becomes bimodal.

The mode becomes 8.

If the dot at 8 is moved to 4, it increases the frequency of 4, making it even more frequent than before, so the mode at 4 becomes even more frequent.

Explanation

If the dot at 8 is moved to 4, it increases the frequency of 4, making it even more frequent than before, so the mode at 4 becomes even more frequent.

7) Which interval contains the mode (use non-overlapping intervals)?

0–2

3–5

6–8

9–11

The mode is 4, and the interval that contains 4 is 3–5.

Explanation

The mode is 4, and the interval that contains 4 is 3–5.

8) A student says the mode is 6 because it is a larger number than 4. Why is this incorrect?

6 is not shown on the plot.

6 has the fewest dots.

Mode depends on frequency, not size of the number.

Mode is the middle number.

The mode is determined by the frequency, not by the size of the number. Since 4 occurs most frequently in the data set, the mode is 4, not 6, regardless of the size of the numbers.

Explanation

The mode is determined by the frequency, not by the size of the number. Since 4 occurs most frequently in the data set, the mode is 4, not 6, regardless of the size of the numbers.

9) What are the modes of the data set?

41

41 and 50

32 and 41

32, 41, and 50

The stem-and-leaf plot shows that 32, 41, and 50 appear most frequently in the data, so the modes are 32, 41, and 50.

Explanation

The stem-and-leaf plot shows that 32, 41, and 50 appear most frequently in the data, so the modes are 32, 41, and 50.

10) Which values occur most frequently?

23 and 25

41 and 50

32, 41, and 50

30 and 32

The most frequent values in the stem-and-leaf plot are 32, 41, and 50.

Explanation

The most frequent values in the stem-and-leaf plot are 32, 41, and 50.

11) If one more 32 is added, what is the new mode?

32

41

50

23

Adding one more 32 increases the frequency of 32, making it the new mode.

Explanation

Adding one more 32 increases the frequency of 32, making it the new mode.

12) What does the mode represent in this context?

The longest time spent on homework

The most common number of minutes students spent on homework

The average time spent on homework

The middle time in the list

The mode represents the most common value in the data set, which is the most frequent number of minutes students spent on homework.

Explanation

The mode represents the most common value in the data set, which is the most frequent number of minutes students spent on homework.

13) If the 49 is changed to 39, how does the mode change?

The mode changes to 49.

The data becomes bimodal.

The mode does not change.

There is no mode.

Changing the 49 to 39 does not affect the mode because 41 and 50 are still the most frequent values.

Explanation

Changing the 49 to 39 does not affect the mode because 41 and 50 are still the most frequent values.

14) Which statement is true about the stem-and-leaf plot?

The mode is 37.

All values occur the same number of times.

The mode is 23.

There are three modes: 32, 41, and 50.

There are three modes: 32, 41, and 50, as they appear most frequently in the stem-and-leaf plot.

Explanation

There are three modes: 32, 41, and 50, as they appear most frequently in the stem-and-leaf plot.

15) What is the mode number of goals?

0

1

2

4

The mode is the most frequently occurring value in the data set. In this case, 2 is the most common number of goals scored.

Explanation

The mode is the most frequently occurring value in the data set. In this case, 2 is the most common number of goals scored.

16) What does the mode tell you about the team’s typical performance?

They usually score the fewest goals possible.

They most often scored 2 goals in a game.

They never scored more than 2 goals.

They most often scored 2 goals in a game.

The mode indicates that the team most frequently scored 2 goals in a game.

Explanation

The mode indicates that the team most frequently scored 2 goals in a game.

17) If two games with 3 goals are added, how does the mode change?

The mode becomes 3.

The mode stays 2.

The mode does not change.

There is no mode.

Adding two games with 3 goals would make 3 the most frequent value, so the mode changes to 3.

Explanation

Adding two games with 3 goals would make 3 the most frequent value, so the mode changes to 3.

18) If every game’s goals are increased by 1, what happens to the mode?

It increases by 1.

It decreases by 1.

It stays the same.

It becomes the median.

If every goal count is increased by 1, the mode would also increase by 1.

Explanation

If every goal count is increased by 1, the mode would also increase by 1.

19) If the distribution becomes bimodal, which could be true?

There are equal highest stacks at 2 and 3.

All values occur once.

The tallest stack is at 4 only.

There are no goals at all.

If the distribution becomes bimodal, there would be equal highest frequencies at 2 and 3 goals.

Explanation

If the distribution becomes bimodal, there would be equal highest frequencies at 2 and 3 goals.

20) Which statement about mode is always true for these displays?

Mode equals mean.

Mode equals median.

Mode is the value or category with the greatest frequency.

Mode is the largest value shown.

The mode is always the value or category that appears most frequently in the data.

Explanation

The mode is always the value or category that appears most frequently in the data.