Analyzing Mode in Real-World Data Sets

1) What is the mode of the first store's data?

5

3

4

7

The mode is the value that appears most frequently. In the first store's data, the number 5 occurs the most often.

Explanation

The mode is the value that appears most frequently. In the first store's data, the number 5 occurs the most often.

2) What is the mode of the second store’s data?

3

2

8

2 and 8

The mode is the most frequent number in a dataset. In the second store's data, both 2 and 8 appear the most often, so the data is bimodal.

Explanation

The mode is the most frequent number in a dataset. In the second store's data, both 2 and 8 appear the most often, so the data is bimodal.

3) Which statement best compares the most common transaction sizes between the stores?

Both stores have the same mode.

The first store’s most common is smaller than the second store’s.

The first store’s most common is 5 items; the second has two common sizes at 2 and 8 items.

The second store’s most common is 5 items.

The first store's most common transaction size is 5 items, while the second store has two common transaction sizes: 2 and 8 items.

Explanation

The first store's most common transaction size is 5 items, while the second store has two common transaction sizes: 2 and 8 items.

4) How does the outlier 12 in the first store’s data affect the mode?

It increases the mode to 12.

It does not affect the mode.

It decreases the mode to 4.

It makes the data bimodal.

The outlier 12 does not affect the mode because the mode is based on frequency, and the most frequent number (5) remains unchanged.

Explanation

The outlier 12 does not affect the mode because the mode is based on frequency, and the most frequent number (5) remains unchanged.

5) Which store shows a bimodal distribution?

Second store

Neither store

First store

Both stores

The second store has two modes (2 and 8), so it is bimodal.

Explanation

The second store has two modes (2 and 8), so it is bimodal.

6) If the first store adds another transaction of 5 items, what happens to its mode?

It becomes bimodal at 3 and 5.

It changes to 3.

It remains 5.

It changes to 4.

Adding another 5 items increases its frequency, making 5 even more frequent. Therefore, the mode remains 5.

Explanation

Adding another 5 items increases its frequency, making 5 even more frequent. Therefore, the mode remains 5.

7) Which store likely has a more consistent 'typical' transaction size based on the mode alone?

First store

Both

Neither

First store

The second store has two modes, indicating a more varied transaction size (small and medium-large baskets), while the first store has a single mode of 5, indicating more consistency.

Explanation

The second store has two modes, indicating a more varied transaction size (small and medium-large baskets), while the first store has a single mode of 5, indicating more consistency.

8) Which is a correct interpretation of the second store’s modes (2 and 8)?

There are two common patterns: small and medium-large baskets.

The average number of items is 2.

There are equal highest stacks at 2 and 8.

The median must be 8.

The modes 2 and 8 suggest that the store experiences two common patterns: small baskets (2 items) and larger baskets (8 items).

Explanation

The modes 2 and 8 suggest that the store experiences two common patterns: small baskets (2 items) and larger baskets (8 items).

9) What is the mode of the gear sizes?

12

14

11

16

The mode is the most frequently occurring value. In the list of gear sizes, 16 occurs the most frequently.

Explanation

The mode is the most frequently occurring value. In the list of gear sizes, 16 occurs the most frequently.

10) If the shop runs a sale that adds two more 12-tooth purchases, what happens to the mode?

Changes to 12

Becomes bimodal at 12 and 16

Remains 16

Changes to 14

Adding two more 12-tooth purchases increases the frequency of 12, making it the new mode.

Explanation

Adding two more 12-tooth purchases increases the frequency of 12, making it the new mode.

11) Which statement best explains what the mode tells the shop?

16-tooth gears are the most frequently sold.

16 is the only gear sold.

Most gears are larger than 16.

16-tooth gears are the most frequently sold.

The mode tells the shop that the most frequently sold gear size is 16 teeth.

Explanation

The mode tells the shop that the most frequently sold gear size is 16 teeth.

12) If the shop wants to stock the most common size, which should they prioritize?

16

14

18

16

The most common size is 16, so the shop should prioritize stocking that size.

Explanation

The most common size is 16, so the shop should prioritize stocking that size.

13) Which additional measure would best complement the mode to understand spread?

Sum

Product

Range or IQR

Factorization

To understand the spread of the data, the range or interquartile range (IQR) would be the best complementary measure.

Explanation

To understand the spread of the data, the range or interquartile range (IQR) would be the best complementary measure.

14) What is the mode of notifications per user?

1

2 and 3

4

0

The mode is the most frequent number. In this case, 2 and 3 both appear the most frequently, making the data bimodal.

Explanation

The mode is the most frequent number. In this case, 2 and 3 both appear the most frequently, making the data bimodal.

15) Which statement is supported by the mode?

Most users get 4 or more notifications.

The most common user experiences 2–3 notifications.

The distribution has no clear peak.

The mode shows that the most common number of notifications is either 2 or 3.

Explanation

The mode shows that the most common number of notifications is either 2 or 3.

16) If a new feature increases 3-notification users by 5, what happens to the mode?

Becomes 2 only

Becomes 3 only

Remains 2 and 3 tied

Becomes 4

Increasing the 3-notification users would make 3 the only mode, as it would now appear more frequently than 2.

Explanation

Increasing the 3-notification users would make 3 the only mode, as it would now appear more frequently than 2.

17) Which change would make the distribution unimodal at 3?

Increase 3 by at least 1

Decrease 2 by 1

Increase 2 by 2

Increase 4 by 3

To make the distribution unimodal at 3, we would need to increase the frequency of 3, making it the only mode.

Explanation

To make the distribution unimodal at 3, we would need to increase the frequency of 3, making it the only mode.

18) A dataset: 6, 6, 6, 7, 8, 9, 10, 12. What is the mode?

6

8

7

12

The mode is the value that appears most frequently. In this case, 6 appears three times, making it the mode.

Explanation

The mode is the value that appears most frequently. In this case, 6 appears three times, making it the mode.

19) Two classes record shoe sizes. Class A: 7, 7, 8, 8, 8, 9 Class B: 6, 6, 7, 7, 7, 7, 10. Which statement is true?

Both classes have the same mode.

Class A’s mode is 8; Class B’s mode is 7.

Class A is bimodal; Class B is unimodal at 8.

Class B is bimodal at 6 and 7.

Class A's mode is 8, while Class B's mode is 7.

Explanation

Class A's mode is 8, while Class B's mode is 7.

20) Which scenario shows the mode as the best measure of center?

A symmetric distribution of test scores.

A nearly normal distribution of heights.

Highly skewed income data with a common most-frequent low value.

A small dataset with all unique values.

The mode is most useful in cases where there is a common most-frequent low value, especially in highly skewed data like income.

Explanation

The mode is most useful in cases where there is a common most-frequent low value, especially in highly skewed data like income.