Mode and Distributions

Shoe sizes: 3, 4, 3, 5, 3, 4, 6, 3. Mode = ___

Test scores: 7, 8, 9, 8, 7, 8, 10. Mode = ___

Ages: 10, 11, 10, 11, 12, 11, 10, 11. Mode = ___

Colours: blue, green, blue, red, green, blue. Mode = ___

Scores: 45, 78, 80, 82, 84, 85, 86, 88, 90. Most scores are ___ (high/low). Mode is ___.

Heights (cm): 120, 121, 125, 130, 130, 130, 131, 135, 160. Is there an outlier? ___

Ages at a party: 8, 9, 9, 10, 10, 10, 10, 11, 11, 35. Mode: ___. Outlier: ___

Daily temperatures: 18, 19, 20, 21, 21, 22, 22, 22, 23. Mode: ___. Are the data clustered or spread out?

Class A ages: 10, 10, 10, 11, 11, 11, 11, 12, 12. Mode: ___

Class B ages: 9, 10, 10, 11, 11, 11, 12, 12, 13. Mode: ___

Which class has more spread? ___

Which class has the same mode? ___

5, 8, 12, 3, 9, 7. Range = ___

20, 22, 25, 19, 21. Range = ___

100, 85, 92, 78, 95. Range = ___

Which data set above has the greatest spread? ___

Data: 5, 6, 5, 7, 6, 5, 50. The outlier is ___. Without it, the mode is ___.

Data: 80, 82, 85, 81, 83, 20. The outlier is ___. Does it affect the mode? ___

Write 8 numbers where the mode is 7: ___

Write 10 numbers where there is no mode: ___

Write 8 numbers where there are two modes (bimodal): ___

Mode: ___

Range: ___

Most of the data is clustered between ___ and ___

Describe the shape of the distribution: ___

Pets: dog, cat, dog, fish, dog, cat, bird. Mode = ___

Numbers: 4, 7, 4, 9, 7, 4, 9, 7, 4. Mode = ___

Colours: blue, red, green, blue, red, blue. Mode = ___

Scores: 85, 90, 85, 92, 90, 85, 88. Mode = ___

Test marks: 65, 70, 72, 73, 74, 75, 75, 76, 78. Mode: ___. Most marks are ___ (high/low/middle).

Daily steps: 3000, 5000, 5500, 6000, 6000, 6500, 6000, 7000, 12000. Mode: ___. Outlier: ___

Set A: 5, 6, 7, 7, 7, 8, 9. Mode: ___. Range: ___

Set B: 2, 5, 7, 7, 7, 9, 12. Mode: ___. Range: ___

Both have the same mode. Which has more spread? ___

Which data set has an outlier? ___

22, 25, 28, 30, 35. Range = ___

100, 102, 104, 106. Range = ___

15, 15, 15, 15, 50. Range = ___

Which data set above is most affected by an outlier? ___

Data: 12, 13, 14, 12, 13, 45. Outlier: ___. Without it, mode: ___. Range without it: ___

Data: 90, 88, 92, 91, 89, 30. Outlier: ___. How does it affect the range?

Write 10 numbers with mode = 15 and range = 8: ___

Write 8 numbers with two modes (bimodal) and range = 10: ___

Write 10 numbers where the mode is the smallest value: ___

Write 10 numbers where removing the outlier changes the mode: ___

Class A test scores: 40, 50, 60, 70, 70, 80, 90. Class B: 65, 68, 70, 70, 72, 75, 78. Which class has more consistent scores? Explain.

Which class has the same mode? Which has a smaller range? What does this tell us?

A shoe shop wants to know the most popular shoe size. They sold: Size 5 (12 pairs), Size 6 (18 pairs), Size 7 (15 pairs), Size 8 (8 pairs). What is the mode? Why is this useful?

A school canteen records sandwich sales: Mon 45, Tue 52, Wed 38, Thu 52, Fri 55. What is the mode day for sales? What might explain this?

Data: 4, 7, 5, 7, 7, 8, 6. Mode: ___ Median (middle value): ___ Mean: ___

Which measure best represents this data? Explain.

Data: 10, 11, 12, 11, 10. Mode: ___. Range: ___. Mean: ___

Add an outlier: 10, 11, 12, 11, 10, 100. New mode: ___. New range: ___. New mean: ___

Which measure was most affected by the outlier? ___

Sales data: 50, 52, 50, 53, 51, 50, 52. Mode: ___. Shape: ___ (clustered/spread)

Rainfall (mm): 0, 0, 5, 20, 50, 80, 100, 120. Shape: ___. Is there an outlier? ___

Create 8 values with mode = 12 and range = 6: ___

Create 6 values with no mode and range = 10: ___

Create 10 values with mode = 5 and mean = 5: ___

A teacher uses mode to set a target for the class. Test scores: 65, 72, 65, 80, 72, 65, 90. Mode = ___. Is mode useful here? Why?

A shoe company uses mode to decide which sizes to make most. Sales: Size 6×30, Size 7×45, Size 8×40, Size 9×20. Mode = ___. How many should they make of each?

House prices: $300k, $320k, $310k, $315k, $2000k. Which measure best represents typical prices? Why?

Ages at a family picnic: 8, 9, 10, 10, 10, 35, 38, 65. Mode: ___. Is mode useful here? ___

Data: 7, 3, 8, 5, 9. Sorted: ___. Median: ___

Data: 12, 8, 15, 10, 6, 14. Sorted: ___. Median (average of 2 middle): ___

Data: 3, 7, 7, 7, 9. Mode = ___. Median = ___. Mean = ___

Data: 42, 45, 48, 51, 53, 57, 62, 65, 69. Create a stem-and-leaf plot (stems: 4, 5, 6).

Median: ___ Mode: ___

Data: 5, 8, 5, 9, 3, 5, 7, 8. Mode: ___ Median: ___ Mean: ___ Range: ___

If you add 10 to every value: New mode: ___ New mean: ___ New range: ___

Which measure changed the most? ___

Set A: 10, 10, 10, 15, 20. Mode: ___ Mean: ___ Range: ___

Set B: 5, 10, 13, 15, 22. Mode: ___ Mean: ___ Range: ___

Both have the same mean (13). Which is more spread out? ___

Which set is skewed? Which is more symmetric? ___

Data: 2, 3, 3, 4, 4, 4, 5, 5, 6. Draw a dot plot from 2 to 6.

Mode: ___ Median: ___ Range: ___

Describe the shape of the distribution:

Heights of all 10-year-olds in Australia would be roughly ___ shaped (bell/skewed/uniform).

Ages of students at a primary school would be roughly ___ distributed (uniform/skewed).

Rainfall data for a dry region would likely be ___ skewed (left/right). Why?

Data: 23, 14, 31, 28, 17, 25, 19, 32, 22. Arrange in order: ___. Median: ___

Data: 45, 38, 52, 41, 47, 39, 50, 43. Arrange in order: ___. Median (average of 2 middle): ___

Temperatures (°C) this week: 22, 24, 23, 22, 25, 22, 21. Mode: ___. Is this a useful statistic for temperature? ___

Shirt sizes sold today: S, M, M, L, XL, M, L, S, M. Mode: ___. Why is mode useful for clothing? ___

A cricketer's scores: 45, 12, 67, 8, 89, 23, 45, 0, 78, 33. Mean: ___ Median: ___ Mode: ___

Which average best represents this player's typical performance? ___. Why?

Boys' steps: 8000, 9500, 7800, 10000, 8500. Girls' steps: 9200, 8800, 10200, 9500, 8900. Boys' mean: ___ Girls' mean: ___

Which group walked more on average? ___

Can you draw any conclusions about the whole school from just 5 students each? Why not?

Question: How do Year 5 students travel to school? Data to collect: ___

How would you collect data from 30 students? ___

What graph would you use? ___. Why?

What conclusion do you expect? ___

Data: 4, 6, 6, 7, 8, 8, 8, 9, 30. Mode: ___ Median: ___ Mean: ___

Which average is most affected by the outlier (30)? ___

Which average would you use to describe 'typical' performance? Why?

Students rate school lunch: 1=terrible, 2=poor, 3=OK, 4=good, 5=great. Ratings: 3,4,4,5,2,3,4,3,4,5. Mode: ___ Mean: ___

Does the mode or mean better describe the data? ___. Why?

Number of goals per game: 0(×3), 1(×5), 2(×6), 3(×4), 4(×2). Total games: ___

Modal number of goals: ___ Median: ___ Mean: ___

In how many games were more than 2 goals scored? ___

Design a short survey (3 questions) about student health and wellbeing at school:

What ethical considerations are important when collecting data about students?

Goals: 0 goals (5 games), 1 goal (8 games), 2 goals (4 games), 3 goals (3 games). Total goals: ___. Total games: ___. Mean: ___

Mode: ___. Median: ___

Class A marks: 65, 70, 72, 75, 78. Class B marks: 50, 65, 72, 85, 88. Mean A: ___ Mean B: ___

Median A: ___ Median B: ___. Range A: ___ Range B: ___

Which class is more consistent? ___. Which has higher scores? ___

A shoe shop wants to know the most common shoe size sold. Which average? ___. Why?

A school wants to know the typical student height. Which average? ___. Why?

A salary report shows data skewed by one very high earner. Which average is more representative? ___

Data: 3,4,4,5,5,5,6,6,7. Is this distribution symmetric, skewed right, or skewed left? ___

Data: 1,1,2,2,3,8,9,10. Which direction is this skewed? ___. Which average is most reliable? ___

What does it mean when a distribution is 'bell-shaped'?