Analysing and displaying data

Once you've collected data, summarising it helps reveal patterns. The mean (average) is found by adding all values and dividing by how many there are. The median is the middle value when data is ordered from smallest to largest (or the average of the two middle values if there's an even number). The mode is the value that appears most often. The range is the difference between the highest and lowest values, showing how spread out the data is. Data can also be displayed visually — in a stem-and-leaf plot, dot plot or column graph — to show its shape, centre and spread at a glance.

Key terms

Mean:

The average, found by adding all values and dividing by how many there are.

Median:

The middle value when data is ordered.

Mode:

The value that appears most often.

Range:

The difference between the highest and lowest values.

Questions

1. 1. The mean is also called the:

   • Middle value
   • Average
   • Most common value
   • Spread

2. 2. To find the mean, you:

   • Find the middle value
   • Add all values and divide by how many there are
   • Find the most common value
   • Subtract the smallest from the largest

3. 3. The median is:

   • The average
   • The middle value when ordered
   • The most common value
   • The range

4. 4. The mode is:

   • The average
   • The middle value
   • The most common value
   • The spread

5. 5. The range is:

   • The average
   • The middle value
   • The most common value
   • The difference between highest and lowest

6. 6. For the data set 2, 4, 4, 6, the mode is:

   • 2
   • 4
   • 6
   • There is no mode

7. 7. For the data set 1, 2, 3, 4, 5, the median is:

   • 1
   • 2
   • 3
   • 5

8. 8. Find the mean of 3, 5, 7, 9, 11.

   • 5
   • 6
   • 7
   • 8

9. 9. Find the median of 2, 8, 4, 10, 6.

   • 2
   • 4
   • 6
   • 8

10. 10. Find the mode of 5, 3, 5, 7, 5, 2.

    • 2
    • 3
    • 5
    • 7

11. 11. Find the range of 12, 5, 9, 20, 3.

    • 8
    • 15
    • 17
    • 20

12. 12. Find the median of 4, 8, 6, 2 (an even number of values).

    • 4
    • 5
    • 6
    • 8

13. 13. Find the mean of 10, 20, 30.

    • 15
    • 20
    • 25
    • 60

14. 14. A data set has no repeated values. What is its mode?

    • 0
    • There is no mode
    • The mean
    • The median

15. 15. A data set is 6, 8, 8, 10, 10, 10, 12. What is the mode?

    • 6
    • 8
    • 10
    • 12

16. 16. Which measure would be most affected by one extremely high outlier value?

    • Mode
    • Median
    • Mean
    • Range only slightly

17. 17. A data set has a mean of 10 and 5 values. What is the sum of all the values?

    • 2
    • 5
    • 15
    • 50

18. 18. Data set A: 5,5,5,5,20. Data set B: 5,6,7,8,9. Given the outlier in A, which set's mean better represents its data?

    • Set A's mean best represents its data
    • Set B's mean best represents its data
    • Both are equally representative
    • Neither has a mean

19. 19. A class's test scores have a median of 75 but a mean of 65. What might this suggest?

    • All scores are exactly 75
    • A few low outlier scores are pulling the mean down
    • The mean is always higher than the median
    • There is an error in the data

20. 20. Why might you choose the median over the mean to describe "typical" income in a country with a few extremely wealthy people?

    • The median is not affected as much by extreme outliers
    • The median is always larger
    • The mean is easier to calculate
    • There is no difference