Topics › KS3 › Statistics
Mean, median, mode & range
-
What is the mode of these numbers? $$5,\ 8,\ 2,\ 8,\ 6,\ 3,\ 8,\ 11$$
A
Option A:
$3$
B
Option B:
$8$
C
Option C:
$9$
D
Option D:
$11$
Answer and misconceptions
A
Option A:
$3$
✗
Gives how often the mode occurs, not its value8 appears 3 times; the student gives the frequency 3 instead of the value 8.
B
Option B:
$8$
✓ Correct
C
Option C:
$9$
✗
Confuses mode with rangeWorks out 11 − 2 = 9, the range.
D
Option D:
$11$
✗
Thinks the mode is the largest valuePicks the biggest number, 11, instead of the most common.
-
What is the median of these numbers? $$6,\ 2,\ 9,\ 4,\ 7$$
A
Option A:
$9$
B
Option B:
$5.6$
C
Option C:
$7$
D
Option D:
$6$
Answer and misconceptions
A
Option A:
$9$
✗
Takes the middle value without ordering first9 is in the middle of the list as written; ordered (2, 4, 6, 7, 9) the median is 6.
B
Option B:
$5.6$
✗
Confuses median with meanAdds to 28 and divides by 5 to get 5.6, the mean.
C
Option C:
$7$
✗
Confuses median with rangeWorks out 9 − 2 = 7, the range.
D
Option D:
$6$
✓ Correct
-
What is the mean of these numbers? $$9,\ 0,\ 6,\ 0,\ 0$$
A
Option A:
$3$
B
Option B:
$7.5$
C
Option C:
$15$
D
Option D:
$0$
Answer and misconceptions
A
Option A:
$3$
✓ Correct
B
Option B:
$7.5$
✗
Leaves zeros out of the countDivides the total 15 by 2, counting only the non-zero values; there are 5 values, so 15 ÷ 5 = 3.
C
Option C:
$15$
✗
Gives the total, forgets to divideAdds the values to get 15 but does not divide by how many there are.
D
Option D:
$0$
✗
Confuses mean with mode0 is the most common value (the mode), not the mean.
-
Temperatures in °C were recorded: $$-4,\ 3,\ 7,\ -1,\ 5$$ What is the range?
A
Option A:
$3$
B
Option B:
$-11$
C
Option C:
$11$
D
Option D:
$9$
Answer and misconceptions
A
Option A:
$3$
✗
Ignores the negative sign when subtractingTreats −4 as 4 and works out 7 − 4 = 3 instead of 7 − (−4) = 11.
B
Option B:
$-11$
✗
Subtracts the largest from the smallestWorks out −4 − 7 = −11; range is largest minus smallest and is never negative.
C
Option C:
$11$
✓ Correct
D
Option D:
$9$
✗
Uses the last value minus the first valueWorks out 5 − (−4) = 9 using the ends of the unordered list.
-
The mean of 6 numbers is $10$. The number $3$ is added to the list. What is the mean of the 7 numbers?
A
Option A:
$6.5$
B
Option B:
$9$
C
Option C:
$10.5$
D
Option D:
$13$
Answer and misconceptions
A
Option A:
$6.5$
✗
Averages the old mean and the new valueWorks out (10 + 3) ÷ 2 = 6.5 instead of new total ÷ new count = 63 ÷ 7 = 9.
B
Option B:
$9$
✓ Correct
C
Option C:
$10.5$
✗
Divides the new total by the old countNew total is 60 + 3 = 63, but divides by 6 instead of 7: 63 ÷ 6 = 10.5.
D
Option D:
$13$
✗
Adds the new value to the meanWorks out 10 + 3 = 13 instead of recalculating total ÷ count.