Topics › KS3 › Statistics
Averages from tables
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The table shows goals scored in some football matches. What is the mode? $$\begin{array}{|l|c|c|c|c|c|}\hline \text{Goals} & 0 & 1 & 2 & 3 & 4\\\hline \text{Frequency} & 1 & 8 & 6 & 5 & 4\\\hline\end{array}$$
A
Option A:
$8$
B
Option B:
$4$
C
Option C:
$2$
D
Option D:
$1$
Answer and misconceptions
A
Option A:
$8$
✗
Gives the highest frequency, not the value8 is how many matches had the most common score; the mode is that score, 1 goal.
B
Option B:
$4$
✗
Thinks the mode is the largest valuePicks the largest number of goals, 4.
C
Option C:
$2$
✗
Confuses mode with median2 is the median (and the middle of the Goals row); the mode is the most common value.
D
Option D:
$1$
✓ Correct
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The table shows how many pets 20 students have. What is the median? $$\begin{array}{|l|c|c|c|c|c|}\hline \text{Pets} & 0 & 1 & 2 & 3 & 4\\\hline \text{Frequency} & 6 & 5 & 4 & 3 & 2\\\hline\end{array}$$
A
Option A:
$1$
B
Option B:
$2$
C
Option C:
$4$
D
Option D:
$10.5$
Answer and misconceptions
A
Option A:
$1$
✓ Correct
B
Option B:
$2$
✗
Takes the middle of the values rowPicks 2 because it is in the middle of 0–4, ignoring the frequencies.
C
Option C:
$4$
✗
Finds the median of the frequenciesFinds the middle frequency (4) instead of the middle student.
D
Option D:
$10.5$
✗
Gives the position, not the value(20 + 1) ÷ 2 = 10.5 is where the median is; the 10th and 11th students both have 1 pet.
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The table shows the scores of 20 students. What is the mean score? $$\begin{array}{|l|c|c|c|c|}\hline \text{Score} & 1 & 2 & 3 & 4\\\hline \text{Frequency} & 2 & 5 & 8 & 5\\\hline\end{array}$$
A
Option A:
$14$
B
Option B:
$2.5$
C
Option C:
$2.8$
D
Option D:
$5$
Answer and misconceptions
A
Option A:
$14$
✗
Divides by the number of rows, not the total frequencyTotal score 56 divided by 4 categories instead of by 20 students.
B
Option B:
$2.5$
✗
Averages the values, ignoring frequenciesWorks out (1 + 2 + 3 + 4) ÷ 4 = 2.5 as if each score happened once.
C
Option C:
$2.8$
✓ Correct
D
Option D:
$5$
✗
Finds the mean of the frequenciesWorks out (2 + 5 + 8 + 5) ÷ 4 = 5.
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The table shows the shoe sizes of some students. What is the range of the shoe sizes? $$\begin{array}{|l|c|c|c|c|c|c|}\hline \text{Size} & 3 & 4 & 5 & 6 & 7 & 8\\\hline \text{Frequency} & 0 & 5 & 9 & 7 & 3 & 0\\\hline\end{array}$$
A
Option A:
$5$
B
Option B:
$3$
C
Option C:
$9$
D
Option D:
$4$
Answer and misconceptions
A
Option A:
$5$
✗
Includes values with a frequency of 0Works out 8 − 3 = 5, but nobody wears size 3 or 8; range is 7 − 4 = 3.
B
Option B:
$3$
✓ Correct
C
Option C:
$9$
✗
Finds the range of the frequenciesWorks out 9 − 0 = 9 from the frequency row.
D
Option D:
$4$
✗
Counts how many different values appearCounts the 4 sizes that students wear (4, 5, 6, 7) instead of subtracting.
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The table shows how long 20 students took to get to school. Estimate the mean time. $$\begin{array}{|l|c|}\hline \text{Time } t \text{ (minutes)} & \text{Frequency}\\\hline 0 < t \le 10 & 4\\\hline 10 < t \le 20 & 10\\\hline 20 < t \le 30 & 6\\\hline\end{array}$$
A
Option A:
$21$ minutes
B
Option B:
$15$ minutes
C
Option C:
$106.7$ minutes
D
Option D:
$16$ minutes
Answer and misconceptions
A
Option A:
$21$ minutes
✗
Uses the upper class boundary, not the midpointUses 10, 20, 30: (40 + 200 + 180) ÷ 20 = 21. Midpoints 5, 15, 25 give 320 ÷ 20 = 16.
B
Option B:
$15$ minutes
✗
Gives the midpoint of the modal class15 is the middle of the group with the highest frequency, not the estimated mean.
C
Option C:
$106.7$ minutes
✗
Divides by the number of groupsWorks out 320 ÷ 3 ≈ 106.7 instead of dividing by the 20 students.
D
Option D:
$16$ minutes
✓ Correct
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The table shows how many books some students read last month. How many students are in the table? $$\begin{array}{|l|c|c|c|c|c|}\hline \text{Books} & 1 & 2 & 3 & 4 & 5\\\hline \text{Frequency} & 3 & 7 & 4 & 2 & 1\\\hline\end{array}$$
A
Option A:
$15$
B
Option B:
$5$
C
Option C:
$17$
D
Option D:
$7$
Answer and misconceptions
A
Option A:
$15$
✗
Adds the values row instead of the frequenciesWorks out $1 + 2 + 3 + 4 + 5 = 15$; the number of students is the total of the Frequency row.
B
Option B:
$5$
✗
Counts the columns in the tableCounts the 5 different numbers of books; each column holds several students.
C
Option C:
$17$
✓ Correct
D
Option D:
$7$
✗
Gives the highest frequency7 is how many students read 2 books, not the total number of students.