Topics › KS3 › Statistics

Interpreting charts

1. chart-01 Present from here

   The pictogram shows books borrowed from a library. How many books were borrowed on Tuesday?

   
   A Option A: $3.5$

   B Option B: $13$

   C Option C: $16$

   D Option D: $14$
   Answer and misconceptions

   A Option A: $3.5$ ✗

   Counts symbols and ignores the keyCounts 3½ circles without multiplying by 4 books per circle.

   B Option B: $13$ ✗

   Treats a part symbol as worth 1Works out 3 × 4 = 12 and adds 1 for the half circle; half a circle is worth 2.

   C Option C: $16$ ✗

   Counts a part symbol as a whole symbolCounts 4 circles and works out 4 × 4 = 16.

   D Option D: $14$ ✓ Correct
2. chart-02 Present from here

   How many students chose swimming?

   
   A Option A: $7$

   B Option B: $3.5$

   C Option C: $6$

   D Option D: $6.5$
   Answer and misconceptions

   A Option A: $7$ ✓ Correct

   B Option B: $3.5$ ✗

   Counts grid squares, ignoring the scaleThe bar is 3½ squares tall, but each square is worth 2.

   C Option C: $6$ ✗

   Reads only the labelled line below the barReads 6 and ignores the part of the bar above the gridline.

   D Option D: $6.5$ ✗

   Treats half a grid gap as 0.5Assumes each gap is worth 1, so halfway past 6 becomes 6.5; halfway between 6 and 8 is 7.
3. chart-03 Present from here

   60 students were asked their favourite sport. How many chose football?

   
   A Option A: $90$

   B Option B: $25$

   C Option C: $15$

   D Option D: $54$
   Answer and misconceptions

   A Option A: $90$ ✗

   Reads the angle as the number of peopleGives 90 because the sector angle is 90°; 90° is ¼ of 360°, so ¼ of 60 = 15.

   B Option B: $25$ ✗

   Gives the percentage, not the numberCorrectly sees a quarter = 25% but gives 25 instead of 25% of 60.

   C Option C: $15$ ✓ Correct

   D Option D: $54$ ✗

   Treats the angle as a percentageWorks out 90% of 60 = 54, as if degrees were percentages.
4. chart-04 Present from here

   The stem-and-leaf diagram shows the ages of people at a party. What is the range of the ages?

   
   A Option A: $3$

   B Option B: $28$

   C Option C: $9$

   D Option D: $2.8$
   Answer and misconceptions

   A Option A: $3$ ✗

   Uses only the stemsWorks out 4 − 1 = 3 from the stems; the values are 42 and 14.

   B Option B: $28$ ✓ Correct

   C Option C: $9$ ✗

   Uses only the leavesWorks out 9 − 0 = 9 from the largest and smallest leaves.

   D Option D: $2.8$ ✗

   Reads stem and leaf as a decimalReads 4 | 2 as 4.2 and 1 | 4 as 1.4, ignoring the key, so gets 2.8.
5. chart-05 Present from here

   Which statement is best supported by the scatter graph?

   
   A Option A: Revising more causes a higher mark

   B Option B: Every student who revised more got a higher mark

   C Option C: Students who revised more tended to get higher marks

   D Option D: Students who revised less tended to get higher marks
   Answer and misconceptions

   A Option A: Revising more causes a higher mark ✗

   Thinks correlation proves causationA scatter graph shows a relationship, not that one thing causes the other.

   B Option B: Every student who revised more got a higher mark ✗

   Thinks correlation applies to every individualCorrelation is a trend; the student at 8 hours and 15 marks breaks it.

   C Option C: Students who revised more tended to get higher marks ✓ Correct

   D Option D: Students who revised less tended to get higher marks ✗

   Confuses positive and negative correlationPoints go up from left to right, so more revision goes with higher marks.