AI generatedStatisticsKS3 / GCSE

Comparing back-to-back stem-and-leaf diagrams

Comparing back-to-back stem-and-leaf diagrams.

  • Use the key. The stem is shared; read the left and right leaves separately.
  • On each side, the smallest leaf is nearest the stem. Keep repeated leaves.
  • Calculate the same average and spread for each group, then compare in context.

Example 1

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1264213380457931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (28 compared with 23) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.

Example 2

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1274213480458931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (28.5 compared with 24) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.

Your turn

Question 1

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1284213580459931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Check answer
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (29 compared with 25) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.
Question 2

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1264213680457931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Check answer
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (28 compared with 26) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.
Question 3

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1274213380458931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Check answer
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (28.5 compared with 23) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.
Question 4

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1284213480459931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Check answer
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (29 compared with 24) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.
Question 5

Compare the two groups’ test marks using their medians and ranges.

Back-to-back stem-and-leaf diagram for marksGroup AStemGroup B1264213580457931590368Key: 4 | 2 | 7A: 24 marks B: 27 marksRead each side away from the stem.
Check answer
Median AA has 9 values. Count to the fifth value: use stems from smallest to largest, and leaves away from the stem.
Median BB has 10 values. Average the fifth and sixth values.
Range AUse the largest minus the smallest value, not the leaves alone.
Range BCompare the same measure of spread for both groups.
Group B has a higher median (28 compared with 25) and a smaller range (24 compared with 27), so its marks are typically higher and more consistent.
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