Worksheet on understanding stem and leaf plots with data from cricket and basketball leagues.

Let’s solve each question step by step using the stem-and-leaf plots.

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First Plot: Cricket League Scores

Stem | Leaf
3 | 4 2 5 → scores: 34, 32, 35
4 | 1 2 3 → scores: 41, 42, 43
5 | 5 3 6 7 → scores: 55, 53, 56, 57
6 | 3 8 → scores: 63, 68
7 | 3 7 → scores: 73, 77
8 | 2 5 7 → scores: 82, 85, 87

Total players = 3 + 3 + 4 + 2 + 2 + 3 = 17 players

List of all scores in order (optional for some questions):
32, 34, 35, 41, 42, 43, 53, 55, 56, 57, 63, 68, 73, 77, 82, 85, 87

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Question 1: How many players scored less than 56?

Look at scores < 56:

From stem 3: 32, 34, 35 → 3 players
From stem 4: 41, 42, 43 → 3 players
From stem 5: 53, 55 → 2 players (56 is NOT included because it says “less than 56”)
→ Total = 3 + 3 + 2 = 8 players

✔ Answer to Q1: 8

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Question 2: How many players scored less than 62?

Scores < 62:

All from stems 3, 4, 5 → that’s 3 + 3 + 4 = 10 players
From stem 6: only 63 and 68 — both are ≥62 → so none added
Wait — let’s list them to be sure:

32, 34, 35, 41, 42, 43, 53, 55, 56, 57 → these are all <62?
57 < 62 → yes
63 > 62 → no
So up to 57: that’s 10 scores (stems 3,4,5)
Is there any score between 57 and 62? No. So total = 10 players

✔ Answer to Q2: 10

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Question 3: What are the lowest 2 scores?

From the ordered list:
Lowest: 32
Second lowest: 34
→ 32 and 34

✔ Answer to Q3: 32 and 34

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Question 4: What are the top 2 scores?

Highest: 87
Second highest: 85
→ 85 and 87

✔ Answer to Q4: 85 and 87

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Question 5: What is the range of the scores?

Range = Highest - Lowest = 87 - 32 = 55

✔ Answer to Q5: 55

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Now second plot: Basketball Teams Games Played

Stem | Leaf
3 | 3 8 6 3 → games: 33, 38, 36, 33
4 | 1 9 9 2 → games: 41, 49, 49, 42
5 | 2 3 6 6 → games: 52, 53, 56, 56
6 | 4 8 → games: 64, 68
7 | 1 3 5 → games: 71, 73, 75
8 | 9 → games: 89

Total teams = 4 + 4 + 4 + 2 + 3 + 1 = 18 teams

Ordered list (for reference):
33, 33, 36, 38, 41, 42, 49, 49, 52, 53, 56, 56, 64, 68, 71, 73, 75, 89

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Question 6: How many teams were in the league?

We counted above: 18 teams

✔ Answer to Q6: 18

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Question 7: How many teams played less than 52 times?

Scores < 52:

Stem 3: 33, 33, 36, 38 → 4 teams
Stem 4: 41, 42, 49, 49 → 4 teams
Stem 5: first value is 52 → not less than 52 → stop here
→ Total = 4 + 4 = 8 teams

✔ Answer to Q7: 8

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Question 8: How many teams played more than 64 times?

Scores > 64:

Stem 6: 64 is not greater → skip; 68 → 1 team
Stem 7: 71, 73, 75 → 3 teams
Stem 8: 89 → 1 team
→ Total = 1 + 3 + 1 = 5 teams

✔ Answer to Q8: 5

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Question 9: What is the mean number of games played?

Mean = sum of all games ÷ number of teams

Add all values:

Stem 3: 33+38+36+33 = let’s compute:
33+33=66, 36+38=74 → 66+74=140

Stem 4: 41+49+49+42 = 41+42=83, 49+49=98 → 83+98=181

Stem 5: 52+53+56+56 = 52+53=105, 56+56=112 → 105+112=217

Stem 6: 64+68 = 132

Stem 7: 71+73+75 = 71+73=144, +75=219

Stem 8: 89

Now add all together:

140 (stem3)
+181 = 321
+217 = 538
+132 = 670
+219 = 889
+89 = 978

Total sum = 978

Number of teams = 18

Mean = 978 ÷ 18

Let’s divide:

18 × 50 = 900
978 - 900 = 78
18 × 4 = 72 → remainder 6
So 54 with remainder 6 → 54 + 6/18 = 54 + 1/3 ≈ 54.333...

But since we’re dealing with whole games, maybe they want exact fraction or decimal?

Actually, let’s check division again:

978 ÷ 18

Divide numerator and denominator by 6:
978 ÷ 6 = 163
18 ÷ 6 = 3
→ 163 ÷ 3 = 54.333...

Or as mixed number: 54 1/3

But in context, probably acceptable as decimal: 54.3 (rounded to one decimal) or exact fraction.

Wait — let me double-check the sum:

Stem 3: 33,33,36,38 → 33+33=66, 36+38=74 → 66+74=140 ✔️
Stem 4: 41,42,49,49 → 41+42=83, 49+49=98 → 83+98=181 ✔️
Stem 5: 52,53,56,56 → 52+53=105, 56+56=112 → 105+112=217 ✔️
Stem 6: 64+68=132 ✔️
Stem 7: 71+73=144, +75=219 ✔️
Stem 8: 89 ✔️

Total: 140+181=321; 321+217=538; 538+132=670; 670+219=889; 889+89=978 ✔️

978 ÷ 18:

Do long division:

18 into 97 → 5 times (90), remainder 7
Bring down 8 → 78
18 into 78 → 4 times (72), remainder 6
So 54 R6 → 54 and 6/18 = 54 and 1/3 → 54.333...

In school contexts, often rounded to nearest tenth: 54.3

But let’s see if problem expects exact value. Since it's "mean", and data is integers, fractional mean is fine.

I’ll write it as 54.3 (if rounding) or 54⅓. But looking at typical worksheets, they might expect decimal.

Alternatively, perhaps I made a mistake? Let me add again differently:

List all numbers:

33,33,36,38,41,42,49,49,52,53,56,56,64,68,71,73,75,89

Group:

(33+33)=66
(36+38)=74 → subtotal 140
(41+42)=83
(49+49)=98 → subtotal 181 → total so far 321
(52+53)=105
(56+56)=112 → subtotal 217 → total 538
(64+68)=132 → total 670
(71+73)=144
+75=219 → total 889
+89=978 ✔️

Yes, correct.

978 ÷ 18 = 54.333... → so 54.3 if rounded to one decimal place.

But let’s check: 18 × 54.333... = 18 × 54 + 18 × 1/3 = 972 + 6 = 978 ✔️

So mean is exactly 54⅓ or approximately 54.3

I think for this level, writing 54.3 is acceptable.

✔ Answer to Q9: 54.3

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Question 10: How many teams played the same number of games?

This means: how many teams have duplicate game counts? Or perhaps: how many teams are part of a group that has the same number?

Looking at the data:

33 appears twice → 2 teams
49 appears twice → 2 teams
56 appears twice → 2 teams
Others appear once.

So teams that played the same number: those in duplicates.

But the question is ambiguous. It could mean:

Option A: How many teams are in groups where at least two teams have same score? → then 2 (for 33) + 2 (for 49) + 2 (for 56) = 6 teams

Option B: How many distinct numbers are repeated? → 3 numbers (33,49,56)

But the wording: “How many teams played the same number of games?” — likely means how many teams are involved in ties.

In most such problems, they mean: count the number of teams that share their game count with at least one other team.

So:

- Two teams played 33 games → both count
- Two teams played 49 games → both count
- Two teams played 56 games → both count
Total = 2 + 2 + 2 = 6 teams

If it meant “how many pairs” or something else, but I think 6 is correct.

Check: total teams 18, unique values: let’s see how many unique:

33,36,38,41,42,49,52,53,56,64,68,71,73,75,89 → that’s 15 unique? Wait no:

Values: 33(x2),36,38,41,42,49(x2),52,53,56(x2),64,68,71,73,75,89 → so 15 distinct values, but 3 values repeated → so 3×2=6 teams are in repeats, rest 12 are unique.

Yes.

✔ Answer to Q10: 6

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Final Answers:

1. 8
2. 10
3. 32 and 34
4. 85 and 87
5. 55
6. 18
7. 8
8. 5
9. 54.3
10. 6

Note: For Q9, if exact fraction is preferred, it’s 54⅓, but 54.3 is standard for such contexts.

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Final Answer:
1. 8
2. 10
3. 32 and 34
4. 85 and 87
5. 55
6. 18
7. 8
8. 5
9. 54.3
10. 6