Let’s solve this step by step.
First, we need to organize the given grades into a stem-and-leaf plot.
The data:
89, 85, 75, 76, 63, 90, 88, 94, 71, 54, 95, 79, 83, 85
Step 1: Sort the numbers from smallest to largest.
Sorted:
54, 63, 71, 75, 76, 79, 83, 85, 85, 88, 89, 90, 94, 95
Step 2: Build the stem-and-leaf plot.
Stem = tens digit
Leaf = ones digit
So:
Stem | Leaf
5 | 4
6 | 3
7 | 1 5 6 9
8 | 3 5 5 8 9
9 | 0 4 5
(We write each leaf in order from smallest to largest.)
Now let’s answer the questions using this plot.
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1. What is the range?
Range = highest value – lowest value
Highest = 95
Lowest = 54
Range = 95 - 54 =
41
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2. What is the mode?
Mode = number that appears most often
Looking at the list: 85 appears twice. All others appear once.
So mode =
85
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3. What is the mean?
Mean = sum of all values ÷ number of values
Add them up:
54 + 63 = 117
117 + 71 = 188
188 + 75 = 263
263 + 76 = 339
339 + 79 = 418
418 + 83 = 501
501 + 85 = 586
586 + 85 = 671
671 + 88 = 759
759 + 89 = 848
848 + 90 = 938
938 + 94 = 1032
1032 + 95 =
1127
There are 14 scores.
Mean = 1127 ÷ 14 =
80.5
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4. What is the median?
Median = middle value when sorted.
We have 14 numbers → even count → average of 7th and 8th values.
Sorted list again:
1: 54
2: 63
3: 71
4: 75
5: 76
6: 79
7: 83 ← 7th
8: 85 ← 8th
9: 85
10: 88
11: 89
12: 90
13: 94
14: 95
Median = (83 + 85) ÷ 2 = 168 ÷ 2 =
84
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5. Which stem has the most leaves? What does that mean in context?
Look at the stems:
Stem 5 → 1 leaf
Stem 6 → 1 leaf
Stem 7 → 4 leaves
Stem 8 → 5 leaves ← MOST
Stem 9 → 3 leaves
So stem
8 has the most leaves.
In context: That means more students scored in the 80s than any other ten-point range. So most students did well — got B’s or high C’s depending on grading scale.
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6. What percentage of the class scored 80 or higher?
Scores ≥ 80:
From sorted list: 83, 85, 85, 88, 89, 90, 94, 95 → that’s 8 scores.
Total students = 14
Percentage = (8 ÷ 14) × 100 ≈ 57.14% → round to nearest whole percent? Let’s keep one decimal if needed, but usually for these problems, we can say about
57%
But let’s calculate exactly:
8 ÷ 14 = 4/7 ≈ 0.5714 →
57.1%
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7. What percentage of the students failed the class (69 or less)?
Failed = score ≤ 69
From sorted list:
54, 63 → only two scores are ≤ 69
Wait — check: 71 is above 69, so yes, only 54 and 63.
That’s 2 students.
Percentage = (2 ÷ 14) × 100 ≈ 14.285... →
14.3%
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Final Answer:
1. Range: 41
2. Mode: 85
3. Mean: 80.5
4. Median: 84
5. Stem 8 has the most leaves; it means most students scored in the 80s.
6. 57.1% scored 80 or higher
7. 14.3% failed (scored 69 or less)
Parent Tip: Review the logic above to help your child master the concept of stem and leaf worksheet.
