Worksheet titled "Reading stem and leaf plots" featuring a stem and leaf plot of math exam scores and related questions.

Let’s go step by step to answer each question using the stem-and-leaf plot.

First, let’s list out all the scores from the plot:

Stem | Leaf → Scores
6 | 4 5 7 → 64, 65, 67
7 | 5 → 75
8 | 0 5 → 80, 85
9 | 0 0 → 90, 90

So the full list of scores is:
64, 65, 67, 75, 80, 85, 90, 90

There are 8 scores total — that means 8 students.

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Now let’s answer each question one by one.

a) How many students were there?
→ Count the number of leaves (or scores). There are 8.
✔ Answer: 8

b) How many students scored less than 90 points?
→ Look at scores below 90: 64, 65, 67, 75, 80, 85 → that’s 6 students.
(The two 90s are NOT less than 90.)
✔ Answer: 6

c) How many students scored between 60 and 80 points?
→ “Between 60 and 80” usually means ≥60 and <80 (not including 80 unless specified). But in school contexts, sometimes it includes both ends. Let’s check the scores:

Scores from 60 to 80 inclusive: 64, 65, 67, 75, 80 → that’s 5 scores.
If it meant strictly between (excluding 80), then only 64, 65, 67, 75 → 4.
But since 80 is listed under stem 8, and the question says “between 60 and 80”, we should include 60–79. Wait — actually, 80 is not less than 80. So if it’s “between 60 and 80”, it likely means 60 ≤ score < 80.

Looking again:
64, 65, 67, 75 → these are all <80 and ≥60 → 4 students.
80 is equal to 80, so if “between 60 and 80” excludes 80, then 4.
But sometimes teachers mean inclusive. Let’s see what makes sense with the data.

Actually, looking at common usage in such problems, “between 60 and 80” often includes 60 up to but not including 80. But let’s double-check the exact wording: “scored between 60 and 80 points”. In math, this can be ambiguous, but in stem-and-leaf plots like this, they usually mean 60–79.

Wait — our scores are:
64, 65, 67 → 60s
75 → 70s
80 → 80s → so if we want scores from 60 to 79, that’s 64,65,67,75 → 4 students.

But let me confirm: Is 80 included? The problem says “between 60 and 80”. If it said “from 60 to 80”, it might include 80. Since it says “between”, I think it’s safer to exclude 80. However, in many school worksheets, they may include both. Let’s look at the next part — maybe we can cross-check.

Alternatively, perhaps the problem intends 60 to 80 inclusive. Let’s count how many scores are ≥60 and ≤80: 64,65,67,75,80 → 5.

I think for this level, they probably mean inclusive. Let’s go with 5, because 80 is a round number and often included. Also, in the plot, 80 is clearly shown, and if they wanted to exclude it, they’d say “less than 80”.

Actually, let’s re-read: “between 60 and 80 points”. In everyday language, if you say “between 60 and 80”, people often include 60 and 80. For example, “ages between 10 and 20” includes 10 and 20.

So I’ll go with inclusive: 64,65,67,75,80 → 5 students.

✔ Answer: 5

d) What was the lowest score?
→ First score in the list: 64
✔ Answer: 64

e) What was the highest score?
→ Last score: 90 (and there are two 90s, but highest is still 90)
✔ Answer: 90

f) What was the mean score?
→ Mean = sum of all scores ÷ number of students

Sum = 64 + 65 + 67 + 75 + 80 + 85 + 90 + 90

Let’s add step by step:

64 + 65 = 129
129 + 67 = 196
196 + 75 = 271
271 + 80 = 351
351 + 85 = 436
436 + 90 = 526
526 + 90 = 616

Total sum = 616
Number of students = 8

Mean = 616 ÷ 8 = ?

8 × 77 = 616 → yes, because 8×70=560, 8×7=56, 560+56=616.

✔ Answer: 77

g) What was the median score?
→ Median is the middle value when ordered. We have 8 scores (even number), so median is average of 4th and 5th values.

Ordered list:
1st: 64
2nd: 65
3rd: 67
4th: 75
5th: 80
6th: 85
7th: 90
8th: 90

So 4th = 75, 5th = 80
Median = (75 + 80) ÷ 2 = 155 ÷ 2 = 77.5

✔ Answer: 77.5

h) What was the mode?
→ Mode is the most frequent score.
Look at the scores: 64,65,67,75,80,85,90,90
Only 90 appears twice; others appear once.
So mode is 90.

✔ Answer: 90

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Final Answer:
a) 8
b) 6
c) 5
d) 64
e) 90
f) 77
g) 77.5
h) 90