SME
Grade 9 Math · Problem type
Dot plot from a data list
Use this for “Books read by 10 students: 3, 5, 2, 4, 5, 9, 5, 1, 4, 2. Make a dot plot and find the mode, median and mean.”
Diagram
10 values in order: 1, 2, 2, 3, 4, 4, 5, 5, 5, 9.
The two middle values are both 4, so the median is 4.
This is an example. Type your own values to start a new problem.
n
Number of values
example
x₁
Value 1
example
x₂
Value 2
example
x₃
Value 3
example
x₄
Value 4
example
x₅
Value 5
example
x₆
Value 6
example
x₇
Value 7
example
x₈
Value 8
example
x₉
Value 9
example
x₁₀
Value 10
example
min
Least
worked out (not typed)
max
Greatest
worked out (not typed)
R
Range
worked out (not typed)
f
Dots in the tallest stack
worked out (not typed)
M
Median
worked out (not typed)
x̄
Mean
worked out (not typed)
Formulas
min
=
least
of
the
n
values
1 = least of the 10 values
max
=
greatest
of
the
n
values
9 = greatest of the 10 values
R
=
max
−
min
8 = 9 − 1
f
=
the
tallest
stack
of
the
n
dots
3 = the tallest stack of the 10 dots
M
=
median
of
the
n
values
4 = median of the 10 values
x̄
=
sum
of
the
n
values
n
4
=
sum
of
the
10
values
10
Assumptions
•
Draw a number line from the least value to the greatest; each value gets a dot, stacked where values repeat.
•
The mode is the value under the tallest stack; a tie gives two modes, and no repeats means no mode.
•
The mean is the balance point of the dots; a long tail pulls it away from the median.
Step-by-step
WE KNOW
n = 10, x₁ = 3, x₂ = 5, x₃ = 2, x₄ = 4, x₅ = 5, x₆ = 9, x₇ = 5, x₈ = 1, x₉ = 4, x₁₀ = 2
FIND
least (min), greatest (max), range (R), dots in the tallest stack (f), median (M), mean (x̄)
Step 1 · Find least (min)
Use min = least of the n values
The smallest value, first in order.
min
=
least
of
x₁
,
x₂
,
x₃
,
x₄
,
x₅
,
x₆
,
x₇
,
x₈
,
x₉
,
x₁₀
min = least of 3, 5, 2, 4, 5, 9, 5, 1, 4, 2
In order: 1, 2, 2, 3, 4, 4, 5, 5, 5, 9
min = 1
Step 2 · Find greatest (max)
Use max = greatest of the n values
The largest value, last in order.
max
=
greatest
of
x₁
,
x₂
,
x₃
,
x₄
,
x₅
,
x₆
,
x₇
,
x₈
,
x₉
,
x₁₀
max = greatest of 3, 5, 2, 4, 5, 9, 5, 1, 4, 2
max = 9
Step 3 · Find range (R)
Use R = max − min
The range is the width the dots cover: greatest minus least.
R
=
9
−
1
R
=
8
Step 4 · Find dots in the tallest stack (f)
Use f = the tallest stack of the n dots
Count the dots at each value; the mode is the value with the most.
f
=
most
dots
at
one
value
of
x₁
,
x₂
,
x₃
,
x₄
,
x₅
,
x₆
,
x₇
,
x₈
,
x₉
,
x₁₀
f
=
most
dots
at
one
value
of
3,
5,
2,
4,
5,
9,
5,
1,
4,
2
1: 1 dot
2: 2 dots
3: 1 dot
4: 2 dots
5: 3 dots
9: 1 dot
f
=
3
→
mode:
5
Step 5 · Find median (M)
Use M = median of the n values
The middle value in order (halfway between the middle two); half the dots lie on each side.
M
=
median
of
x₁
,
x₂
,
x₃
,
x₄
,
x₅
,
x₆
,
x₇
,
x₈
,
x₉
,
x₁₀
M
=
median
of
3,
5,
2,
4,
5,
9,
5,
1,
4,
2
The middle two are 4 and 4.
4 + 4
2
=
4
M
=
4
Step 6 · Find mean (x̄)
Use x̄ = sum of the n values ÷ n
Add the values, then divide by how many there are.
x̄
=
(
x₁
+
x₂
+
x₃
+
x₄
+
x₅
+
x₆
+
x₇
+
x₈
+
x₉
+
x₁₀
)
÷
n
x̄
=
(3
+
5
+
2
+
4
+
5
+
9
+
5
+
1
+
4
+
2)
÷
10
3 + 5 + 2 + 4 + 5 + 9 + 5 + 1 + 4 + 2 = 40
40
10
=
4
x̄
=
4
Check
Put the numbers back in. Both sides should match.
1 = least of 3, 5, 2, 4, 5, 9, 5, 1, 4, 2 ✓
9 = greatest of 3, 5, 2, 4, 5, 9, 5, 1, 4, 2 ✓
8 = 9 − 1 ✓
3 = most dots at one value of 3, 5, 2, 4, 5, 9, 5, 1, 4, 2 ✓
4 = median of 3, 5, 2, 4, 5, 9, 5, 1, 4, 2 ✓
(3 + 5 + 2 + 4 + 5 + 9 + 5 + 1 + 4 + 2) ÷ 10 = 4 ✓
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