The shape of data: symmetric, uniform and bimodal
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. A histogram has one tall peak in the middle and the bars fall away evenly on both sides. What shape is it?
2. A histogram of test marks has two separate tall peaks with a dip between them. What is the shape called?
3. A histogram where every bar is about the same height has which shape?
4. Which statement describes a gap in a histogram?
5. In a symmetric distribution, where do most values cluster?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1Symmetric (bell-shaped) | AOne central peak with the left and right sides roughly mirror images, so most values cluster around the middle | |
| 2Bimodal | BTwo peaks make the shape bimodal, not symmetric. A bell-shaped distribution has only one central peak. | |
| 3A uniform distribution has bars of roughly equal height, so values are spread evenly across the range | CBars of equal height form a flat, uniform distribution. Bimodal needs two distinct peaks with a dip between them. | |
| 4A gap in a histogram shows an interval where few or no values fall, which may reveal two separate groups | DTwo separate peaks on a histogram, suggesting two groups of values within the one data set | |
| 5A histogram has two clear peaks, so it is symmetric (bell-shaped). | EGap between peaks | |
| 6All bars are about the same height, so the distribution is bimodal. | FUniform (flat) |
C
Definitions
distribution shape
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
=AVERAGE(B2:B30)-______(B2:B30)
2.
plt.____(marks, bins=5)
3.
IF peaks = _ THEN
shape ← "bimodal"
END IF
4.
IF ___(counts) - MIN(counts) <= 2 THEN
shape ← "uniform"
END IF
5.
=COUNTIF(D2:D10,_)
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
counts = [2, 6, 10, 6, 2]
B
shape = "bimodal"
C
print(shape)
Question 2
A
c = [8, 8, 9, 8, 8]
B
if max(c) - min(c) < 2
C
print("uniform")
Question 3
A
counts = [3, 9, 3, 2, 9, 3]
B
peaks = 2
C
if peaks = 2:
D
print("bimodal")
Question 4
A
# Symmetric: two peaks
B
counts = [1, 4, 9, 4, 1]
C
print(max(counts))
Question 5
A
c = [5, 5, 6, 5, 5]
B
average = sum(c) / 5
C
spread = max(c) + min(c)
D
print("Small spread: flat")
Answer Key
The shape of data: symmetric, uniform and bimodal
Section A: Quick Questions
Q1
B — Symmetric (bell-shaped)
Q2
A — Bimodal
Q3
A — Uniform
Q4
B — A range of values where few or no data points fall
Q5
A — Around the centre, with fewer values towards both ends
Section B: Match the Pairs
Q1
Symmetric (bell-shaped) → One central peak with the left and right sides roughly mirror images, so most values cluster around the middle
Q2
Bimodal → Two separate peaks on a histogram, suggesting two groups of values within the one data set
Q3
A uniform distribution has bars of roughly equal height, so values are spread evenly across the range → Uniform (flat)
Q4
A gap in a histogram shows an interval where few or no values fall, which may reveal two separate groups → Gap between peaks
Q5
A histogram has two clear peaks, so it is symmetric (bell-shaped). → Two peaks make the shape bimodal, not symmetric. A bell-shaped distribution has only one central peak.
Q6
All bars are about the same height, so the distribution is bimodal. → Bars of equal height form a flat, uniform distribution. Bimodal needs two distinct peaks with a dip between them.
Section C: Definitions
Q1
distribution shape — How values cluster and spread on a histogram: symmetric (bell-shaped), uniform (flat), or bimodal (two peaks), with gaps showing where few or no values fall.Section D: Fill in the Blanks
Q1
=AVERAGE(B2:B30)-MEDIAN(B2:B30)Q2
plt.hist(marks, bins=5)Q3
IF peaks = 2 THEN
shape ← "bimodal"
END IFQ4
IF MAX(counts) - MIN(counts) <= 2 THEN
shape ← "uniform"
END IFQ5
=COUNTIF(D2:D10,0)Section E: Spot the Error
Q1
B — The counts rise to one peak in the middle and fall away evenly on both sides. That is a symmetric (bell-shaped) distribution, not bimodal. The line should be shape = "symmetric".
Q2
B — An if statement must end with a colon. The line should be if max(c) - min(c) < 2: so the indented print belongs to the if. Bars of almost equal height make a uniform shape.
Q3
C — A single = assigns a value, while == compares two values. The test should be if peaks == 2: because a bimodal distribution has two peaks.
Q4
A — A symmetric (bell-shaped) distribution has one central peak with matching sides. Two peaks would make it bimodal. The comment should say one central peak.
Q5
C — The spread of the bar heights is the largest minus the smallest, so it needs - not +. A small difference means the bars are about equal, which is a uniform shape.