The shape of a data distribution

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. A histogram has one peak in the middle and the two sides are mirror images. What shape is this?

A Bimodal

B Symmetrical (bell-shaped)

2. A histogram shows two clear peaks with a dip between them. What shape is this?

A Bimodal

B Symmetrical with one peak

3. Which statement about a uniform distribution is correct?

A All the bars are about the same height

B One tall bar sits in the middle

4. Which tool shows the shape of a numeric data set most clearly?

A Pie chart

B Histogram

5. Test marks for a class show one peak near 40 and another near 85. What is the most likely explanation?

A Two different groups of students are in the data

B The data is perfectly bell-shaped

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1Symmetrical, bell-shaped histogram		AThis has one central peak with matching sides, so it is symmetrical and bell-shaped, not bimodal.
2Bimodal histogram		BBin counts: 10, 11, 10, 9, 10
3A uniform distribution is symmetrical, with every bin having about the same frequency		CThe counts are almost equal across all bins, so the shape is uniform, not bell-shaped.
4To read shape from a histogram, look for the number and position of the peaks		DBin counts: 3, 12, 4, 5, 13, 2
5Bin counts: 2, 8, 15, 8, 2 = bimodal		EMost values cluster around the middle, with the left side mirroring the right side
6Bin counts: 9, 10, 10, 9, 10 = bell-shaped		FThe data has two separate peaks, which often suggests two different groups are mixed together

Definitions

distribution shape

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=________(B2:B30,">=60",B2:B30,"<70")

# Histogram bars: 3, 9, 4, 9, 3 peaks = _ shape = "bimodal"

counts = [4, 10, 18, 10, 4] if counts[0] == counts[_]: print("symmetrical")

peaks = 2 if peaks __ 2: shape = "bimodal"

=___(C2:C6)

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A Counts: 3, 12, 3

B Tallest bar: first bin

C Shape: symmetrical, bell-shaped

Question 2

A Counts: 8, 8, 8, 8

B Shape: bell-shaped

C All bars are about equal height

Question 3

A Counts: 2, 9, 3, 8, 1

B Peaks at bins 2 and 4

C Number of peaks: 1

D Shape: bimodal

Question 4

A peaks ← 2

B IF peaks = 2 THEN

C shape ← "uniform"

D END IF

Question 5

A Histogram: two equal peaks

B Bars drop evenly each side

C Shape: bell-shaped

Answer Key

The shape of a data distribution

Section A: Quick Questions

B — Symmetrical (bell-shaped)

A — Bimodal

A — All the bars are about the same height

B — Histogram

A — Two different groups of students are in the data

Section B: Match the Pairs

Symmetrical, bell-shaped histogram → Most values cluster around the middle, with the left side mirroring the right side

Bimodal histogram → The data has two separate peaks, which often suggests two different groups are mixed together

A uniform distribution is symmetrical, with every bin having about the same frequency → Bin counts: 10, 11, 10, 9, 10

To read shape from a histogram, look for the number and position of the peaks → Bin counts: 3, 12, 4, 5, 13, 2

Bin counts: 2, 8, 15, 8, 2 = bimodal → This has one central peak with matching sides, so it is symmetrical and bell-shaped, not bimodal.

Bin counts: 9, 10, 10, 9, 10 = bell-shaped → The counts are almost equal across all bins, so the shape is uniform, not bell-shaped.

Section C: Definitions

distribution shape — How data values are spread out, seen on a histogram: symmetrical (bell-shaped or uniform) or bimodal, which has two peaks. Skew is covered separately.

Section D: Fill in the Blanks

=COUNTIFS(B2:B30,">=60",B2:B30,"<70")

# Histogram bars: 3, 9, 4, 9, 3
peaks = 2
shape = "bimodal"

counts = [4, 10, 18, 10, 4]
if counts[0] == counts[4]:
    print("symmetrical")

peaks = 2
if peaks == 2:
    shape = "bimodal"

=MAX(C2:C6)

Section E: Spot the Error

B — The counts 3, 12, 3 show the tallest bar (12) is in the middle bin, not the first. A single central peak with matching sides gives a symmetrical, bell-shaped distribution.

B — When every bar is about the same height the shape is uniform. A bell shape needs a tall centre with lower bars on both sides.

C — The counts 2, 9, 3, 8, 1 have two peaks (9 and 8) with a dip between them, so the number of peaks is 2. That is what makes the shape bimodal.

C — A distribution with two peaks is bimodal. Uniform means all bars are roughly equal height, so the shape should be set to "bimodal".

A — A bell-shaped histogram has one peak in the centre with bars falling away evenly on both sides. Two equal peaks would make it bimodal, so line 1 should say one centre peak.