# Create and interpret cumulative frequency tables

## Interactive practice questions

A pair of dice are rolled $50$50 times and the numbers appearing on the uppermost face are added to give a score.

a

What is the lowest possible score when a single pair of dice are rolled?

b

What is the highest possible score when a single pair of dice are rolled?

c

The frequency of each score is given in the table. Complete the cumulative frequency values.

Score ($x$x) Frequency ($f$f) Cumulative Frequency ($cf$cf)
$2$2 $1$1 $\editable{}$
$3$3 $2$2 $\editable{}$
$4$4 $5$5 $\editable{}$
$5$5 $5$5 $\editable{}$
$6$6 $5$5 $\editable{}$
$7$7 $9$9 $\editable{}$
$8$8 $7$7 $\editable{}$
$9$9 $5$5 $\editable{}$
$10$10 $8$8 $\editable{}$
$11$11 $1$1 $\editable{}$
$12$12 $2$2 $\editable{}$
d

How many times did a score of $8$8 appear?

e

How many times did a score more than $9$9 appear?

f

How many times did a score of at most $6$6 appear?

Easy
Approx 4 minutes

The number of sightings of the Northern Lights were recorded across various Canadian locations over a period of $1$1 month. The numbers below represent the number of sightings at each location.

$12,8,9,8,11,7,7,11,10,9,9,11,7,10,11,7,8,9,11,9$12,8,9,8,11,7,7,11,10,9,9,11,7,10,11,7,8,9,11,9

Consider the table.

The marks received by a group of $20$20 students are given below:

$75,75,95,60,95,75,60,75,95,70,70,70,60,83,75,83,70,60,75,70$75,75,95,60,95,75,60,75,95,70,70,70,60,83,75,83,70,60,75,70

### Outcomes

#### S5-1

Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data;– using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings

#### S5-2

Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings