New Zealand
Level 7 - NCEA Level 2

# Misrepresentation of Results

## Interactive practice questions

Lachlan asks $120$120 Year 12 students at his school how much time they spend on homework per night. $78$78 Year 12 students say they do more than $3$3 hours. At a meeting of the student council Lachlan reports "$65%$65% of students at this school do too much homework.

Which of the following explain why this is misleading?

The survey does not represent the population of the school.

A

The question should have been multiple choice.

B

The question was biased.

C

The sample size was too small.

D

The survey does not represent the population of the school.

A

The question should have been multiple choice.

B

The question was biased.

C

The sample size was too small.

D
Easy
Less than a minute

How does this graph misrepresent the statistics?

Choose all appropriate options.

A newspaper states: "Oil prices have risen by $33%$33% over the last two years."

In the article it states that in 2010 the oil prices increased by $10%$10% and in 2011 the oil price increased by $23%$23%.

An online company asks all its customers to complete a survey and $58%$58% respond. In the survey there was a question which asked “How happy are you with our service?”. Respondents could tick either “Very Happy” or “Somewhat Happy”.

In their annual newsletter the company wrote an article reporting “$100%$100% of customers are happy with our service”.

### Outcomes

#### S7-1

Carry out investigations of phenomena, using the statistical enquiry cycle: A conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets B evaluating the choice of measures for variables and the sampling and data collection methods used C using relevant contextual knowledge, exploratory data analysis, and statistical inference.

#### S7-3

S7-3 Evaluate statistically based reports: A interpreting risk and relative risk B identifying sampling and possible non-sampling errors in surveys, including polls

#### 91265

Conduct an experiment to investigate a situation using statistical methods

#### 91266

Evaluate a statistically based report