Seeing Is Believing Statistics In Your World 
Student Notes
Teachers Notes
Getting the Results
 
The Most Successful Illusion
 
The Mode
 
Ordering The Results
 
The Distribution
 
The Median
 
Another Class
 

The Illusions

Getting the Results
You will need pages R1, R2 and R3.

REMEMBER: WE ARE TESTING THE ILLUSIONS. WE ARE NOT TESTING YOU!

You will not be asked how many you got right.

Write down the answer that looks correct.

Do not use a ruler.

a Look at the illusions on page R1 quickly one at a time. Answer the questions on page R2.

Your teacher will collect the results.

a Record on page R3 the class results which your teacher will give you.

 

The Most Successful Illusion

a Find the correct answer to each illusion. Use a ruler where necessary.
b Tick the correct answer on page R3.
c Write down how many pupils had the correct answer to each illusion.

Illusions aim to fool people. The least successful fools fewest people and has most correct answers. The most successful illusion fools most people and has fewest correct answers.

In your class:

d Which illusion was the least successful?
e Which illusion was the most successful?
f Write down the illusions in order of their success.
Put the most successful one last.

 

The Mode
The 29 children in Class 2J looked at illusion 6 on page R1. Their results are shown in Table 1.

Answer Number of pupils
line AB 7
line CD 8
line EF 1
line GH 13

Table 1 - Class 2J's answer to illusion 6

In Class 2J more pupils answered 'line GH' than any other line.

For Class 2J line GH is the MODE. The mode is the answer that most pupils chose.

Use your class results to answer these questions about each of the seven illusions.

a Which is the mode?
b Is the mode the correct answer?
c Write down a sentence about the results altogether.

 

Ordering the Results
The true lengths of the lines in illusion 6 are:

AB 6.0 cm, CD = 6.5 cm,
EF 5.5 cm and GH = 6.2 cm.

Illusion 6 asked for the longest line.

These lengths can be put in order of length (5.5, 6-0, 6.2, 6.5).

We can put the lines in the same order (EF, AB, GH, CD).

This is the order of lines based on length.

Table 2 shows the results of Class 2J put in this order.

Answer Number of pupils
line EF 1
line AB 7
line GH 13
line CD 8

Table 2 - Class 2Js answer to illusion 6

a Make atable to show your class results to illusion 6, with the answers in order of length.

Illusion 1 asked about the position of' four lines.

b Put the four possible answers to illusion 1 in order based on position. Write down your class results in the same order.

Illusions 2 to 5 ask about size.

c Put the three possible answers to one of these four illusions in an order based on size.

 

The Distribution
We can show the results of illusion 6 as a bar chart.

Figure 1 uses Class 2J's original order from Table 1. Figure 2 uses Class 2J's order based on size from Table 2.

The arrows point to the longest line (the correct answer).


Figure 1 - Class 2J: Results of illusion 6


Figure 2 - Class 2J: Results of illusion 6. Lines chosen in order of length

Which figure makes it clear that:

a Most pupils chose the second longest line,
b Very few pupils chose the shortest line?
c How is Figure 2 better than Figure 1?
d Draw a barchart ofyour classanswers toillusion 6.
Put the lines in order of increasing length. Leave gaps between the bars.
e Write down two sentences about your class results in illusion 6.

 

The Median
The lines in illusion 6 have been put in order of length by C'lass 2J. We can put the pupils in the same order by looking at their answers.

The pupil who said 'line EF' is pupil number 1.
The 7 pupils who sardine AB' are numbered 2 to 8.
The 13 pupils who said 'line GH' are numbered 9 to 2 1.
The 8 pupils who said 'line CD' are numbered 22 to 29.

These figures are shown in Table 3.

Line Number of pupils Pupils numbered
EF 2 1
AB 7 2 to 8
GH 13 9 to 21
CD 8 22 to 29

Table 3 - Class 2J: Illusion 6. Numbering the pupils

Pupil number 15 is the middle pupil. 14 pupils chose lines the same length or shorter, the other 14 chose lines the same length or longer.

His answer is called the MEDIAN. The median is the answer of the middle person. In Class 2J the median answer is line GH.

a Make a table like Table 3 of your class results.
b What is the number of the middle pupil?
c What is the median?
d Was the class median the correct answer?

Class 2J were trying to find the longest of four lengths. The median helps to show how well they did.

GH, the median, is the second longest length. So at least half the class chose the correct or next-to-correct length.

e Draw a bar chart of your class answers to illusion 1.
f Find the median.

 

*Another Class
Table 4 shows the results obtained by Class 2Z for illusion 6.

a What is the median of these results?

 

Line Number of pupils
EF 1
AB 4
GH 7
CD 13

Table 4 - Class 2Z: illusion 6

b On which of the two classes was the illusion more effective, Class 2Z or Class 2J?

 

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