Let the people know that we want quick answers which require no thought.
B
b
The height of each bar should represent the number of people who answered with each specific option.
C
c
When answers are given randomly, the heights of the bars tend to be equal and no answer dominates the graph.
D
d
Why might some answers be preferable to others? Do people have favorite numbers, letters, or colors which they might rather choose?
E
e
How often do people answer questions asked in posts on social websites? Is it more often than in face-to-face conversations?
A
a
See solution.
B
b
See solution.
C
c
See solution.
D
d
See solution.
E
e
See solution.
Practice makes perfect
a
We want to perform a survey to gather information from people. We want to ask them three questions. Before we start surveying, we should think about the exact wording we want to use for each question. Let's start with the first one.
1. Pick a number between1and4.
Because we want our respondents to ask randomly, we should specify that we do not want them to think about their answers for too long. Also, we should use a word like can to make the question less aggressive.
Example Question: Quickly and without much thinking, can you pick a number between1and4?
Next, let's think about the second question.
2. Pick a vowel (a, e, i, o, or u).
For this question, it might be better if we do not list the vowels. When we list some options to choose from in any survey, people tend to have biased answers towards the first and last option listed. We want to avoid this kind of bias in our survey.
Example Question: Can you name a vowel?
Let's move on to the last question.
3. Choose a color.
Here, it might be a problem if many people give a less common color as an answer. For this reason, let's ask if they could choose a color in the rainbow. That way, we limit the number of options, and we do not affect the randomness of the given responses.
Also, using could makes the question sound less aggressive.
Example Question: For the last question, could you choose a color in the rainbow?
b
We are asked to make bar graphs for the responses to our questions. Since each survey performed in real life will get different results, this solution will use sample data to create the bar graphs. The graph for the first question might look something like this.
The histogram for the second question might look like this.
Let's also create the bar graph for the last question.
c
Let's take another look at the first bar graph.
If the given answers were random, the bars in the bar graph would have similar heights. This is not the case in this bar graph, so the responses in this survey were not truly random. Let's see the bar graph for the second question.
The responses in this survey were also not truly random because the heights of the bars are not all similar. Let's see the bar graph for the third question.
The responses here were also not truly random.
d
Let's look at the first bar graph one more time.
In our case, most people answered with either 2 or 3. This might be because of two reasons.
People usually prefer even numbers to odd numbers.
They also have a tendency to pick prime numbers like 3, 7, 13 and 17.
Let's see the bar graph for the second question.
For this question, a lot more people have chosen a and e rather than i, o, and u. This might be because a and e are more common in the English language and so people have a bias towards them. Let's see the bar graph for the third question.
We can see that more people have chosen blue than yellow, indigo, and violet combined! This might be because people tend to choose their favorite color in this kind of survey and blue is the most common favorite color.
e
Let's try to think why text messaging, phone calls, or personal interviews might be a better option for surveying than using a mass email or a social networking site. When we make a post with our questions on a social website, our friends can either give us answers or ignore the post.
Social Website Post ⇒ Fewer Answers
The same thing can be said for emails, which some may argue will yield even worse results. However, people are way less likely to ignore our questions when we call them or ask face-to-face. This might be why those are better methods for our survey.
