Collecting, Organizing and Describing Data

Collecting, Organizing and Describing Data

Census vs Sample

• census: the collection of data from an entire population

• sample: a small group selected from a larger group (or population) for the purposes of collecting data about the larger group

Multiple Choice

Would it be better to use a census or sample if you:

Want to find out your classes favourite colour

• Census

• Sample

Multiple Choice

Would it be better to use a census or sample if you:

If you wanted to know if a new medication will work

• Census

• Sample

Remember that if you can ask everyone then you can conduct a census, if you cannot ask every single person due to time or financial reasons, you would choose a sample

Representative vs Random Sample

• random sample: a selection of a population chosen so that any member of the population has an equal probability of being selected

• representative sample: a sample created to ensure that distinct parts of the population of interest are included in the sample, in such a way that the sample is similar to the population

Multiple Select

How can you create a random sample? (more than one response)

• picking names from a hat

• assigning numbers to people/items and randomly choosing numbers

• asking every third person you see

• choose who to ask

Multiple Select

How do you create a representative sample?

• Consider the population

• Consider subgroups

• Consider how many of each subgroup to ask

• Consider what pencil to use when collecting data

Multiple Choice

Is it best to use a Random or Representative sample when you:

Are testing to see if a new medication works

• Representative

• Random

Multiple Choice

Is it best to use a Random or Representative sample when you:

When you are asking customers about their shopping experience

• Representative

• Random

Multiple Choice

Is it best to use a Random or Representative sample when you:

Are checking the quality of orange juice being made in a factory

• Representative

• Random

Bias in Surveys

• bias: a characteristic of a set of survey data about a sample group that might cause the data to not represent the larger group; e.g., collecting data about children’s favourite books by asking only four-year-olds would probably produce biased results

Multiple Select

Which two factors below should you MOST consider when trying to create an unbiased survey.

• Population (who you will ask)

• Wording of survey questions

• What to pay people

• How many people to ask

Multiple Choice

Which question is the most useful?

• What's your favourite colour?

• What is your favourite colour to wear?

• What is your favourite colour shirt to wear?

• What is your favourite colour shirt to wear to school?

Multiple Select

Which of these questions are biased? (more than one answer)

• Do you think ice cream is good?

• Video games are the best! Do you like video games?

• Who is your favourite band to see live in concert?

• Why are you so happy?

Multiple Select

What should you consider when creating an unbiased sample?

• your friends

• your family

• subgroups that represent the population

• how to create a random sample

Multiple Select

What subgroup would you consider if you were wanting to survey if the school needs a new baseball diamond?

• principal

• students

• parents

• teachers

Multiple Choice

Which would be the best represent sample at our school?

• principal (1), students (50), parents (25), teachers (10)

• Principal (3), students (47), parents (15), teachers (20)

• Principal (1), students (50), parents (50), teachers (50)

• Principal (1), students (15), parents (15), teachers (15)

Poll

How are you feeling about your understanding of representative vs random sample and how to avoid bias?

• Good!

• Meh.

• I'm kinda getting it

• Yikes! I will need more practice with this.

Discrete or Continuous Data

• discrete data: data that can have only certain fixed values; discrete data are usually counted rather than measured; e.g., the grade children are in at school is discrete, but the children’s heights are not

• continuous data: data with values that can be represented on a number line or a graph axis; continuous data are usually measured rather than counted; e.g., children’s heights are continuous, but the grades children are in at school are not

Multiple Choice

Is this discrete or continuous data?

Baseball standings for 2014/2015 found on the internet

• Discrete

• Continuous

Multiple Choice

Is this discrete or continuous data?

Measuring the length of every baby at the hospital

• Discrete

• Continuous

Multiple Choice

Is this discrete or continuous data?

Asking your friends who is left handed and who is right handed

• Discrete

• Continuous

Multiple Choice

Is this discrete or continuous data?

Time how long your friends take to answer a multiplication question

• Discrete

• Continuous

Multiple Choice

Is this discrete or continuous data?

Counting votes for class president

• Discrete

• Continuous

Relative-frequency table:

• a table that shows the number of occurrences for each category in a data set (its frequency) and shows each frequency as a comparison against the whole sample (for instance, as a fraction)

Multiple Choice

If I asked 15 people their favourite colour and 3 people said red, what would be the relative frequency?

• $\frac{1}{2}$

• $\frac{3}{4}$

• $\frac{3}{15}$

• $\frac{15}{3}$

Poll

How well are you understanding discrete vs continuous data and relative frequency tables?

• I get it!

• I understand

• I'm not too sure

• I have no idea

Central Tendencies

Mean, Median, Mode and Range

Mean:

• one measure of the centre of a set of data, sometimes called average, determined by sharing all the data values equally among the number of values; e.g., the mean of the data 3, 5, 7, 10, 15 is (3 + 5 + 7 + 10 + 15) ÷ 5 = 8

Multiple Choice

What is the mean of this data:

2, 54, 12, 6, 6

• 15

• 16

• 17

• 18

Median:

• the middle number of a set of data that is ordered from least to greatest, sometimes called average; e.g., 7 is the median of this set of data: 3, 5, 7, 10, 15

Multiple Choice

What is the median of this data:

2, 54, 12, 6, 6

• 12

• 6

• 54

• 2

Multiple Choice

What is the median of this data:

11, 12, 13, 14, 15, 16

• 13

• 13.5

• 14

• 14.5

Mode:

• the number that occurs most often in a set of numeric data; some data sets have no mode, some have one, and some have more than one; e.g., 7 is the mode of this set of data: 5, 7, 7, 7, 8, 10, 10

Multiple Choice

What is the mode of this data:

2, 54, 12, 6, 6

• 54

• 12

• 6

• 2

Multiple Select

Find the mode for this data.

1, 1, 2, 2, 3, 4, 5, 6, 6

• 1

• 2

• 5

• 6

Range:

• the difference between the greatest and least values in a set of data; e.g., for the data 3, 7, 19, 20, 45, the range is from 3 to 45, or 42

Multiple Choice

What is the range for this data:

2, 54, 12, 6, 6

• 51

• 52

• 12

• 54

Multiple Choice

What is the range of this data:

11, 12, 13, 14, 15, 16

• 11

• 9

• 7

• 5

Poll

How are you feeling about understanding mean, median, mode and range?

• I am not having any issues.

• I find it easy!

• I would like more practice.

• I can do it with some mistakes.