Statistics

New Zealand

Level 3

Lesson

Let's say we've decided to conduct an experiment about what is the most common coloured car in the neighbourhood and we decide to record the colours of the next $50$50 cars that drive past. How would we keep track of what we saw? Well we could write a list but that might look a bit messy and be a bit hard to understand like the list below:

Green, white, yellow, white, black, green, black, blue, blue, gold, silver, white, black, gold, green, blue, purple, blue, white, black, gold, silver, silver, red, red, red, black, gold, red, blue, white, black, silver, silver, purple, pink, white, blue, red, black, yellow, blue, white, white, red, green, pink, black, white, red.

One common way to keep track of data is to create a frequency table and keep a tally of the results.

Let's watch a video about using tallies and tables now.

Frequency refers to how often an event occurs. We often construct frequency tables as an easy way to keep track of and display data because we can have:

- One column as a list showing the possible outcomes that may occur,
- A second column with tally marks of the frequency of each event (although this column isn't always included), and
- A third with the total frequency as a number.

When we're collecting data, a score may occur more than once. So, rather than cross out a number and rewrite the new frequency each time, we can use a tally system. Each time a score occurs, we draw a line like so:

When a score occurs for the fifth time, we draw a line through the other four like this:

This just makes it easy to count when we finish recording results. For example, in the picture below, there are $3$3 groups of $5$5 and $2$2 extra lines. What would the total frequency be in this case?

Well, $3\times5+2=17$3×5+2=17, so the total frequency in this case is $17$17.

So, for our car experiment, we could create a frequency table that looked like this:

Colour of Car |
Tally |
Frequency |
---|---|---|

Black | $8$8 | |

White | $9$9 | |

Blue | $7$7 | |

Green | |||| | $4$4 |

Purple | || | $2$2 |

Pink | || | $2$2 |

Silver | $5$5 | |

Gold | |||| | $4$4 |

Yellow | || | $2$2 |

Red | $7$7 |

So what coloured car drove past most often? White cars! Did you think that was easier to read than in the list?

We made not always need to include the tally column. It depends how many values you need to record. You may be able to count the numbers easily and just record the frequencies. Let's look at some more of these kinds of examples now.

Mr. Rodriguez recorded the number of pets owned by each of the students in his class. He found that $15$15 people had no pets, $19$19 people had one pet, $3$3 people had two pets and $8$8 people had three pets.

Write Mr. Rodriguez's results in the frequency table below.

Number of Pets Frequency $0$0 $\editable{}$ $1$1 $\editable{}$ $2$2 $\editable{}$ $3$3 $\editable{}$

Sophia asked $33$33 of her students to pick their favourite sport. $8$8 picked Football, $15$15 picked Volleyball, $5$5 picked Basketball, and $5$5 picked Tennis.

Sport | Frequency |
---|---|

$A$A |
$8$8 |

$B$B |
$15$15 |

$C$C |
$5$5 |

$D$D |
$5$5 |

Which sport belongs in positions $A$

`A`, $B$`B`, $C$`C`, $D$`D`?A- Volleyball

B- Football

C- Tennis

D- Basketball

AA- Football

B- Tennis

C- Basketball

D- Volleyball

BA- Tennis

B- Volleyball

C- Basketball

D- Football

CA- Football

B- Volleyball

C- Basketball

D- Tennis

D

Conduct investigations using the statistical enquiry cycle: – gathering, sorting, and displaying multivariate category and wholenumber data and simple time-series data to answer questions;– identifying patterns and trends in context, within and between data sets; – communicating findings, using data displays

Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.