# Statistics - Section 1

```Year 7 Core Mathematics
Strand – Statistics and Probability
Data representation and interpretation
Chapter 3 – Statistics
Year 7 Content Descriptors

Identify and investigate issues involving numerical data collected from primary and secondary
sources.

Construct and compare a range of data displays including stem-and-leaf plots and dot plots.

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context
of data.

Describe and interpret data displays using median, mean and range
Year 7 Achievement Standards

Students identify issues involving the collection of continuous data. They describe the
relationship between the median and mean in data displays.

They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots
and dot-plots.
Teachers
 Horan, McHugh, Williams
Version
 Term One – February - 2022
1|Page
Internet Activity - Statistics Smart Start
Complete this simple online activity
Displaying Data
Data is the name we give to a collection of facts, numbers, words, or items of information. The smart
start showed data in the very simple forms of numbers and pictures. But there are a lot of ways to
display (show) data. Do a “Google Image” search and find an example of each of the following ways to
display data.
Frequency table, Circle graph (pie graph), Stem and Leaf graph, line graph,
dot plot, picture graph, histogram
When you have found an example, do a quick sketch in the appropriate section, in the table below and
on the next page. An example of a Vertical bar graph is provided for you.
Vertical Bar graph
Frequency Table
Circle Graph (Pie Graph)
Stem and Leaf Plot
2|Page
Picture Graph
Line Graph
Histogram
Dot Plot
3|Page
Displaying Data
In the space below each graph, write the name which best represents the data. You should have found
similar graphs in the previous activity.
4|Page
Internet Activity - Displaying Data
Play the matching game at Quizlet. Have three attempts and record your best time in the space below.
My Best Time:
Match the terms on the left with the definitions on the right.
A graph with points connected by
lines to show how something changes
in value:
• as time goes by,
• or as something else changes.
Circle Graph
A data display that uses images to
represent numbers or quantities.
Histogram
A graph that displays data using
rectangular bars of different heights,
with spaces between the bars.
Line Graph
A special chart that uses &quot;pie slices&quot; to
show the relative sizes of data.
Picture Graph
A table that lists a set of scores and
how often they occur.
Bar Graph
A graph, similar to a bar graph that
displays data using rectangular bars
with no spaces and numbers in
ranges.
5|Page
Frequency Table
Displaying Data
Below are a collection of line graphs and histograms. Write an “L” on those that are a line graph and a
“H” on those that are the histograms.
6|Page
When reading data tables or graphs you should always look for the following:




Labels on the x and y axis.
Numbers, figures, letters, words or percentages.
An increase or a decrease in the data or figures.
A title.
The ‘titles’ of the graphs below have been removed and placed in the text box. Look for the clues on the
graphs and match the titles that best fit each of the graphs. Write the appropriate title next to the
graph in the table on the next page.
“Computer parts sold in 1000’s over a four-year period”, “Sit ups in one minute by the first
13”, “Ways of travelling to School”, “The number of ways to roll between 2 and 12 with two
dice”, “Favourite types of movies”, “Distance travelled and time taken”.
7|Page
Internet Activity - Play the learning game at Quizlet
8|Page
Collecting and displaying Data
Record the height, weight and middle finger length of each student in your maths class. Once you have
recorded the data, be sure to put it in ascending order (from the smallest value to the largest value).
This makes it easier to use the data to produce tables and graphs.
Anytime you take measurements, the data is described as continuous data.
Heights
Weights
Middle Finger Length
9|Page
Frequency tables
Follow your teacher’s instructions and create a frequency table for Class height and Class weight.
Frequency Table for Class Heights
Score (Heights)
Tally
Frequency Table for Class Weights
Frequency
Score (Weights)
Tally
Total
Internet Activity - Quick Quiz (Reading Frequency Tables)
10 | P a g e
Frequency
Total
Frequency Table Individual Practice
Create a frequency table using the middle finger data.
Frequency Table for Middle Finger Length
Score (Middle Finger)
Tally
Frequency
Total
More Frequency Table Practice
1. Create your own frequency tables for the Math test scores from a Year 8 class. Be sure to include a
title and identify the score.
Frequency Table for
Score ()
11 | P a g e
Tally
Frequency
2. Make a frequency table for the information showing the number of bicycles in each household of
some Year 9 students.
Frequency Table
Score ()
Tally
Frequency
Total
Internet Activity - Reading Data Revision
12 | P a g e
Individual Activity
A student recorded the number of times the letters, A, B, C, D and E appeared on a page in her poetry
book.
The results were as follows:
Complete the table to find the answers to the following questions:
1) How many letters did the student record?
2) What was the most frequent letter?
Score
Tally
Frequency
Total
Individual Activity
Create a Bar Graph of the data from the frequency table above.
13 | P a g e
Homework or Extra Activity - Reading Frequency Tables
Frequency Table for the weights of children in
Year 6, in kilograms.
Questions
How many students had their weight taken?
What was the most common weight of the Year 6
students?
What was the greatest weight of a Year 6 student?
What was the minimum weight of a Year 6
student?
How many more students weighed 34kgs than
weighed 36kgs?
What two weight ranges had no students?
How many students weighed less than 36kgs?
14 | P a g e
Displaying Data – Dot Plots
A dot plot is constructed by putting a dot for each item above a scale. They are most useful for small
sets of numbers.
Work with your teacher to construct a dot plot for the data shown below
1. Create a dot plot of the ages of second time fathers.
15 | P a g e
2. Make a dot plot of the length of students’ feet in centimetres.
Internet Activity - Revising Data in Tables
Want more help?
16 | P a g e
Homework or Extra Activity
Rule a line joining each set of data to its graph. Some lines will go through a letter and a number. For
each number in the grid on the next page, write the letter that is on the same line in the puzzle to
discover the answer to the riddle.
17 | P a g e
What do you call a country where all the cars are red?
18 | P a g e
Mean, Median &amp; Mode (Measures of Central Tendency)
Watch the short tutorial with your teacher and then complete the first activity together.
Q1. Find the mean, median and mode for the data set below.
5, 7, 2, 7, 6, 10, 9, 3, 10, 7, 8, 7
Mean
Median =
Mode
Q2 Find the mean, median and mode for the data. Record your answers in the table below the set.
Mean
Median
Mode
19 | P a g e
Q3 Find the mean, median and mode for the data. Record your answers in the table below the set.
Mean
Median
Mode
Q4 Find the mean, median and mode for the data. Record your answers in the table below the set.
Mean
Median
Mode
Internet Activity
20 | P a g e
Median Activities (odd data set)
When you have an odd data set, the median can be found by placing the numbers in ascending order
and crossing off the same number of numbers from each end - until you have found the middle number.
Work with your teacher to find the median of the odd data set below.
Individual Activity (odd data sets)
1. Find the median for each of the data sets below.
21 | P a g e
2. The image below is from a popular on-line game where you find the median of the numbered ball
then shoot it with the cannon. Which ball would you shoot?
Classifying Data Kahoot
22 | P a g e
The range is the difference between the lowest number in the data set and the highest number in the
data set. To find the range, subtract the smallest number from the largest. An example is shown below:
Range = 8 – 2
Range = 6
Find the range for each of the data sets below.
Data Set
More Mean, Median, Mode and Range Activities
23 | P a g e
Range
Individual Activity
Find the mean (average) of the numbers in each data set below and rule a line to join each set to its
mean. Each line will go through a letter. The numbers in the grid on the next page are the means.
Place the letter that goes with the mean in the correct box to discover a well know saying.
24 | P a g e
Well Known Saying
Internet Activity
25 | P a g e
Individual Activity
The data below is of the results for Mr Horan and Mr McHugh’s Maths test. Find the mean, median, and
mode for each class and state which teacher’s class performed the best. Place your results in the table
below.
Grades for Mr Horan’s class: 60, 68, 70, 75, 84, 86, 90, 91, 92, 94, 94, 96
Grades for Mr McHugh’s class: 60, 60, 70, 71, 73, 73, 75, 76, 77, 84, 85, 86
Horan
McHugh
Mean
Mean
Median
Median
Mode
Mode
Internet Activity - Mean, Median and Mode
26 | P a g e
Using a Formula to Find the Median
It is often difficult to find the median when you have a very large set of numbers, so when faced with
this problem we use a formula.
The formula is :
(n + 1) / 2
n = the number of numbers in the data set
Odd data set
Median = (n + 1) / 2
Example: The data set below has 13 numbers
Median = (13 + 1) /2
Median = (14)/2
Median = 6, which is the 7th number in the data set below
Individual Activity
Work with your teacher to find the median of the data sets by using the formula (N+1) / 2.
1.
27 | P a g e
Individual Activity
1. Use the formula to find the median shoe size for the under 12 soccer team.
2. Calculate the median age of apprentices at O’Toole’s Industrial Welding Company, using
the formula.
28 | P a g e
Using a Formula to Find the Median
Even data set
Example: The data set below has 14 numbers.
Median = (14 + 1) /2
Median = (15) /2
Median = 7.5, or the 7.5th number.
*Add the 7th and the 8th number together and divide by 2
Median = 23 + 25 or 48
Median = 24
Individual Activity
Work with your teacher to find the median of the data set below by using the formula (N+1) / 2.
1. The median age of an apprentice at Mr Horan’s Industrial Welding Company.
29 | P a g e
Individual Activity
1. Use the formula to find the median number of hours worked by the teachers in the English
department last week.
2. Use the formula to find the median number of homework detentions given by the teachers in the
mathematics department last term.
Internet Activity
Want More Help?
30 | P a g e
Finding the Measures of central tendency visually
With your teacher, create three rules for finding the median, mean and mode from data displays, rather
than data sets. Then use the rules to determine the mean, median and mode of each of the dot plots on
the next page.
You will want to look at the dot plots below to get some ideas for the rules.
31 | P a g e
Individual Activity - Finding the measures of central tendency and spread
visually
Find each of the measures indicated in the table below.
Median:
Median:
Mode:
Mode:
Mean:
Mean:
Range:
Range:
Internet Activity - Partner Mean, median and Mode Game
32 | P a g e
Individual Activity
Find the median, mean, mode and range of the dot plots. Record your answers in the table below.
Median:
Median:
Mode:
Mode:
Mean:
Mean:
Range:
Range:
33 | P a g e
Flip Card Revision
Write your answers to the teacher’s flip card questions in the spaces below
1.
2.
3.
4.
5.
6.
7.
8.
34 | P a g e
1. The pictograph below represents the most popular videos hired from Mathsville video stores.
a) How many times was Bermuda Triangle hired?
b) How many times was Quadrilateral blues hired?
c) How many more hirings of the Pentagon Conspiracy video were there than the Quadrilateral Blues video?
35 | P a g e
2.
a)
b)
c)
d)
e)
36 | P a g e
3. The graph below shows the test marks of a group of students
a) What is the title for this graph?
b) What is the label on the vertical axis?
c) What is the label on the horizontal axis?
d) Which student has the highest mark?
g) What was Paul’s mark?
h) What was George’s mark?
37 | P a g e
4. Play Zap, zap math.
5. Create a frequency table of the results (out of 75) by students in a mathematics test.
69, 58, 66, 58, 66, 64, 64, 66, 69, 66, 83, 66, 63, 69, 66, 66, 64, 58, 64, 69, 62, 60, 59
6. Create a frequency table of the first 50 decimal places in π :
3.14159265358979323846264338327950288419716939937510
Frequency Table for Math Scores
Score (Results)
Total
38 | P a g e
Tally
Frequency Table for π decimals
Frequency
Score (π decimal) Tally
Frequency
Total
7. Find the mode, median and mean of the following:
a) 3, 12, 11, 7, 5, 5, 6, 4, 10
b) 16, 19, 10, 24, 19
c) 8, 2, 8, 5, 5, 8
d) 28, 39, 42, 29, 39, 40, 36, 46, 41, 30
e) 133, 215, 250, 108, 206, 159, 206, 178
39 | P a g e
```