Pencils and cars

Pencils and cars

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about mean, median, and quartiles.

Aaron measured the lengths of ten pencils. Here are his results recorded in centimetres (cm).
 
4.1,  6.4,  7.3,  7.8,  8.0,  12.0,  13.4,  15.2,  18.1,  20.7
  
a)
i)
 
ii)
What is the average (mean) length of the pencils? __________ cm
 
What is the median length of the pencils? __________ cm

  

Zoe counted the number of cars that passed her school gate each minute.
Here are her results.
 
0,  2,  4,  4,  5,  7,  8,  11,  11,  16,  16,  19,  28
  
b)
Work out each of these statistics for Zoe's data.
 
 
i)
 
ii)
 
iii)
The median = __________ cars per minute 
 
The lower quartile = __________ cars per minute
 
The upper quartile = __________ cars per minute
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Statistics, Statistical investigations
Keywords: 
data measures, mean, median, quartiles
Description of task: 
Students firstly find the mean and median length of pencils. Secondly students find the median, and lower and upper quartile for the number of cars that passed through the school gate.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y11 (03/2001)

a)

i)
ii)

11.3
10.0 [accept 10]

easy
moderate

b)

i)
ii)
iii)

8
4
16

easy
moderate
moderate
Diagnostic and formative information: 
 

Common error

Likely miscalculation

a) i)
a) ii)
b) i)

10
11.3
10

Confuses mean and median.