Is it true that university students sleep late into the morning and even into the afternoon?

1
Is it true that university students sleep late
into the morning and even into the afternoon?

• Suppose we want to find out what time
• university students get up in the morning.
• Although there are many ways we might research
  this question, the simplest way is probably to
  ask them.
• Imagine that for one day perhaps next Tuesday
  we surveyed students by arranging for the
  computer system to ask them 3 or 4 questions when
  they first log in.
• One of the questions might be
• What time did you get up today?

2
Answers to our survey question What time did
you get up today?

• Here are some data that we might have collected

1030 800 1130 1030 1000 1130 1100 120
0 1030 1200 1100 930 1100 1100 1030 1
230 1130 1100 1300 1000
How can we use these data to answer our research
question?
Is it true that university students sleep late
into the morning and even into the afternoon?
3
How can we use these data (from our survey
question) to answer our research question?
1030 800 1130 1030 1000 1130 1100 120
0 1030 1200 1100 930 1100 1100 1030 1
230 1130 1100 1300 1000
800 1100 930 1100 1000 1100 1000 1130 103
0 1130 1030 1130 1030 1200 1030 1200 1100
1230 1100 1300

• We should start by seeing how many students wake
  up at each of the times.
• To make this task easier, we can arrange our data
  in order by time, so that the ones that are the
  same appear together in the list ?

4
How can we use these data (from our survey
question) to answer our research question?

• Count how many students woke up at each time
• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

800 1100 930 1100 1000 1100 1000 1130 103
0 1130 1030 1130 1030 1200 1030 1200 1100
1230 1100 1300
You dont need to type in the numbers just
write them down on a scrap of paper.
5
How can we use these data (from our survey
question) to answer our research question?

• Count how many students woke up at each time
• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
These counts (or frequencies) describe how the
people were spaced out (or distributed) across
the range of times. This set of numbers is
called the frequency distribution.
6
How can we use these data (from our survey
question) to answer our research question?

• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
It can sometimes be easier to see the data if
they are shown as a graph. A bar graph that has
the categories along the x-axis (the bottom) and
how often they occur (the frequencies) along the
y-axis (the side) is called a frequency
histogram.
7
Describing the data
The frequency histogram is a useful way to see
what the data look like. But sometimes its
necessary to describe the data with words (and
numbers). For someone else to be able to see what
the data look like, without going through all of
the data or seeing the graph, what sort of
information would they need? Type in your best
answer below, and then well examine the
possibilities together.
8
Describing the data

• To describe the data, we need to communicate . .
  .
• where the middle or bulk of the data are (if
  there is a place where the data are thickest)
• measures of central tendency
• how spread out the data are
• measures of dispersion
• whether the data are spread evenly on both sides
  of the middle, or not
• Are the data normal or skewed?

9
Describing where the centre of the data
ismeasures of central tendency

• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
There are three main measures of central tendency
Mean (or average) Median (or mid-point) Mode
(or most frequent point)
10
Describing where the centre of the data is

• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
What time is the median value? Part 1 Type in
your answer below. (If you dont know or dont
remember what the median is, type ?)
Text input item
11
Describing where the centre of the data is
What time is the median value? Part 2 Select
your answer from the list below. A 1000 B
1030 C 1100 D 1130 E Dont know

• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
Multiple choice
12
Describing where the centre of the data is
What time is the median value? Part 2 Select
your answer from the list below. A 1000 B
1030 C 1100 D 1130 E Dont know

• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
Well done!
The average of 1100 and 1100 is 1100
13
Describing where the centre of the data is
Sorted dataset
The median value is the value that is exactly in
the middle of the list when the data have been
sorted. When there is an odd number of cases, the
median is the value of the case in the middle of
the sorted list. When there is an even number of
cases, the median is the average of the values
for the pair in the middle of the sorted list.

• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
1 11 2 12 3 13 4 14 5 15 6 16 7 17
8 18 9 19 10 20
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
For 1st error on median
14
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 250, 165, 325, 195, 175
• First, sort the data
• Which is the lowest cost?
• Type in your answer below.

Number entry
15
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 250, 165, 325, 195, 175
• First, sort the data
• Which is the lowest cost?
• Woops! The lowest value is 165!

16
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 250, 165, 325, 195, 175
• First, sort the data
• 165, ?
• Which is the next lowest cost?
• Type in your answer below.

Number entry
17
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 250, 165, 325, 195, 175
• First, sort the data
• 165, ?
• Which is the next lowest cost?
• Woops! The next lowest value is 175!

18
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 250, 165, 325, 195, 175
• First, sort the data
• 165, 175, . . .
• Which is the next lowest cost?
• Type in your answer below.

Number entry
19
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 250, 165, 325, 195, 175
• First, sort the data
• 165, 175, . . .
• Which is the next lowest cost?
• Woops! The next lowest value is 180!

20
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• For the sake of this exercise, we will just look
  at a small sample of their data just 7 replies
• 180, 200, 280, 165, 325, 185, 175
• First, sort the data
• 165, 175, 180, . . .
• You have the idea . . . the sorted costs are
• 165, 175, 180, 185, 200, 280, 325
• The median is the value of the data point in the
  middle of the sorted list.

21
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• The sorted costs are
• 165, 175, 180, 185, 200, 280, 325
• The median is the value of the data point in the
  middle of the sorted list.
• There are two easy ways to find the median for a
  short list(1) Cancel data points from each end
  of the list until there is just one (or two)
  remaining
• 165, 175, 180, 185, 200, 280, 325
• 165, 175, 180, 185, 200, 280, 325
• 165, 175, 180, 185, 200, 280, 325

Median
If there had been two points left in the middle,
the average of those two values would be the
median.
22
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their monthly accommodation costs.
• The sorted costs are
• 165, 175, 180, 185, 200, 280, 325
• The median is the value of the data point in the
  middle of the sorted list.
• There are two easy ways to find the median for a
  short list(2) Count the number of scores and
  divide by 2.
• When there are an odd number of data points,
  the result will include a fraction (e.g. 3.5).
  Count up from the beginning of the sorted list
  for the whole number part (e.g. 3) of the result,
  and select the value of the next data point in
  the list. That value is the median.
• When there are an even number of data points,
  the result will not include a fraction (e.g., 3).
  Count up from the beginning of the sorted list
  for that result. Select the number you finish
  with and the next number in the list average
  those two numbers. That average is the median.
• 7 ? 2 3.5 Count up 3 (165, 175, 180),
• Select the next data point is 185 which
  is the median.

23
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• For the sake of this exercise, we will just look
  at a small sample of their data just 10
  replies
• 5.10, 6.00, 5.50, 6.00, 15.00, 20.00,
  6.50, 8.00, 6.80, 6.10
• First, sort the data.
• Write down a sorted list.

24
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• For the sake of this exercise, we will just look
  at a small sample of their data just 10
  replies
• 5.10, 6.00, 5.50, 6.00, 15.00, 20.00,
  6.50, 8.00, 6.80, 6.10
• Check your sorted list against the following.
• 5.10, 5.50, 6.00, 6.00, 6.10, 6.50, 6.80,
  8.00, 15.00, 20.00
• Now, identify the median value and type it below.

Number entry
25
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• For the sake of this exercise, we will just look
  at a small sample of their data just 10
  replies
• 5.10, 6.00, 5.50, 6.00, 15.00, 20.00,
  6.50, 8.00, 6.80, 6.10
• Check your sorted list against the following.
• 5.10, 5.50, 6.00, 6.00, 6.10, 6.50, 6.80,
  8.00, 15.00, 20.00
• Hmmm. . . That wasnt the correct value.
• If you want to try again, you can.
• If youre just not clear on the concept, just
  type ?

Number entry
26
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Okay, to make it a bit simpler, lets just look
  at 3 replies these are already sorted
• 5.10, 5.50, 6.00
• The median value is the one in the middle of the
  set of data.
• Which value is the median?

Number entry
27
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Okay, to make it a bit simpler, lets just look
  at 3 replies these are already sorted
• 5.10, 5.50, 6.00
• The median value is the one in the middle of the
  set of data.
• The value you typed was not the median value.
• The median value the middle value is 5.50.
• Its the one in the middle.

28
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Okay, to make it a bit simpler, lets just look
  at 3 replies these are already sorted
• 5.10, 5.50, 6.00
• The median value is the one in the middle of the
  set of data.
• Right!
• The median value the middle value is 5.50
  for this set of data.

Number entry
29
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Now lets consider a set of 4 replies these are
  already sorted
• 5.10, 5.50, 6.00, 6.00
• The median value is the one in the middle of the
  set of data.
• When the middle of the set is a pair of data
  points when the data set has an even number of
  data points the median is the average of the
  two data points in the middle.
• Which value is the median for this set of 4 data
  points?

Number entry
30
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Now lets consider a set of 4 replies these are
  already sorted
• 5.10, 5.50, 6.00, 6.00
• The median value is the one in the middle of the
  set of data.
• When the middle of the set is a pair of data
  points when the data set has an even number of
  data points the median is the average of the
  two data points in the middle.
• The value you typed was not the median value.
• The median value is the average of the two values
  in the middle
• 5.50 and 6.00, which is 5.75.

31
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Consider another set of 4 replies these are
  already sorted
• 6.10, 6.40, 6.60, 8.00
• The median value is the one in the middle of the
  set of data.
• When the middle of the set is a pair of data
  points when the data set has an even number of
  data points the median is the average of the
  two data points in the middle.
• Which value is the median for this set of 4 data
  points?

Number entry
32
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Consider another set of 4 replies these are
  already sorted
• 6.10, 6.40, 6.60, 8.00
• The median value is the one in the middle of the
  set of data.
• When the middle of the set is a pair of data
  points when the data set has an even number of
  data points the median is the average of the
  two data points in the middle.
• The value you typed was not the median value.
• The median value is the average of the two values
  in the middle
• 6.40 and 6.60, which is 6.50.

33
An brief exercise on the median score

• Please contact your tutor and/or read about the
  median value in your textbook.
• There seems to be some confusion here, and it
  looks like you really ought to talk to a tutor to
  get it sorted out.

34
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Consider another set of 4 replies these are
  already sorted
• 6.10, 6.40, 6.60, 8.00
• The median value is the one in the middle of the
  set of data.
• When the middle of the set is a pair of data
  points when the data set has an even number of
  data points the median is the average of the
  two data points in the middle.
• It looks like youve got it! Well done!
• The median value is the average of the two values
  in the middle
• 6.40 and 6.60, which is 6.50.

35
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• Now lets consider a set of 4 replies these are
  already sorted
• 5.10, 5.50, 6.00, 6.00
• The median value is the one in the middle of the
  set of data.
• When the middle of the set is a pair of data
  points when the data set has an even number of
  data points the median is the average of the
  two data points in the middle.
• Well done!
• The median value is the average of the two values
  in the middle
• 5.50 and 6.00, which is 5.75.

36
An brief exercise on the median score

• Imagine that the student union surveyed students
  about their hourly earnings.
• For the sake of this exercise, we will just look
  at a small sample of their data just 10
  replies
• 5.10, 6.00, 5.50, 6.00, 15.00, 20.00,
  6.50, 8.00, 6.80, 6.10
• Check your sorted list against the following.
• 5.10, 5.50, 6.00, 6.00, 6.10, 6.50, 6.80,
  8.00, 15.00, 20.00
• Now, identify the median value and type it below.

The points in the middle were 6.10 and
6.50. (6.10 6.50) ? 2 12.60
? 2 6.30
Well done!
37
Describing where the centre of the data is

• Count how many students woke up at each time
• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
What time is the modal value? (If you dont know
or dont remember what the mode is, type ?)
38
Describing where the centre of the data is

• Count how many students woke up at each time
• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
What time is the mean value? (If you dont know
or dont remember what the mean is, type ?)
39
Describing how the data are spread out

• Count how many students woke up at each time
• Before 830 ____
• 830 ____
• 900 ____
• 930 ____
• 1000 ____
• 1030 ____
• 1100 ____
• 1130 ____
• 1200 ____
• 1230 ____
• After 1230 ____

Before 830 1 830 0 900
0 930 1 1000 2 1030 4
1100 5 1130 3 1200 2
1230 1 After 1230 1
800 1100 930 1100 1000 1100 1000 1130
1030 1130 1030 1130 1030 1200 1030 1200 11
00 1230 1100 1300
xx
40
Youve reached the end of this session