Transcript 3 - Dynamic Learning

Steps
Grouped frequency
Estimating the mean
Comparing distributions
Mastering Mathematics © Hodder and Stoughton 2014
Using grouped frequency tables – Developing Understanding
Grouped frequency
Mr Harris has given his class a test.
He has given each student a mark out of 50.
Here is a tally chart to show his results.
1. Is it possible to find an exact value for the
range of the marks from the table?
2. What can you say abut the median and the
mode?
The marks go
from 1 to 50 so
the range is 50.
You can’t find the
range because you
don’t know the exact
marks.
The 31-40
group has most
people .
For the median we are
looking for the middle
two scores.
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Vocabulary
Mastering Mathematics © Hodder and Stoughton 2014
Q1
data
No,
can Grouped
only
estimate
Bothyou
opinions
gave
part
of the
the range.
correct
This
is used where there are many
answer.
possible
values
for the
data.
It is aonly
We do not
the exact
data
values,
convenient
way
handling
large
which
groupclass
theyofisare
in.
The modal
31–40.
amounts
of data.
possible
values
For
theth The
range
could
be
50in– 1
The example,
15th and
16
student
are both
for
the
are
grouped
(usually
into
=
49
at data
most
or 41
–1 0=
31 atisleast.
the
31–40
group.
The
median
equal
groups).
The groups
are
often
somewhere
between
31 and
40.
called ‘Classes’.
Modal class
The group with the highest frequency is
called the modal class.
Opinion 1 Opinion 2 Answer
Q2
Opinion 1 Opinion 2 Answer
Using grouped frequency tables – Developing Understanding
Grouped frequency
Abby is doing a survey on homework.
Here are her results from one of the
questions on her questionnaire.
1. What do the symbols < and ≤ mean?
Write down some different ways of
describing her groups.
A < B means that number A is less
than number B.
0 < t ≤ 1 means that t is bigger than
zero and also less than or equal to 1.
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Q1
< stands for ‘is less than’ and we read it
from
left to
right.
Variable
is the
general name for what is
≤being
stands
for ‘is less than or equal to’.
measured.
Putting them together with a variable in
between
shows
exactly
thetake
range
that
Continuous
variables
can
anyfor
value.
group. In Abby’s survey the variable is t
which is a continuous variable. t is the
number of hours spent on homework.
3< t ≤ 5 can be read as:
• t is more than 3 and less than or equal
to 5
• t can have any value from 3 to 5 but not
including 3
• t must be more than 3 and not more
than 5.
Opinion 1 Opinion 2 Answer
Using grouped frequency tables – Developing Understanding
Grouped frequency
Abby is processing the data from her
survey on homework.
Here are her results from one of the
questions on her questionnaire.
Abby has written the frequency of each
response in each box.
1. Compare Abby’s data with the marks
for Mr Harris’s class. What is the
difference between the types of data?
Abby’s data is hours
and the other is
days.
The absences
can only be
whole numbers.
Discuss
which
Discretedifferent
variablesnumerical
can only variables
take particular
you
might measure in a survey. Decide
values.
whether they are discrete or continuous.
The number of absences and hours are
both examples of variables.
The number of absences can only take
whole numbers. This a discrete variable.
The number of hours can take any value.
This is a continuous variable.
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Opinion 1 Opinion 2 Answer
Using grouped frequency tables – Developing Understanding
Estimating the mean
Ms Shah is head of Year 8 at Hodder High
School. She made this table showing pupils’
absences for one term.
1. Ms Shah needs to report the mean number of
absences. She asks some pupils to work it
out. Can you help them?
2. Now do the calculation for Ms Shah. Make
your answer a sensible estimate.
Shewe
needs
to find
Do
divide
by 6
the totalthere
number
because
are of
6
pupils. 
groups?
Would
it helpuse
to the
show
She could
themiddle
working
in extra
number
in
each group.
columns?

She needs to Mid-interval
find the total values
frequency. She can
These
find
an are
estimate
the central
of thevalues
mean for
by pretending
each group.that
They are used
everyone
scored
to the
findhalfway
approximate
number
totals
in the
for
each group.
group:
2, 7, 12, 17, 22, 27. Both opinions are
good.
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Vocabulary
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Q1
Days absent Frequency
Days
Mid-interval Midpoints
×
0–4
25
Frequency
Answer
absent
values
frequency
5–9
38
0–4
25
2 × 25
50
10–14 2
16
5–9
38
7 × 38
266
15–19 7
4
10–14
16
12 × 16
192
20–24 12
2
15–19
4
17 × 4
68
25–29 17
1
20–24
22
22 × 2
44
Total2
25–29
1
Total
86
27
27 × 1
Total
27
647
Estimate for the mean = 647 ÷ 86
= 7.523256.
This is not a sensible estimate.
The number of days absent can only be
a whole number.
A sensible estimate is 8 days.
Opinion  was incorrect. You must
divide by the number of pupils.
Opinion 1 Opinion 2 Answer
Q2
Opinion 1 Opinion 2 Answer
Using grouped frequency tables – Developing Understanding
Estimating the mean
Abby is processing the data from her
survey on homework.
Abby has written the information in a
table and has begun to calculate an
estimate for the mean.
Part of her calculations are shown
below.
1. Complete Abby’s working for the
estimated mean.
2. The estimated mean was given as
1.4 hours. Is that a sensible
answer? If not suggest a more
suitable answer.
The
midIt worked
interval
out exactly
values
so it is are
1.5,
good.2.5,

3.5.
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Mid-interval value = 1.5
Mid-interval value = 2.5
Mid-interval value = 3.5
Total = 42
Mean = 42 ÷ 30 = 1.4 hours.
Both opinions are good.
Opinion  is correct. The answer of 1 hours would
be more suitable.
The
table
it
There
are makes
60
easier
to in
show
minutes
an the
calculations.
hour so it is not
sensible to give a
decimal answer. 
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Mastering Mathematics © Hodder and Stoughton 2014
11 × 1.5 = 16.5
5 × 2.5 = 12.5
2 × 3.5 = 7
Q1
Opinion 1 Opinion 2 Answer
Q2
Opinion 1 Opinion 2 Answer
Using grouped frequency tables – Developing Understanding
Comparing distributions
Ask your teacher to obtain the handspan
GRO-RITE
measurements
for
an
older
or younger
class.
Mid-way
Mid-way
Height
(7h) value the
f
Height (h) the
value results
f
h×f
h×f
Calculate
mean
and compare
0 < h ≤ 10
6
30
0 < h ≤ 10
5 18
90
for the two5 classes.
A botanist wants to compare two
different seed composts, COMPO and
GRO-RITE.
150 seeds are sown in each compost
and after three weeks, the heights of
the seedlings which have germinated
are measured.
This table shows the heights, h mm, of
each set of seedlings.
COMPO
10 < h ≤ 20
20 < h ≤ 30
30 < h ≤ 40
40 < h ≤ 50
10
15
20
25
Totals
23
45
36
11
121
230
675
720
275
1930
Mean
= 1930 ÷ 121 = 15.95
1. Estimate the mean height and the
modal class for each set of
seedlings. Which compost performs
better?
10 < h ≤ 20
20 < h ≤ 30
30 < h ≤ 40
40 < h ≤ 50
10
15
20
25
Totals
16
20
48
31
133
160
300
960
775
2285
= 2285÷133
= 17.18
Estimated mean
COMPO 16 mm
GRORITE 17 mm
Modal class
COMPO 20–30 mm GRO-RITE 30–40 mm
(The modal class has the highest frequency so
opinion  is wrong).
We need to find the mid-way values
for each group; 5,10,15 etc. 
There is no modal class because all the
classes are the same size. 
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