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This task is about peoples ability to estimate lengths and angles.

Guesstimate

22

Sarah asked 200 people to estimate the length of a short line and a longer line, they were also

asked to estimate the size of a small angle and a larger angle.

Guesstimate

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Guesstimate

Put away all rulers and protractors.

Before we look at that data you are going to be given a sheet with two lines and two angles drawn on it.

Write down in the back of your books how long you think each line is to the nearest mm (e.g. 17.3cm) and how large each angle is to the nearest degree (e.g. 520)

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Guesstimate

The actual lengths were:

Small line = 6.2cm

Long line = 21.3cm

Small angle = 480

Large angle = 1240

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GuesstimateComplete this table and your teacher will collect in your gender and 4 error results for later.

Actual My My estimatesestimates

ErrorError

Small line = 6.2cm

Long line = 21.3cm

Small angle = 480

Large angle = 1240

66

 

Ag

e

6.2 cm E

rror

21.3 Erro

r

48 deg

ree Erro

r

124 deg

ree E

rror

1 F 8 2 6 3 1

2 F 11 1 4 5 4

3 F 11 3 1 7 0

4 F 11 3 2 2 5

Which of these 4 girls was the best at estimating?

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HypothesisHypothesis

Boys are better at estimating lengths than girls.Boys are better at estimating lengths than girls.

It is easier to estimate lengths than anglesIt is easier to estimate lengths than angles

Adults are better at estimating than young people.Adults are better at estimating than young people.

15 year old pupils are better than 11 years olds at 15 year old pupils are better than 11 years olds at

estimating angles.estimating angles.

Smaller angles are easier to estimate than larger Smaller angles are easier to estimate than larger

onesones

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Males are better at estimating Males are better at estimating lengths than females.lengths than females.

I believe this because boys are seen as being more I believe this because boys are seen as being more

practical than girls.practical than girls.

I will test this by using the estimates given for the I will test this by using the estimates given for the

shorter lengthsshorter lengths

I will take a quota sample of 40 males and 40 femalesI will take a quota sample of 40 males and 40 females

I have decided on 40 as it is sufficient to give an I have decided on 40 as it is sufficient to give an

accurate result but not so many as to make the task accurate result but not so many as to make the task

tedious and time consuming.tedious and time consuming.

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Key Questions.Key Questions.

Sample Size – How large and how will you choose Sample Size – How large and how will you choose

randomly?randomly?

Statistical Calculations – Which ones do we know and Statistical Calculations – Which ones do we know and

which ones could we use?which ones could we use?

Graphs – What graphs can we draw and which ones Graphs – What graphs can we draw and which ones

are best?are best?

Comment on all your graphs and calculations. Comment on all your graphs and calculations.

Always ask does this support my hypothesis.Always ask does this support my hypothesis.

1010

Data CalculationsData Calculations• To find the mean value of a set of data you add up all

the data

values then divide by how many there are.

• To find the median you put the data in order and find

the

middle value.

• The mode is the most common value

• The range is a measure of spread and is the largest

data value –

the smallest data value.

• 25% of the results lie between each of the quartile values

• The interquartile range is the upper quartile value

– the

lower quartile value. This is the spread of the middle

50% of the

data and excludes any extreme values

1111

Comparative Bar ChartsComparative Bar Charts

The number of older people dying has increased each year, whereas the number of young people dying has reduced. The number of deaths in the 45-74 age group has gone up and then down but still remains high.

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Comparative Bar ChartsComparative Bar Charts

This comparative bar chart shows the same information but it enables me to compare the total number of deaths each year.

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Pie ChartsPie Charts

I can see from this pie chart that in 1901 that about 25% of the deaths were babies under 1 year old and about a 1/3 were aged 45-74 years old.

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Scatter GraphsScatter Graphs

The older the car the more miles it has done, although it is not a big difference, petrol cars have a lower mileage than diesel ones, this might be because many company cars run on diesel.

1515

Line GraphsLine Graphs

This graph enables me to see how in 1902 many people died young whereas in 1999 deaths were low until they reached about 50 when it starts to increase noticeably.

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Box PlotsBox Plots

The age at death has increased dramatically since the 1902 figure as can be seen by the box plot being skewed to the right. In 1902 50% of the population would be dead by the age of 35, this age rose to 68 in 1950 and 80 in 1999.

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Frequency PolygonsFrequency Polygons

The shape of both frequency polygons is similar although the Championship polygon is wider indicating that the median and mean are similar for both but the spread is larger for the championship.

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Cumulative Frequency Cumulative Frequency GraphGraph

I have drawn this cumulative frequency curve as I had a lot of data and it will enable me to draw a boxplot to compare the two sets of results for Set 1 and Set 2.