statistical concepts
DESCRIPTION
Statistical concepts. What students ( and teachers) don’t know. Centre of a distribution. What do we mean by “centre”?. Score playing first game of SKUNK. Centre of a distribution. The centre is the one best number to describe the position of the whole group. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/1.jpg)
Statistical conceptsWhat students (and teachers) don’t
know
![Page 2: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/2.jpg)
Centre of a distribution What do we mean by “centre”?
Score playing first game of SKUNK
![Page 3: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/3.jpg)
Centre of a distribution The centre is the one best number to
describe the position of the whole group.
Score playing first game of SKUNK
![Page 4: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/4.jpg)
Centre of a distribution Mean score 50.1, median 55 Which is better? Mean or median?
Score playing first game of SKUNK
![Page 5: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/5.jpg)
Centre of a distribution The mean is a more efficient measure
than the median. The sample mean tends to be a better
estimator of the population mean than the sample median is of the population median.
This means that confidence intervals for the mean tend to be narrower than for the median.
![Page 6: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/6.jpg)
Mean or median?
![Page 7: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/7.jpg)
Comparing length of Lake Taupo trout in 1995 and 1998 – can you make a call?
![Page 8: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/8.jpg)
Spread of a distribution What do we mean by “spread”?
Score playing SKUNK with a strategy
![Page 9: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/9.jpg)
Spread of a distribution Spread describes how far the values in
the group are from the centre, how variable they are.
Score playing SKUNK with a strategy
![Page 10: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/10.jpg)
Range is not a useful measure of spread because it is determined only by extreme values.
Students should not use range in any NCEA standard (except the numeracy unit standards).
![Page 11: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/11.jpg)
IQR measures the spread of the whole distribution
IQR is calculated using the width of the middle 50% but it is a measure of the variability of the whole group (just as SD measures the variability of the whole group).
Score playing SKUNK at first and then with a strategy
![Page 12: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/12.jpg)
Shift and overlap are comparisons of centre
Shift answers the question “Which is bigger?”
Overlap answers the question “How much bigger, relative to the spread?”
Score playing SKUNK at first and then with a strategy
![Page 13: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/13.jpg)
Beyond centre and spreadStatistical error is the difference between the sample statistic and the (unknown) population
parameter.
![Page 14: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/14.jpg)
What is sampling error?
![Page 15: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/15.jpg)
What is sampling error?It depends where you ask. It is defined differently in different countries.
In NZ (from Statistics NZ): Sampling error arises due to the
variability that occurs by chance because a random sample, rather than an entire population, is surveyed.
Non-sampling error is all error that is not sampling error.
![Page 16: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/16.jpg)
Non-sampling errorNon-sampling error is all error that is not sampling error.Non-sampling error includes bias due to: A sampling frame which does not
represent the population Sampling method The sampling process and anything else except sampling
variability and choice of sample size.
![Page 17: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/17.jpg)
Sample size There is no statistical basis for insisting on a
sample size of 30. A sample doesn’t have to be very big to give a
rough estimate of the centre of the population. A comment that a bigger sample size would
give a better estimate of the population centre would have to be justified by explaining why it would be important to have a better estimate in that context.
Sample size needs to be fairly large (over 200) to get a reasonable estimate of the population distribution.
![Page 18: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/18.jpg)
Maths teachers teaching literacy
How do we teach students to cope with unfamiliar contexts in exams?
![Page 19: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/19.jpg)
How do we teach students to cope with unfamiliar contexts in exams?
One approach is to start with problems they can do in familiar contexts.1. Solve the familiar problem, then replace the
familiar context with an unfamiliar one, one word at a time.
2. Give them a problem in a familiar context beside an identical problem in an unfamiliar context.
3. Give them the familiar problem followed by the unfamiliar problem.
4. Give them a mix of problems in familiar and unfamiliar contexts.
![Page 20: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/20.jpg)
L2 probability examA pilot study investigated if people showed some symptoms of arthritis.The results were summarised in the table shown below.
gender No symptoms of arthritis shown
Some symptoms of arthritis shown
Total
male 167 33 200female 405 195 600total 572 228 800
![Page 21: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/21.jpg)
Start with a context they know.A student asked if people were sleepy.The results are in the table shown below.
gender Not sleepy
Sleepy Total
male 167 33 200female 405 195 600total 572 228 800
![Page 22: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/22.jpg)
A pilot study asked if people were sleepy.The results are in the table shown below.
gender Not sleepy
Sleepy Total
male 167 33 200female 405 195 600total 572 228 800
![Page 23: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/23.jpg)
A pilot study investigated if people were sleepy.The results are in the table shown below.
gender Not sleepy
Sleepy Total
male 167 33 200female 405 195 600total 572 228 800
![Page 24: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/24.jpg)
A pilot study investigated if people showed some symptoms of arthritis.The results are in the table shown below.
gender Not sleepy
Sleepy Total
male 167 33 200female 405 195 600total 572 228 800
![Page 25: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/25.jpg)
A pilot study investigated if people showed some symptoms of arthritis.The results were summarised in the table shown below.
gender No symptoms of arthritis shown
Some symptoms of arthritis shown
Total
male 167 33 200female 405 195 600total 572 228 800
![Page 26: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/26.jpg)
Side by sideA student asked if people were sleepy.The results are in the table shown below.
A pilot study investigated if people showed some symptoms of arthritis.The results were summarised in the table shown below.
![Page 27: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/27.jpg)
familiarA student asked if people were sleepy.The results are in the table shown below.
gender Not sleepy
Sleepy Total
male 167 33 200female 405 195 600total 572 228 800
![Page 28: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/28.jpg)
followed by unfamiliarA pilot study investigated if people showed some symptoms of arthritis.The results were summarised in the table shown below.
gender No symptoms of arthritis shown
Some symptoms of arthritis shown
Total
male 167 33 200female 405 195 600total 572 228 800
![Page 29: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/29.jpg)
Two-way Venn diagrams are not good problem solving tools.
Students who use two-way tables are much more successful at solvingProbability problems than students who use Venn diagrams.
![Page 30: Statistical concepts](https://reader036.vdocuments.net/reader036/viewer/2022081520/56816280550346895dd2ed3e/html5/thumbnails/30.jpg)
the end