To continue talking about Ireland, we have introduced a new course for teaching mathematics to secondary school (high school) students. It is known as "Project Maths". From the Project Maths website, it says:
Project Maths is an exciting, dynamic development in Irish education.
It makes maths relevant to the everyday lives of teenagers, and helps
them understand it better using interesting and practical techniques.
Students are empowered in developing essential problem-solving skills
for higher education and the workplace.
In terms of statistics (for students taking higher level), the topics covered are:
- Collecting data
- Quantitative data
- Qualitative data
- Frequency distribution for discrete (countable) data
- Mean, mode, median for discrete or continuous grouped frequency distributions
- Variability of data
- Standard deviation of a frequency distribution
- Frequency Curves
- Distributions and shapes of histograms
- Stem and leaf diagrams
- Scatter plots (scatter graphs)
- Correlation and causality
- The normal curve and the standard deviation as a ruler
- Shifting data (transforming data)
- Standardizing scores
- Hypothesis testing
- Margin of error and confidence intervals for population proportions
- Sampling theory (distribution of the sample mean)
- Pitfalls and misuses of statistics
It is correctly pointed out by @richiemorrisroe that probability is treated as a separate chapter from statistics, but there is some overlap. Some of the topics in probability (again, for students taking higher level) are:
- Normal distribution and probability
- Finding areas under normal curves
- Probability distributions (including the notion of r.v. and expected value)
Some people have spoken out against Project Maths (for example, see here), but talking in terms of the sections on statistics and probability, I think it's a rather good course.
Since I have come across University lectures (both undergrad and postgrad!) that cover some of the above topics in no greater depth than the material we are presenting to our secondary school (high school) students then my reading of the situation is that we must be doing something right in this area.
In my own experience, I am not a high-school teacher, but I do help friends of family with their mathematics - particularly leaving certificate higher level. For me, it's enjoyable to teach statistics and probability to these young students and I do believe that they are learning material that is both useful and of a significantly high standard.
If you seek any further information, please visit the Project Maths website or watch this video by the National Council for Curriculum and Assessment.