# Ib math sl ia statistics examples

Jun 20, 2018

`If you look in real life, it is very hard to describe people as good people, bad people, heroes or villains. People aren't bad people. They all have their justifications. Lennie James`

**Quick links**:

► downloadable teaching materials for descriptive statistics

► syllabus content for the Algebra Topic: **SL syllabus** (see syllabus section 5.1); **HL syllabus** (see syllabus section 5.1).

Many students will have some prior knowledge of several of the important facts and concepts in this part of the syllabus - such as mean, median, mode, frequency tables, histograms and scatter diagrams (SL). Nevertheless a thorough coverage of **descriptive statistics **is very important because many of the basic concepts covered/reviewed in this part of the syllabus are essential for understanding **probability distributions, **specially continuous probability distributions in HL.

Something that is worth noting is that there is a significant difference between the SL syllabus and the HL syllabus in terms of the quantity of information on what should be covered for descriptive statistics. In the HL syllabus there is one syllabus section (5.1) for descriptive stats which contains only 29 words of 'content'. Whereas, the SL syllabus has three sections (5.1, 5.2 & 5.3) and contains nearly 3 times as many words to describe the 'content' for descriptive statistics. I would recommend that anyone teaching HL should refer to sections 5.1, 5.2 & 5.3 in the SL syllabus and be sure to cover all the content indicated there. For example, there is no specific mention of **cumulative frequency graphs** in the HL syllabus, but questions involving cumulative frequency graphs are sometimes included in HL exams. For example, the question in the 'hidden box' below was on an HL Paper 2 exam not too long ago.

question with **cumulative frequency graph **on an HL exam

**4 questions - **‘accessible’ to ‘discriminating’

download: 4_Qs_statistics_1_with_answers_v2

**accessible SL question**

**moderate SL / accessible HL question**

**discriminating SL / moderate HL question**

**discriminating HL question**

**Answers**

#### Course planning / teaching notes:

##### ♦ teaching materials

EXS_5-1_20v1_SLHL_stats_no_GDC

Set of 7 exercises covering basic statistical computations such as mean, median, mode & standard deviation. Two questions involve a frequency table and one question has grouped data. SL students can use GDC for computing standard deviation; otherwise, all questions require students to perform the computations manually without a GDC. **Answers **included.

EXS_5-1-30v1_HL_descriptive_stats

Set of 7 exercises that focuses on HL content of descriptive statistics. Could be suitable for use with SL students. Some of the exercises allow a GDC; some do not allow a GDC. **Answers **included

I’m assuming this is for your math IA and since I haven’t done any or been debrief and such, I don’t really know much about it. However, I’ve had several seniors who told me some of their topics (that I find pretty interesting) so maybe it could help you.

1. Traffic Flow

2. Impact Earth

3. Birthday Paradox

Also, I found a website to provide you with further information and will be more helpful than any answer I could give:

Thanks for the a2a, beforehand.I’m assuming this is for your math IA and since I haven’t done any or been debrief and such, I don’t really know much about it. However, I’ve had several seniors who told me some of their topics (that I find pretty interesting) so maybe it could help you.1. Traffic Flow2. Impact Earth3. Birthday ParadoxAlso, I found a website to provide you with further information and will be more helpful than any answer I could give:

First, I will establish that the group I want to study is specifically junior IB Theory of Knowledge (TOK) students at my school. In that group, there are 83 students that I will observe. There are two TOK teachers that all meet with students during Learning Lab, or study hall, the second to last block of the school’s schedule; one meets on Mondays and Wednesdays and the other on Tuesdays and Thursdays. For this reason, I will travel during Learning Lab on a Monday to the two teachers of the TOK classes and again on the following day. If some students are absent those two days, I will take the time to collect their information on Wednesday and/or Thursday during Learning Lab, and if need be, I will continue my investigation the following week, since TOK classes do not meet on Fridays.

After the schedule is decided, I will create a chart for each of the two classes that records the number of people with the following hair and eye color. Both of the charts will look like this:

I will then set out to each of the classes to obtain my data in tally marks until all 83 students have been studied. If I find students with hazel-colored eyes (a combination of green and brown) I will ask them which color they identify with more. After all information has been collected I will add up the data and combine the two charts into one, then I will conduct a *χ*2 to decide if eye color is dependent on hair color using a table of critical values of the *χ*2 distribution with two degrees of freedom (df) and 5% level of significance. The critical value for two degrees of freedom and 5% level of significance is 5.991, so if my *χ*2 value is less than 5.991, I will accept the null hypothesis, that the factors are independent, but if the *χ*2 value is greater than 5.991, I will reject the null hypothesis and accept the alternative hypothesis, that the factors are dependent.