# Comparative Numbers

Certain numbers help illustrate the performance of learners relative to that of a whole class or **express any irregularities** in the average performance of a class.

# Standard Deviation

The **Standard Deviation** indicates how **far** a quantity is likely to deviate **from its average value**. In LearningSpace, it corresponds to a **range** where **most of a group of learners' results belong, in other words, how close the learners' results** are to each other.  


:::info
This can help

* **compare a learner's result to that of the whole class**
* and, by extension, it can also provide **feedback about the applicability** of the Cases.

:::

If the standard deviation is either *too big* or *too small*, it could mean that something needs to be **adjusted in the Activity** management.

 ![](https://outline-production-attachments.s3-accelerate.amazonaws.com/uploads/48ddf0a7-308b-4fe9-b28a-e3ce1797eaa8/e5ba07e7-802b-4bf3-afcf-fbc72d00f218/12616003.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA4EOUDTOVUICLPZ4P%2F20260909%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20260909T120000Z&X-Amz-Expires=86400&X-Amz-Signature=0b36b964ab9de75fc767c3af50b7d82215c17da4dedb8ae1f9a79deca28acb1c&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject "right-50 =314x83")


**x** = one particular kind of score of each learner in a learner group  
**m** = **mean performance** of the learner group - calculated from the same kind of scores  
**n** = number of learners in the learner group

You can calculate standard deviations for different groups of data, for example, for **different levels of scores**:

* item results,
* section results,
* Case results
* and Activity results.

 ![](https://outline-production-attachments.s3-accelerate.amazonaws.com/uploads/48ddf0a7-308b-4fe9-b28a-e3ce1797eaa8/0d31d4a7-8929-4817-83ff-fa921a6f6129/76909709.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA4EOUDTOVUICLPZ4P%2F20260909%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20260909T120000Z&X-Amz-Expires=86400&X-Amz-Signature=994ce17a3991708e40f6b54e0dc819006ca8c6d2e398e2d840e1c077f88989d5&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)

# Z-score

The **Z-score** always refers to the **performance of a single learne**r: it reflects **how much a specific learner's performance differs from the average**. It is calculated from the *learner score* for a particular part of the Activity, a *class average for the same scores,* and the *standard deviation* calculated from the preceding two numbers. ![](https://outline-production-attachments.s3-accelerate.amazonaws.com/uploads/48ddf0a7-308b-4fe9-b28a-e3ce1797eaa8/a93c17fb-dc60-4c3e-988c-1e5700896c87/12616004.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA4EOUDTOVUICLPZ4P%2F20260909%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20260909T120000Z&X-Amz-Expires=86400&X-Amz-Signature=5487806ce8991a09b078d342624e7f70fb93da169536cc610682aa3201947ece&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject "right-50 =134x39")

**l** = any kind of learner score  
**a** = the **class average** calculated from the same kind of scores  
**d** = the standard deviation calculated from the same scores and average

If this value is *below -1 or exceeds +1*, it means that the learner's section performance **falls outside the class standard deviation**. They performed much *better* or worse than average in that section of the Activity. If a learner's Z-score is *near 0*, it means his section score is *near the class average*.  
  

 ![](https://outline-production-attachments.s3-accelerate.amazonaws.com/uploads/48ddf0a7-308b-4fe9-b28a-e3ce1797eaa8/579a2635-f993-474e-9546-ba8ad54c716b/76909708.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA4EOUDTOVUICLPZ4P%2F20260909%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20260909T120000Z&X-Amz-Expires=86400&X-Amz-Signature=7c77b3cd08a799f5877afed1fe62da873016023f0500ac039778b39162f98296&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)

# Percentile Score

The **Percentile Score** refers to a specific learner and indicates **what percentage of the class** (more precisely, the learner group) **performed worse than (or the same as)** that learner.


:::info
 ![](https://outline-production-attachments.s3-accelerate.amazonaws.com/uploads/48ddf0a7-308b-4fe9-b28a-e3ce1797eaa8/d9404752-ff73-4d1f-94ec-bd2b86dd4233/12616005.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA4EOUDTOVUICLPZ4P%2F20260909%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20260909T120000Z&X-Amz-Expires=86400&X-Amz-Signature=6f80ffc68d4aea3cef8c8ee1a7969a6f989ef05546be3ea5669c0710d9306c24&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject "right-50 =272x38")The Percentile Score is always a **percentage:** the **number of learners** whose performance was *worse than or equal* to that of **the learner whose percentile score is being calculated**, divided by the **number of learners** in the Activity's learner group w**ith a record of that score**.

:::

**nw** = number of learners whose particular performance was *worse than or the same* as that of the learner  
**n** = number of learners of the learner group of the Activity *who have a record* for the certain score

Percentile scores can be calculated for different scores, such as section, Case, and Activity results. The percentile score is **100% for the best-performing learner(s), while 0% for the weakest one**.


:::warning
***IMPORTANT:*** Due to the calculation method, the percentile score is 100% for the strongest learners, even if there is more than one with the same result, whereas it will be slightly above 0% for the weakest learners if there is more than one. The value of this score also depends on the [**decimal**](/doc/report-formatting-BL3Xh0msVE) **display setting**s made on the [**Activity Reporting Setup**](/doc/activity-reporting-setup-mIabTibem4) page, because the **percentile score calculation uses the displayed values**.

:::


:::tip
For further information, see the [Reports - How to](/doc/reports-how-to-qnSWC08QSs) pages and the [Reports Module Training Videos](/doc/reports-module-training-videos-dr44xGB4HN).

:::

---

**Documents**

- [User Guide](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/user-guide-WPv4VxhtWB)
- [FAQ](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/faq-YoxOQOjvnY)
- [Training Videos](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/training-videos-D2ycsEwqPt)
- [Module Introduction Videos](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/module-introduction-videos-I6OQ6H7SUT)
- [Release Notes](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/release-notes-BcFFMsc0RV)
- [Distance Learning with LearningSpace](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/distance-learning-with-learningspace-eAfwW23Hxg)
- [Preventing Copy-Paste in LearningSpace](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/preventing-copy-paste-in-learningspace-sPD0IIUuk0)
- [Important Technical Notification Regarding Adobe Flash Player](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/important-technical-notification-regarding-adobe-flash-player-eQtMLwLmTJ)
- [iPad support - Technical information](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/ipad-support-technical-information-dLmeFvKofC)
- [TeamViewer Link](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/teamviewer-link-QyKZBMqUT9)
- [YouTube videos about LearningSpace](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/youtube-videos-about-learningspace-TMb3zdc0LC)
- [Customer Aftercare One-Pager](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/customer-aftercare-one-pager-GBWMe1BcfS)
- [Case Studies](https://kb.learningspace.elevatehealth.net/s/ent-hs/doc/case-studies-VcAbFqXSz7)