# Stanine scores

-

Stanine scores are standardized scores that express the data in single-digit values which gives us an idea about the distribution of our data. If a point is higher compared to the mean then it is given a stanine score from 6 to 9 and if the data point is lesser compared to the mean it is given a stanine score from 1 to 4.

In all the stanine score takes nine values from one to nine. Here 1 is the lowest score and 9 is the highest stanine score. For example, suppose we are given data about the IQ of students in a class in terms of stanine scores. If a student has a stanine score of 7 it means that the student has above average IQ compared to the rest of the students in the class. A stanine score of 9 would mean that the student has the highest IQ among all the students in the class.

Procedure to find stanine scores/convert data in stanine scores:

1. Find the mean µ of the data.
2. Calculate the standard deviation σ for the given data.
3. Covert the data into Z scores using the formula, Z=(X-µ)/σ
4. Replace the Z score value by the corresponding stanine score by using the below table.

Example: We are given the heights of 1000 people living in a particular town. The average height of the people is 168cm with a standard deviation of 3cm. If John has a height of 163cm, express it in the form of a stanine score.

Solution:

Step 1: We note down the mean and standard deviation given as,

µ = 168cm and σ = 3cm

Step 2: Given X = 163cm we convert it to Z score using the formula,

Z=(X-µ)/σ

Z = (163-168)/3 = -1.67

Step 3: Convert the Z score to the stanine scale by looking at the above table.

Hence, Stanine score = 2 which means that John has a much smaller height compared to the average.

Hey 👋

I'm currently pursuing a Ph.D. in Maths. Prior to this, I completed my master's in Maths & bachelors in Statistics.

I created this website for explaining maths and statistics concepts in the simplest possible manner.

If you've found value from reading my content, feel free to support me in even the smallest way you can.