Interpeting data figures - its rather simple but not soo simple

[SavvyAA3]

Can Someone please tell me how I can interpret the skewness of a distribution using quartiles.

I know that if Q2 – Q1 > Q3 – Q2 : Negative skew and if Q3 – Q2 > Q2 – Q1: Positive Skew and if Q2 –Q1 = Q3 – Q1: Symmetrical data dispersion

What I really need to know is how to use the above to interpret data sets and be able to apply it to all situations. I’ve never really been able to say more than the above in GCSE and A-level and this got me an A in math at both stages but at Uni I really need to interpret this stuff.

Can I say that if the data is negatively skewed then the data values tend to be generally very small? What confuses me is that we will always have 25% of the data lying below Q1 and 50% of the data lying either side of the median and 75% below Q3. But how can we use this to give analysis??

Thanks.

 

[EnumaElish]

What confuses me is that we will always have 25% of the data lying below Q1 and 50% of the data lying either side of the median and 75% below Q3. But how can we use this to give analysis??

That is correct; but the data values of Q1 and Q3 will differ from one sample to the other.

 

[tacman]

Interpreting skewness in a distribution using quartiles is a useful tool in understanding the shape of the data. Skewness refers to the asymmetry of the distribution, where a positive skew indicates a longer tail on the right side of the distribution and a negative skew indicates a longer tail on the left side of the distribution. Quartiles, specifically Q1, Q2, and Q3, represent the 25th, 50th, and 75th percentiles of the data, respectively.

To interpret skewness using quartiles, you can compare the differences between Q2 and Q1, and Q3 and Q2. If Q2-Q1 is greater than Q3-Q2, then the distribution is negatively skewed. This means that there are more values on the left side of the distribution, causing the tail to be longer on the left. On the other hand, if Q3-Q2 is greater than Q2-Q1, then the distribution is positively skewed. This indicates that there are more values on the right side of the distribution, causing the tail to be longer on the right.

You can also use the quartiles to analyze the data further. For example, if the data is negatively skewed, you can say that the majority of the data values are smaller than the median (Q2) and the mean. This is because the tail on the left side of the distribution is longer, indicating that there are more values on the smaller end of the data.

It is important to note that quartiles alone may not provide a complete understanding of the data. It is always recommended to also consider other measures of central tendency, such as the mean, and measures of spread, such as standard deviation, to get a more comprehensive understanding of the data.

In summary, interpreting skewness using quartiles is a helpful way to understand the shape of the data and the distribution of values. However, it should be used in conjunction with other measures to fully interpret and analyze the data.