what is the upper quartile?

Question

The statistics education marks (given as percentage) of 50 students in the math module were: 35;53;44;79;76;58;65;54;53;39;54;44;52;47;95;77;51;45;69;72;36;82;33;50;87;52;69;70;47;52;80;90;64;69;45;38;52;67;78;92;56;55;77;45;78;45;66;72;87;60.

Answer 1

To find the quartile the dataset must be arranged in order, least to greatest.

Then we divide the data into two lots of 25, and we can then define the median which in this case lies midway between X₂₅ and X₂₆, that is, between 56 and 58, so the median, also known as quartile 2 (Q2), is 57.

Next we find the middle datum of the two lots of data, so that gives us Q1 (lower quartile)=X₁₃=47 and Q3= (upper quartile)=X₃₈=76.

The quartiles are markers dividing the whole dataset into quarters.