Explaining why arrays are important for statisticians I am a computer engineer, and I’m teaching computer sciences one hour per week to a student who failed her second-year university degree. She needed some help to have a better understanding of programming, and increase her grade in this field. Computer science is not the main subject of her degree which is based on maths and physics.

I asked her if she wanted to emphasise on a difficult subject for her, or if I should start from scratch and explain programming as if it was totally new for her. She chose the second solution, so I started to explain her the base of programming, binary, variables, functions, conditional statements, loops. And now I emphasis on the most common data structure ever, the array.

I teach her how to use an array, manipulate its element, etc...
As she had to use programming to solve problems of graph theory, physics measurements, and mathematical algorithms which use a lot of matrices and arrays, I spend about six hours to make her be more familiar with it. 

I simplified it to make her use one-dimensional arrays with a simple algorithm, and she just told me that she can’t understand how arrays will be of any use for her, for her everyday life. She aims to get job in the field of statistics.

I explained to her, that she uses array everyday without thinking about it. For example when you log in a website, there’s somewhere an array (or an object) which stores your username, password, email, and compares it to what is stored in a database. But she didn’t feel very enthusiastic.

So  I can understand that not everybody enjoys programming, and as I am not a statistician I can’t really tell her about how useful this can be for a statistician.

What can I do to actually make her change her mind about programming or show her the use of it for a statistician ?

EDIT:
I work as Web developper so I am not used to statistics. I can't think about useful example or exercise to show her the usage of arrays in statistics.

EDIT:
She already saw by herself that was I taugh her about arrays is usefull in various situation. She saw that know, as she understood arrays, she can now solve problems she wasn't able to solve before.
If you are tutoring her, it is wonderful that you are trying to motivate the material in a practical way, but don't beat yourself up too much if you aren't that successful at persuading her. Some people just get themselves into a sort of myopic headspace where the only things that they need to learn are the exact operations that they will perform later on in their life.

However, it has been my experience that there is often something else going on in these situations. People aren't creating these excuses because of what will be practical in the future. They have no idea what the future holds. They actually create these utilitarian excuses simply because they don't find the topic intrinsically fun yet.

This also explains why you make no headway when you show her the utilitarian benefits; they aren't truly what is preventing her from diving in. Your best bet, then, is to show her why you think this whole field is amazing.

And if all else fails, go back to a utilitarian approach, but stick to the most direct reason: she needs this so that she will pass her class next semester.  That was a strong enough motivation for her to meet with you in the first place, so it should work out well enough to at least get you through the lessons.

Good luck!