Get an image from a random entry
I think something like this should work

{# First get all the stats #}
{% set stats = craft.entries.section('statistics') %}

{# iterate over those stat in a random order %}
{% for stat in stats.order('RAND()') %}

    {% if stat.image | length %}

        {% set image = stat.image.first %}

    {% else %}

        {# If there's no image, query for a random stat, excluding those without images #}
        {% set randomStat = stats.image(':notempty:').limit(1).order('RAND()') %}
        {% set image = randomStat.first.image.first %}

    {% endif %}

{% endfor %}