Page 131 - Data Science class 10
P. 131
2. Remove one snap cube from the highest stack and place it on one of the lowest stacks, continuing until
all the stacks are leveled out.
Both these approaches yield an equal family size of three, which we can consider as an equal share or a fair
share.
For the second approach, you can start with removing a snap cube from the highest stack and placing it on
one of the lowest stacks. This will result in a new arrangement of cubes as shown in the figure given below.
Moving one snap cube from the highest stack
We will continue this process until all the stacks are level, or nearly level when there is a remainder as shown
in the figure given below.
Snap cubes representing an average family size
After the final move, all five stacks are levelled with three cubes each. This represents that the family size
of three is an equal share. That means, if all five family sizes were the same, the number of people in the
household would have been three. This equal share is nothing but the mean of the distribution.
By now, we know how to calculate the mean by adding up all the observations and dividing it by the
number of observations. However, we still need to find answers to the questions given ahead. What does
mean tell us about the distribution? How are we expected to interpret the mean? How are we expected to
describe the variability in a distribution in relation to its mean?
We can investigate the following problem to get an
answer to these questions: Group 1
Suppose two other groups of five students in the
classroom found their equal share value to be six. What
are some different snap cube representations that they
could have constructed?
To answer this, we should first realise that we need to
start with 30 snap cubes. We can then create two different
distributions of family size where the equal share value is 6.
For example, consider the following two groups, Group 1
and Group 2 (shown in the two figures given below) of data
on five family sizes from the classroom where the equal
share family size for each group is 6.
Group 1 arrangement with average 6
Use of Statistics in Data Science 129

