Question

Find the median and mode of the data: $35,32,35,42,38,32,34$

Answer 1

Given data is $35,32,35,42,38,32,34$

Arranging the data in ascending order such that same numbers are put together, we get:

$32,32,34,35,35,38,42$.

Here, number of observations $\left(n\right)=7$ is odd number.

If number of observations of the data is odd then it's median is $(\frac{n+1}{2}{)}^{\text{th}}$ term.

$\Rightarrow$ Median $=(\frac{7+1}{2}{)}^{\text{th}}$ observation.

$\Rightarrow$ Median $=4^{\text{th}}$ observation.

$\Rightarrow$ Median $=35$ ---(1)

Mode: Most number of times recurring observation.

In $35,32,35,42,38,32,34$

$32$ and $35$, both occur twice.

Therefore, $32$ and $35$ are the two modes. --(2)