Q. 18 - Elementary Statistics

Question

Fossil Argonauts. In the article "Fossil Argonauts (Mollusca: Cephalopoda: Octopodida) from Late Miocene Slitstones of the Los Angeles Basin, California"  paleontologists L. Saul and C. Stadium discussed fossilized Argonaut cgg cases from the late Miocene period found in California. A sample of $10$ fossilized egg cases yielded the following data on height, in millimeters. Obtain the mean. median. and mode(s) of these data.

Step-by-Step Solution

Answer

The mean, mode and median of given sample are $30.53, 33, 32.5$ respectively

Step 1: Given information

We are given sample of fossilized egg we have to find mean,median , mode of these data.

Step 2: Simplify

Given data is $37.5, 31.5, 27.4, 21.0, 32.0, 33.0, 33.0, 38.0, 17.4, 34.5$

Mean $\overline{x}=\frac{\underset{i=10}{\sum x_i}}{n}$

where, $n=$Total number of data in Sample

$$\begin{gathered} \overline{x}=\frac{37.5+31.5+27.4+21+32+33+33+38+17.4+34.5}{10} \\ \overline{x}=30.53 \end{gathered}$$

Mode - Highest occuring data in sample.

Mode $=33.0$

Median is middle data when arranged in ascending order.

Given data in ascending order will be 

$17.4, 21, 27.4, 31.5, 32, 33, 33, 34.5, 37.5, 38$

Here, we can see $32$ and $33$ are middle value. So we have to take average value.

Median $=\frac{32+33}{2}=32.5$