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.

Short answer

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

Step-by-step solution

Given information

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

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