Question

Use the following information to answer the next twelve$12$exercises. The graph shown is based on more than $170,000$interviews done by Gallup that took place from January through December $2012$. The sample consists of employed Americans $18$years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

Compute the average EHIS.

Short answer

The average of Emotional health index scores is$81.3$.

Step-by-step solution

Definition for Average

An average may be a single number that represents a set of numbers, often the sum of the quantity's divided by the number of numbers within the collection (the arithmetic mean).

$\overline{\mathrm{x}}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}}$

localid="1649372305444" $\mathrm{n}$is number of events.

Calculation for Average

There are$14$events in total.

We'll work out the common EHIS by putting all of the scores together and dividing the overall by$14$.

$\overline{\mathrm{EHIS}}=\frac{1}{14}\sum _{\mathrm{i}=1}^{14}{\mathrm{EHIS}}_{\mathrm{i}}$

$=\frac{\left(\begin{array}{l}79.6+80+80.1+80.2+80.3\\ +80.7+80.9+81.5+81.7\\ +81.8+82.3+82.7+82.7+83.7\end{array}\right)}{14}$

$\overline{\mathrm{EHIS}}=\frac{1}{14}\left[1138.2\right]$

localid="1649366495851" $=\frac{1138.2}{14}$

$=81.3$