Question

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.

$87;87;87;87;87;88;89;89;90;91$

Short answer

The data is skewed to the right.

Step-by-step solution

Given information

The data given is:

$87;87;87;87;87;88;89;89;90;91$

Explanation

The mean can be calculated as:

$\text{Mean}=\frac{87+87+87+87+87+88+89+89+90+91}{10}=\frac{882}{10}=88.2$

The median is calculated as:

First, we need to sort the data in ascending order as:

$$\begin{gathered} 87,87,87,87,87,88,89,89,90,91 \\ \therefore \text{Median}={\left(\frac{10+1}{2}\right)}^{\text{th}}item \\ ={\left(5.5\right)}^{th}item \\ =87+0.5\left(88-87\right) \\ =87.5 \end{gathered}$$

The mode is the most frequently occurring observation and in the given data, we clearly see $87$occur four times.

$Mode=87$