Question

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.

$$\begin{gathered} \mu =1000FTES \\ median=1014FTES \\ \sigma =474FTES \\ firstquartile=528.5FTES \\ thirdquartile=1447.5FTES \\ n=29years \end{gathered}$$

A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer.

Short answer

Because the median value is the middle value in the ordered set of data values, six years are projected to have an FTES of $1014$or higher. The number in the sequence will be the median value of a set of 11. As a result, six years' totals will be $1014$or above.

Step-by-step solution

Introduction

How many are expected to have a FTES of $1014$or above.

Explanation

A median is a number that splits the data into two equal halves and is one of the measures of central tendency in statistics. The data in the $50$per cent range is below the median value while the data in the $50$per cent range is above the median value. We must sort the data in ascending order of magnitude to obtain the median. The median can then be calculated using the formula below:

Median $={\left(\frac{N+1}{2}\right)}^{\text{th}}$item

N= Number of observations

We have the following data,

$7,8,9,10,11,12,13,14,15$

$\begin{array}{r}\text{Median}={\left(\frac{9+1}{2}\right)}^{\text{th}}\text{item}\\ =5^{\text{th}}\text{item}\\ =11\end{array}$

Since the data is in ascending order, we can apply the formula.

The median value in the given problem is the median value in the ordered set of data values. The localid="1648921560885" $6^{th}$number in the sequence will be the median value of a set of $11$. As a result, six years' totals will be $1014$or above.