Question

On a baseball team, the ages of each of the players are as follows:

$21;21;22;23;24;24;25;25;28;29;29;31;32;33;33;34;35;36;36;36;36;38;38;38;40$

Use your calculator or computer to find the mean and standard deviation. Then find the value that is two standard deviations above the mean.

Short answer

$\text{Sample mean}=30.68,\text{Sample standard deviation}=6.09,(\overline{x}+2\times s)=42.86$

Step-by-step solution

Introduction

The mean is one of the measurements of central tendency in statistics. It's calculated by dividing the total number of observations by the number of observations.

One of the metrics of dispersion is the standard deviation. It's a metric for how far data values deviate from the mean.

Explanation

1. Clear list L1: Press STAT and then scroll down to $4:$ClrList. Enter $2$nd $1$for L$1$

2. Enter data into the list editor: Press STAT and then scroll down to $1$: EDIT and Enter.

Put the data values into list L$1$

$(21,21,22,23,24,24,25,25,28,29,29,31,32,33,33,34,35,36,36,36,36,38,38,38,40)$

3. Press STAT and scroll right to CALC. Press $1:1$-VarStats and Press Enter.

4. The output will contain various statistics, but we just need to check the $\overline{x}=30.68$(mean) and $Sx=6.09$(standard deviation)

Now to find the two standard deviations above the mean, we need to use the below formula:

$\overline{x}+2\times s=30.68+2\times 6.09=30.68+12.18=42.86$