Question

a student of statistics and fan of baseball is looking over the player stats for a list she is compiling of \top ten players nobody remembers.\ the data for the batting averages of these 10 players are reproduced in the table below. calculate the mean, median, and mode using a ti-83, ti-83 plus, or ti-84 graphing calculator (round your answers to three decimal places).
baseball player batting
averages
0.272
0.272
0.212
0.293
0.322
0.262
0.285
0.250
0.243
0.277
provide your answer below:
mean = \\(\square\\), median = \\(\square\\), mode = \\(\square\\)

Explanation:

Step1: Enter data into calculator

First, we need to enter the data values (0.272, 0.272, 0.212, 0.293, 0.322, 0.262, 0.285, 0.250, 0.243, 0.277) into the list editor of the TI - 83/84 calculator.

Step2: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 10$ and $x_{i}$ are the data points.
Using the calculator's 1 - Var Stats function, we sum up all the values:
$0.272+0.272 + 0.212+0.293+0.322+0.262+0.285+0.250+0.243+0.277$
$=(0.272\times2)+0.212 + 0.293+0.322+0.262+0.285+0.250+0.243+0.277$
$=0.544+0.212+0.293 + 0.322+0.262+0.285+0.250+0.243+0.277$
$=0.544 + 0.212=0.756;0.756+0.293 = 1.049;1.049+0.322=1.371;1.371+0.262 = 1.633;1.633+0.285=1.918;1.918+0.250 = 2.168;2.168+0.243=2.411;2.411+0.277 = 2.688$
Then the mean $\bar{x}=\frac{2.688}{10}=0.2688\approx0.269$ (rounded to three decimal places)

Step3: Calculate the median

First, we sort the data in ascending order: 0.212, 0.243, 0.250, 0.262, 0.272, 0.272, 0.277, 0.285, 0.293, 0.322
Since $n = 10$ (even), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th values.
$\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5 - th value is 0.272 and the 6 - th value is 0.272.
Median $=\frac{0.272 + 0.272}{2}=\frac{0.544}{2}=0.272$

Step4: Calculate the mode

The mode is the value that appears most frequently. In the data set, 0.272 appears twice and all other values appear once. So the mode is 0.272.

Answer:

Mean $=\boldsymbol{0.269}$, Median $=\boldsymbol{0.272}$, Mode $=\boldsymbol{0.272}$