Question

in this problem, you will use desmos to compute a few statistics.

• open a new browser window to the page: https://www.desmos.com/calculator.
• enter the command below, by copying and pasting the data between the brackets:

a = paste data here

• to compute the mean and median, enter the commands below:

mean(a)
median(a)

• to compute the midrange of the data set, you will need the minimum and maximum values, which are computed in desmos by entering:

min(a)
max(a)

the heights of 60 randomly selected women are recorded below.
{ 51.4, 52.3, 53.1, 53.5, 56.5, 56.6, 57.3, 58.2, 58.7, 58.8, 59.8, 60, 60.2, 60.2, 60.3, 60.6, 60.8, 60.8, 60.9, 61.6, 61.6, 61.7, 61.8, 61.9, 62.3, 62.4, 63.3, 63.4, 63.9, 64.2, 64.5, 64.5, 64.5, 64.7, 64.9, 65, 65, 65.2, 65.3, 65.6, 65.6, 65.8, 65.9, 66.1, 66.1, 66.3, 66.4, 67.1, 67.5, 67.6, 68.3, 68.4, 68.6, 69.1, 69.5, 69.8, 70, 70.8, 71.4, 72.8 }.

give the mean of the data set.

Explanation:

Step1: Define the data set

Let $A=\{51.4, 52.3, 53.1, 53.5, 56.5, 56.6, 57.3, 58.2, 58.7, 58.8, 59.8, 60, 60.2, 60.2, 60.3, 60.6, 60.8, 60.8, 60.9, 61.6, 61.6, 61.7, 61.8, 61.9, 62.3, 62.4, 63.3, 63.4, 63.9, 64.2, 64.5, 64.5, 64.5, 64.7, 64.9, 65, 65, 65.2, 65.3, 65.6, 65.6, 65.8, 65.9, 66.1, 66.1, 66.3, 66.4, 67.1, 67.5, 67.6, 68.3, 68.4, 68.6, 69.1, 69.5, 69.8, 70, 70.8, 71.4, 72.8\}$

Step2: Calculate the sum of data

The sum of the elements in $A$, denoted as $\sum_{i = 1}^{60}a_i$, is:
\[

$$\begin{align*} \sum_{i=1}^{60}a_i&=51.4 + 52.3+53.1+53.5+56.5+56.6+57.3+58.2+58.7+58.8+59.8+60+60.2+60.2+60.3+60.6+60.8+60.8+60.9+61.6+61.6+61.7+61.8+61.9+62.3+62.4+63.3+63.4+63.9+64.2+64.5+64.5+64.5+64.7+64.9+65+65+65.2+65.3+65.6+65.6+65.8+65.9+66.1+66.1+66.3+66.4+67.1+67.5+67.6+68.3+68.4+68.6+69.1+69.5+69.8+70+70.8+71.4+72.8\\ &=3816.9 \end{align*}$$

\]

Step3: Calculate the mean

The mean $\bar{x}$ of a data - set with $n$ elements is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here $n = 60$.
So, $\bar{x}=\frac{3816.9}{60}=63.615$

Answer:

$63.615$