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.

{ 54, 54.9, 57.1, 58.8, 58.8, 59.5, 59.9, 60.1, 60.3, 60.3, 61, 61, 61.3, 61.5, 61.5, 61.6, 61.7, 61.8, 61.8, 62.2, 62.3, 62.3, 62.4, 62.4, 62.5, 62.8, 62.8, 63.1, 63.1, 63.4, 63.5, 63.5, 63.5, 63.5, 63.6, 63.7, 64.4, 64.5, 64.6, 64.8, 64.9, 64.9, 65, 65.1, 65.3, 65.4, 65.4, 65.4, 65.7, 66.2, 66.2, 66.8, 67, 67.2, 67.6, 67.7, 68, 68.6, 70.1, 71 }.

give the mean of the data set.

give the median of the data set.

Explanation:

Step1: Define the data set

The data set of women's heights is given as: $\{ 54, 54.9, 57.1, 58.8, 58.8, 59.5, 59.9, 60.1, 60.3, 60.3, 61, 61, 61.3, 61.5, 61.5, 61.6, 61.7, 61.8, 61.8, 62.2, 62.3, 62.3, 62.4, 62.4, 62.5, 62.8, 62.8, 63.1, 63.1, 63.4, 63.5, 63.5, 63.5, 63.5, 63.6, 63.7, 64.4, 64.5, 64.6, 64.8, 64.9, 64.9, 65, 65.1, 65.3, 65.4, 65.4, 65.4, 65.7, 66.2, 66.2, 66.8, 67, 67.2, 67.6, 67.7, 68, 68.6, 70.1, 71 \}$

Step2: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 60$ and $x_{i}$ are the individual data - points. Using a calculator or software like Desmos with the command mean(A) (where $A$ is the data - set), we find that the sum of all the data points $\sum_{i=1}^{60}x_{i}=3816$ and $\bar{x}=\frac{3816}{60}=63.6$

Step3: Calculate the median

Since $n = 60$ (an even number), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th ordered data points. First, order the data set. The 30 - th and 31 - st ordered data points are $63.5$ and $63.5$. So the median $M=\frac{63.5 + 63.5}{2}=63.5$

Answer:

Mean: 63.6
Median: 63.5