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, 54.7, 55.3, 55.6, 55.9, 56.4, 56.7, 57.5, 57.6, 57.8, 59.4, 59.8, 59.9, 60, 60.3, 61, 61, 61, 61, 61.2, 61.8, 62, 62.3, 62.5, 62.6, 62.7, 63, 63.4, 63.5, 63.6, 63.7, 63.7, 63.8, 63.8, 64.3, 64.4, 64.5, 64.6, 64.8, 65, 65, 65, 65.1, 65.1, 65.3, 65.4, 65.4, 66.1, 66.6, 66.6, 66.6, 67.3, 67.4, 68.4, 68.5, 69.1, 70.7, 71, 71.4, 72.2 }.

give the mean of the data set.

62.385

part 2 of 4

give the median of the data set.

Explanation:

Step1: Define the data set

Let \(A=\{54, 54.7, 55.3, 55.6, 55.9, 56.4, 56.7, 57.5, 57.6, 57.8, 59.4, 59.8, 59.9, 60, 60.3, 61, 61, 61, 61, 61.2, 61.8, 62, 62.3, 62.5, 62.6, 62.7, 63, 63.4, 63.5, 63.6, 63.7, 63.7, 63.8, 63.8, 64.3, 64.4, 64.5, 64.6, 64.8, 65, 65, 65, 65.1, 65.1, 65.3, 65.4, 65.4, 66.1, 66.6, 66.6, 66.6, 67.3, 67.4, 68.4, 68.5, 69.1, 70.7, 71, 71.4, 72.2\}\)

Step2: Calculate the number of data - points

The number of data - points \(n = 60\)

Step3: Calculate the sum of the data - points

\(\sum_{i = 1}^{60}x_{i}=54 + 54.7+55.3+\cdots+72.2=3743.1\)

Step4: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{3743.1}{60}=62.385\)

Step5: Arrange the data in ascending order (already given in ascending - like order)

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.
\(\frac{n}{2}=30\) and \(\frac{n}{2}+1 = 31\)
The 30th value is \(63.7\) and the 31st value is \(63.8\)
The median \(M=\frac{63.7 + 63.8}{2}=63.75\)

Answer:

Mean: \(62.385\)
Median: \(63.75\)