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 standard deviation, enter the commands below: mean(a) stdev(a)

the i.q. scores of 100 randomly selected women are recorded below.
{ 69, 74, 77, 78, 78, 81, 81, 83, 84, 85, 86, 86, 86, 86, 87, 87, 88, 88, 89, 90, 92, 92, 92, 92, 92, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 97, 98, 98, 98, 99, 99, 100, 100, 100, 100, 101, 101, 101, 101, 101, 102, 102, 102, 103, 103, 104, 104, 104, 104, 105, 105, 105, 106, 106, 106, 107, 107, 108, 108, 108, 108, 109, 110, 110, 111, 111, 111, 112, 112, 113, 113, 114, 114, 114, 114, 114, 115, 117, 118, 119, 119, 119, 119, 120, 127, 128, 133, 133 }.
the values are summarized by the histogram below. while the values are sampled from a normal population, once in a while the distribution will be skewed due to randomness.
the computations below should be rounded to one place more after the decimal than the data values above.
give the sample mean of the data set.

Explanation:

Step1: Recall the formula for sample mean

The sample mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n$ is the number of data - points and $x_{i}$ are the individual data - points. Here $n = 100$.

Step2: Calculate the sum of the data

$\sum_{i=1}^{100}x_{i}=69 + 74+77+\cdots+133$.
$69+74 + 77+78+78+81+81+83+84+85+86+86+86+86+87+87+88+88+89+90+92+92+92+92+92+92+92+93+93+94+94+95+95+96+96+97+97+97+98+98+98+99+99+100+100+100+100+101+101+101+101+101+102+102+102+103+103+104+104+104+104+105+105+105+106+106+106+107+107+108+108+108+108+109+110+110+111+111+111+112+112+113+113+114+114+114+114+114+115+117+118+119+119+119+119+120+127+128+133+133=10190$.

Step3: Compute the sample mean

$\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{10190}{100}=101.9$.

Answer:

$101.9$