Question

based on the two data sets represented below, complete the following sentences. data set x data set y answer attempt 1 out of 2 the mean of data set x is than the mean of data set y. the median of data set x is than the median of data set y.

Explanation:

Step1: Count data - points in each set

Data Set X has 20 data - points. Data Set Y has 20 data - points.

Step2: Estimate the mean of Data Set X

The data in Data Set X is more spread out towards the higher values (94 - 99). The sum of the values in Data Set X:
\[

$$\begin{align*} &(91\times3)+(92\times3)+(93\times1)+(94\times3)+(95\times2)+(96\times3)+(97\times4)+(98\times2)+(99\times2)\\ =&273 + 276+93 + 282+190+288+388+196+198\\ =&1994 \end{align*}$$

\]
The mean of Data Set X, $\bar{x}=\frac{1994}{20}=99.7$.

Step3: Estimate the mean of Data Set Y

The data in Data Set Y has more values concentrated towards the lower values (89 - 93). The sum of the values in Data Set Y:
\[

$$\begin{align*} &(89\times5)+(90\times2)+(91\times2)+(92\times1)+(93\times4)+(94\times2)+(95\times2)+(96\times2)+(97\times2)\\ =&445+180 + 182+92+372+184+190+192+194\\ =&1931 \end{align*}$$

\]
The mean of Data Set Y, $\bar{y}=\frac{1931}{20}=96.55$.

Step4: Find the median of Data Set X

Arrange the 20 data - points in ascending order. Since $n = 20$ (even), the median is the average of the 10th and 11th ordered data - points. The 10th and 11th values are 96, so the median of Data Set X is 96.

Step5: Find the median of Data Set Y

Arrange the 20 data - points in ascending order. Since $n = 20$ (even), the median is the average of the 10th and 11th ordered data - points. The 10th and 11th values are 93, so the median of Data Set Y is 93.

Answer:

The mean of Data Set X is greater than the mean of Data Set Y. The median of Data Set X is greater than the median of Data Set Y.