Question

the numbers of words defined on randomly selected pages from a dictionary are shown below. find the mean, median, and mode of the listed numbers. 44 59 73 49 37 50 30 39 63 62 55
what is the mean? select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the mean is 50.6 (round to one decimal place as needed.)
b. there is no mean.
what is the median? select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the median is (round to one decimal place as needed.)
b. there is no median.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 10$, and the data set is $\{44,59,73,49,37,50,30,39,63,62\}$. So, $\sum_{i=1}^{10}x_{i}=44 + 59+73+49+37+50+30+39+63+62 = 506$. Then $\bar{x}=\frac{506}{10}=50.6$.

Step2: Calculate the median

First, arrange the data in ascending order: $\{30,37,39,44,49,50,59,62,63,73\}$. Since $n = 10$ (an even number), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. So, $x_{5}=49$ and $x_{6}=50$, and $M=\frac{49 + 50}{2}=49.5$.

Step3: Calculate the mode

The mode is the number that appears most frequently in the data - set. In the data set $\{44,59,73,49,37,50,30,39,63,62\}$, each number appears only once, so there is no mode.

Answer:

What is the mean? A. The mean is $50.6$
What is the median? A. The median is $49.5$
What is the mode? There is no mode.