Question

the numbers of words defined on randomly selected pages from a dictionary are shown below. find the mean, median, and mode of the 36 76 38 31 51 73 77 78 74 48
what is the mean? select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the mean is (round to one decimal place as needed.)
b. there is no mean.

Explanation:

Step1: Calculate sum of data

$36 + 76+38 + 31+51+73+77+78+74+48=582$

Step2: Calculate the mean

The number of data points $n = 10$. Mean $\bar{x}=\frac{\text{Sum of data}}{n}=\frac{582}{10}=58.2$

Step3: Arrange data in ascending order

$31,36,38,48,51,73,74,76,77,78$

Step4: Calculate the median

Since $n = 10$ (even), median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+ 1)$-th ordered - data values. $\frac{n}{2}=5$, $\frac{n}{2}+1 = 6$. Median $=\frac{51 + 73}{2}=\frac{124}{2}=62$

Step5: Find the mode

No number repeats in the data - set, so there is no mode.

Answer:

A. The mean is $58.2$
Median: $62$
Mode: There is no mode.