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
30 31 34 65 40 53 37 45 71 33
what is the mean? select the correct choice below and, if necessary, fill in the answer box within your choice
a. the mean is 43.9 (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 38.5 (round to one decimal place as needed.)
b. there is no median
what is(are) the mode(s)? select the correct choice below and, if necessary, fill in the answer box within your choice
a. the mode(s) is(are) (round to one decimal place as needed. use a comma to separate answers as needed.)
b. there is no mode

Explanation:

Step1: Find the Mean

To find the mean, we sum all the numbers and divide by the count of numbers. The numbers are 30, 31, 34, 65, 40, 53, 37, 45, 71, 33.
Sum = \( 30 + 31 + 34 + 65 + 40 + 53 + 37 + 45 + 71 + 33 \)
\( = 30 + 31 = 61; 61 + 34 = 95; 95 + 65 = 160; 160 + 40 = 200; 200 + 53 = 253; 253 + 37 = 290; 290 + 45 = 335; 335 + 71 = 406; 406 + 33 = 439 \)
Count = 10.
Mean = \( \frac{439}{10} = 43.9 \) (matches option A).

Step2: Find the Median

First, sort the numbers: 30, 31, 33, 34, 37, 40, 45, 53, 65, 71.
There are 10 numbers (even count), so median is the average of the 5th and 6th terms.
5th term = 37, 6th term = 40.
Median = \( \frac{37 + 40}{2} = \frac{77}{2} = 38.5 \) (matches option A).

Step3: Find the Mode

The mode is the number that appears most frequently. Looking at the sorted list: 30, 31, 33, 34, 37, 40, 45, 53, 65, 71. Each number appears exactly once. So there is no mode (option B is correct).

Answer:

• Mean: A. The mean is 43.9 (Round to one decimal place as needed.)
• Median: A. The median is 38.5 (Round to one decimal place as needed.)
• Mode: B. There is no mode