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 \boxed{} (round to one decimal place as needed.) b. there is no mean

Explanation:

Step1: Sum the numbers

First, we add up all the given numbers: \(30 + 31 + 34 + 65 + 40 + 53 + 37 + 45 + 71 + 33\). Let's calculate that: \(30+31 = 61\), \(61+34 = 95\), \(95+65 = 160\), \(160+40 = 200\), \(200+53 = 253\), \(253+37 = 290\), \(290+45 = 335\), \(335+71 = 406\), \(406+33 = 439\). Wait, wait, no, let's count the numbers again. Wait, the numbers are 30, 31, 34, 65, 40, 53, 37, 45, 71, 33. Wait, that's 10 numbers? Wait, 30,31,34,65,40,53,37,45,71,33. Let's add them again: 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? Wait, no, 30+31=61, +34=95, +65=160, +40=200, +53=253, +37=290, +45=335, +71=406, +33=439? Wait, but 30+31+34+65+40+53+37+45+71+33. Let's list them: 30,31,33,34,37,40,45,53,65,71. Wait, maybe I missed a number? Wait, the original list: 30, 31, 34, 65, 40, 53, 37, 45, 71, 33. Yes, 10 numbers. So sum is 30+31=61, +34=95, +65=160, +40=200, +53=253, +37=290, +45=335, +71=406, +33=439? Wait, no, 30+31=61, +34=95, +65=160, +40=200, +53=253, +37=290, +45=335, +71=406, +33=439. Wait, but 30+31+33+34+37+40+45+53+65+71. Let's add in order: 30+31=61; +33=94; +34=128; +37=165; +40=205; +45=250; +53=303; +65=368; +71=439. Yes, sum is 439.

Step2: Calculate the mean

The mean is the sum divided by the number of values (n). Here, n=10. So mean = \( \frac{439}{10} = 43.9 \)? Wait, wait, no, wait, 30+31=61, +34=95, +65=160, +40=200, +53=253, +37=290, +45=335, +71=406, +33=439. Wait, 439 divided by 10 is 43.9? Wait, but let's check again. Wait, 30+31=61, +34=95, +65=160, +40=200, +53=253, +37=290, +45=335, +71=406, +33=439. Yes, sum is 439. Number of values is 10. So mean is \( \frac{439}{10} = 43.9 \).

Answer:

A. The mean is \( \boldsymbol{43.9} \) (Round to one decimal place as needed)