Answer :
Let's solve the problem step by step.
We have the following scores: [tex]\(68, 62, 60, 64, 70, 66,\)[/tex] and [tex]\(72\)[/tex].
### Step 1: Calculate the Mean
The mean is found by adding all the scores together and dividing by the number of scores.
[tex]\[
\text{Mean} = \frac{68 + 62 + 60 + 64 + 70 + 66 + 72}{7}
\][/tex]
First, sum the scores:
[tex]\[
68 + 62 + 60 + 64 + 70 + 66 + 72 = 462
\][/tex]
Now, divide by the number of scores (which is 7):
[tex]\[
\text{Mean} = \frac{462}{7} = 66
\][/tex]
### Step 2: Calculate the Median
The median is the middle number when all the scores are arranged in ascending order.
First, sort the scores:
[tex]\[
60, 62, 64, 66, 68, 70, 72
\][/tex]
Since there are 7 scores, the median is the 4th number in the ordered list:
[tex]\[
\text{Median} = 66
\][/tex]
### Step 3: Calculate the Midrange
The midrange is found by averaging the smallest and largest scores.
The smallest score is 60 and the largest score is 72.
[tex]\[
\text{Midrange} = \frac{60 + 72}{2} = \frac{132}{2} = 66
\][/tex]
Now, let's check each answer choice:
a. Mean [tex]\( = 64\)[/tex], median [tex]\( = 64\)[/tex], midrange [tex]\( = 64\)[/tex]
b. Mean [tex]\( = 65\)[/tex], median [tex]\( = 64\)[/tex], midrange [tex]\( = 66\)[/tex]
c. Mean [tex]\( = 66\)[/tex], median [tex]\( = 77\)[/tex], midrange [tex]\( = 65\)[/tex]
d. Mean [tex]\( = 66\)[/tex], median [tex]\( = 66\)[/tex], midrange [tex]\( = 66\)[/tex]
Based on our calculated values, the correct combination is:
[tex]\[
\text{Mean} = 66, \text{Median} = 66, \text{Midrange} = 66
\][/tex]
So, the correct answer is:
d. Mean [tex]\( = 66\)[/tex], median [tex]\( = 66\)[/tex], midrange [tex]\( = 66\)[/tex]
Answer choice D is correct.
We have the following scores: [tex]\(68, 62, 60, 64, 70, 66,\)[/tex] and [tex]\(72\)[/tex].
### Step 1: Calculate the Mean
The mean is found by adding all the scores together and dividing by the number of scores.
[tex]\[
\text{Mean} = \frac{68 + 62 + 60 + 64 + 70 + 66 + 72}{7}
\][/tex]
First, sum the scores:
[tex]\[
68 + 62 + 60 + 64 + 70 + 66 + 72 = 462
\][/tex]
Now, divide by the number of scores (which is 7):
[tex]\[
\text{Mean} = \frac{462}{7} = 66
\][/tex]
### Step 2: Calculate the Median
The median is the middle number when all the scores are arranged in ascending order.
First, sort the scores:
[tex]\[
60, 62, 64, 66, 68, 70, 72
\][/tex]
Since there are 7 scores, the median is the 4th number in the ordered list:
[tex]\[
\text{Median} = 66
\][/tex]
### Step 3: Calculate the Midrange
The midrange is found by averaging the smallest and largest scores.
The smallest score is 60 and the largest score is 72.
[tex]\[
\text{Midrange} = \frac{60 + 72}{2} = \frac{132}{2} = 66
\][/tex]
Now, let's check each answer choice:
a. Mean [tex]\( = 64\)[/tex], median [tex]\( = 64\)[/tex], midrange [tex]\( = 64\)[/tex]
b. Mean [tex]\( = 65\)[/tex], median [tex]\( = 64\)[/tex], midrange [tex]\( = 66\)[/tex]
c. Mean [tex]\( = 66\)[/tex], median [tex]\( = 77\)[/tex], midrange [tex]\( = 65\)[/tex]
d. Mean [tex]\( = 66\)[/tex], median [tex]\( = 66\)[/tex], midrange [tex]\( = 66\)[/tex]
Based on our calculated values, the correct combination is:
[tex]\[
\text{Mean} = 66, \text{Median} = 66, \text{Midrange} = 66
\][/tex]
So, the correct answer is:
d. Mean [tex]\( = 66\)[/tex], median [tex]\( = 66\)[/tex], midrange [tex]\( = 66\)[/tex]
Answer choice D is correct.
