Homework #1-8: Determine the mean, median, mode, and midrange for the given data.
1) 2, 3, 5, 5, 20
Mean =
2+3+5+5+20
5
=7
Median: the numbers are ordered start by removing the first and last number
355
Repeat and remove the first and the last number. The median is left.
Median 5
Mode equals 5 as it occurs most.
Midrange =
2+20
2
= 11
3) 11,13,15,12,18,5,1,13
Mean =
11+13+15+12+18+5+1+13
8
= 11
Median: order the numbers
1 5 11 12 13 13 15 18
Remove the first and last number
5 11 12 13 13 15
Repeat
11 12 13 13
Repeat
12 13
I need to average these to find the median.
Median =
12+13
2
= 12.5
Mode equals 13 as it occurs most.
Midrange =
1+19
2
= 9.5
5) 1,1,1,5,5,5
Mean =
1+ 1+1+5+5+5
6
=3
Median:
Numbers are already in order.
Remove the first and last number
1 1 5 5
Repeat
1 5
I need to average these to find the median.
Median =
1+5
2
=3
Mode is both 1 and 3. We say this is bi-modal
Midrange =
1+5
=3
2
7) 1,2,3,4,9,8,7
Mean =
1+2+3+4+9+8+7
7
Median:
Order the numbers.
1234789
Remove first and last
23478
Repeat
347
Repeat
4
Median = 4
Mode – no mode
Midrange =
1+9
2
=5
= 4.86
9) Greg’s mean average on five exams is 81. Find the sum of his scores.
Answer: 5*81 = 405
11) Jan’s mean average on four exams is 90. Find the sum of her scores.
Answer: 90*4 = 360
13) Lemont plays high school basketball. After 20 games Lemont averaged 18.5 points per
game. How many total points did Lemont score?
Answer: 20*18.5 = 370
15) A new sub shop sells 70 sandwiches each day on average. How many sandwiches do they
sell in a week?
Answer: 70*7 = 490
17) A mean average of 80 or greater for five exams is needed for a final grade of B in a course.
Thurston’s first four exam grades were 73,69,85 and 80.
a) What grade does Thurston need on the fifth exam to get a B for the course?
Total needed for a B: 80*5 = 400
Total so far 73+69+85+80 = 307
Answer: 400 – 307 = 93
b) An average of 70 is needed to pass the course. What grade does Thurston need to pass the
course?
Total needed to pass: 70*5 = 350
Total so far 73+69+85+80 = 307
Answer: 350 – 307 = 43
c) If her lowest grade of the exams already taken is to be dropped, what grade must he receive
on his last exam to pass the class?
Total needed to pass: 70*4 = 280 (only keeping 4 scores)
Total so far 73+85+80 = 238 (dropped the 69)
Answer: 280 – 238 = 42
19) A mean average of 80 or greater for five exams is needed for a final grade of B in a course.
Thurston’s first four exam grades were 73,69,85 and 80. The first four tests were worth 100
points, the fifth exam is worth 200 points.
a) What grade does Thurston need on the fifth exam to get a B for the course?
There will be 600 points possible. (100 + 100 + 100 +100 + 200)
Total needed for a B: 600*.8 = 480
Total so far: 73 + 69 + 85 + 80 = 307
Answer: 480 – 307 = 173
b) An average of 70 is needed to pass the course. What grade does Thurston need to pass the
course?
There will be 600 points possible. (100 + 100 + 100 +100 + 200)
Total needed for a B: 600*.7 = 420
Total so far: 73 + 69 + 85 + 80 = 307
Answer: 420 – 307 = 113