Median
Thomas hiked 12 miles on Monday, 10 miles on Tuesday, and 8 miles on Wednesday. Which value is closest to the median number of miles he hiked over the 3-day period?
a) 4 miles
b) 6 miles
c) 10 miles
d) 12 miles
10 miles is the middle value, so it is the median.
c) 10 miles
What is the mean of the data if there are 2-21s, 4- 22s, 6-23s, and 2-24s? (Round to the nearest tenth.)
a) 22
b) 23
c) 22.5
d) 22.6
If you add all the numbers together, you get 316. 340/13 is about 22.6.
d) 22.6
How would you know if a particular interval had a certain number of items in it?
example answer: You would need to look at how high on the y-axis the particular interval went. (Lining up the top of the interval column horizontally with the y-axis will give you the best results.)
Use the information to answer the question.
Homework Hours: Number of Students:
0-3 9
4-7 18
8-11 6
12-15 3
How long do the smallest number of students spend on homework per week?
The smallest number of students is 3. 3 students take between 12 and 15 hours to complete their homework per week.
What is the median of the data set?
8, 10, 6, 4, 12, 6, 7, and 14
a) 6
b) 6.5
c) 7
d) 7.5
7 and 8 are in the middle. The average of the two is 7.5.
c) 7.5
What is the mean absolute deviation of the data? {1,1,2,3,4,4,5,12}
a) 2
b) 2.25
c) 2.5
d) 3
The mean is 4. So, you then subtract 4 from all the numbers (You then have, {-3, -3, -2, -1, 0, 0, 1, 8}.) and take the absolute values of the differences. (You then have, {3,3,2,1,0,0,1,8}). Once you take the mean of those numbers. (18/8=?) The mean absolute deviation is...
b) 2.25
How would you calculate the difference between the number of items in two different intervals?
example answer:
Step 1: Find the number of items in each interval by taking the top of the interval bar and lining it up with the y-axis.
Step 2: Subtract the smaller number of items from the larger number of items.
What is the median of the data set {0.5, 2.0, 3.5, 4.0}?
a) 1.5
b) 2.0
c) 2.25
d) 2.75
The median is the average of the two middle numbers. 2.0+3.5=5.5 5.5/2=2.75
d) 2.75
If the upper quartile is about 70 and the lower quartile is about 30, what is the approximate IQR?
a) 20
b) 30
c) 40
d) 60
70-30=40
c) 40
When drawing a histogram, what are 3 important things to remember?
1) The intervals should be on the x-axis.
2) Include the axis labels.
3) NO spaces exist between the columns.
Given:
Student Scores: 88, 80, 95, 90, 84, 72, 81, 88, 98, 100, 86, 92, 92, 94, and 95
What is the median score?
Put the numbers in increasing order: 72, 80, 81, 84, 86, 88, 88, 90, 92, 92, 94, 95, 95, 98, and 100
Find the middle number: 88
The median is 88.
Given:
Student Scores: 88, 80, 95, 90, 84, 72, 81, 88, 98, 100, 86, 92, 92, 94, and 95
What is the mean score?
(88+80+95+90+84+72+81+88+98+100+86+92+92+94+95)/15 = 1335/15 = 89
When would you choose to represent data using a histogram instead of a bar chart?
Example Answer: You would use a histogram when you have interval data that demonstrates a continuous data set.
When you make a box plot, what are the 5 important points to include?
1) Maximum (form the whiskers)
2) Minimum (form the whiskers)
3) Median (form the box)
4) Upper quartile (form the box and whiskers)
5) Lower quartile (form the box and whiskers)
Given:
Student Scores: 88, 80, 95, 90, 84, 72, 81, 88, 98, 100, 86, 92, 92, 94, and 95
What is the IQR score?
The lower quartile is 84 (median of the lower half of the data).
The upper quartile is 95 (median of the upper half of the data).
The IQR is 95-84=11.
Can you tell how many items fall into a subsection of an interval? (ex: The interval is 1-5, and you want to know how many items fall into the 3 category.)
No, interval data is not specific enough for that!