Statistical Questions
Is the following a statistical question:
Is Gary taller than Patrick?
No. This is a yes or no question with only one correct answer.
Find the mode(s):
3, 3, 2, 4, 4, 5, 5, 5, 3, 3, 6, 2, 3, 7, 7, 7
3
Minimum, Maximum, First Quartile, Second Quartile (or median), Third Quartile
What does MAD stand for? (Spelling Counts)
Mean Absolute Deviation
Ms. Sieber will put up an image of a data set. Describe the shape of the data.
Asymmetrical- Skewed to the right.
Is the following a statistical question:
What day of the week is it today?
No. This question has one correct answer.
Find the range
2.5, 4, 5, 6, 3.5, 1.5, 9, 10, 11.5, 9.5, 8, 19
19-1.5 = 17.5
The range is 17.5
Find the first, second, and third quartiles of the data set below:
1, 2, 2, 3, 3, 3, 4, 5, 6,
1, 2, 2, 3, 3, 3, 4, 5, 6,
Q1: 2
Q2: 3
Q3: 4.5
Which of the following is not a measure of variability?
A) Range
B) Mean Absolute Deviation
C) Interquartile Range
D) Mean
D) Mean
The mean is a measure of centrality (it tells us what the "typical" or "average" score is)
Find the outlier. Then, describe how the outlier will affect the mean and median.
15, 15, 17, 18, 19, 19.5, 20, 21, 30
30
The median will not be affected but the mean will be dragged up by the outlier.
Describe: What makes a question statistical?
The question must have multiple correct answers. The answer will change based on who you ask.
Find the median of the data set below
1, 2, 3, 4, 5, 6, 7, 8
The median is between 4 and 5
(4+5) divided by 2 is 4.5
The following statistical measures were found:
Min: 11
Max: 30
Q1: 15
Q2: 20
Q3: 26
Write 3 conclusions about the data using the quartiles.
25% of the scores are below 15
50% of the scores fall between 15 and 26
25% of the scores are above 26
What do measures of variability tell us about the set of data?
They tell us how spread out or how far apart the scores are.
Which measure of variability would be most appropriate to describe the data set below?
Time spent studying (minutes)
0, 20, 20, 25, 30, 35, 40, 40, 45
0 is an outlier which will affect the mean and mean absolute deviation.
The interquartile range will best describe the variability of the data set.
Is the following a statistical question:
How many siblings do you have?
Explain why it is statistical
Yes. It is statistical because the answer will change depending on who is asked.
Find the median of the set of numbers below
10, 11, 9, 11, 9, 9, 9, 11.5, 12.5, 13
10.5
Describe in words how to find the interquartile range. Then, find the interquartile range of the set of numbers below.
1, 2, 2, 3, 3, 3, 4, 5, 6,
You need to find the difference between the third quartile and the first quartile.
Q1: 2
Q2: 3
Q3: 4.5
4.5 - 2 = 2.5
Find the mean of the set of data below. Then, find out how far away from the mean each score is. Then, find the average of those deviations.
9, 8, 13, 9, 11
Mean: 10
Absolute Deviations: 1, 2, 3, 1, 1
MAD: 8 divided by 5 = 1.6
Name and find the best measure to describe the center of the data below.
A group of friends played a board game over the weekend. These are the number of rounds each person won:
6, 7, 7, 8, 7
There is no outlier so the best measure would be the mean.
The mean is 6 + 7 + 7 + 7 + 8 divided by 5
35 divided by 5 = 7
Ask me an original statistical question. You have 10 seconds.
Answers will vary.
Find the mean of the set of numbers below
9, 9, 9, 9, 10, 11, 11, 11.5, 12.5, 13
10.5
Find the interquartile range of the set of numbers below:
12.5, 13, 13.5, 14, 16, 16, 17, 18
Q1: 13.25
Q2: 15
Q3: 16.5
IQR: 16.5- 13.25 = 3.25
Find the mean absolute deviation of the set of numbers below:
1, 2, 3, 4, 5, 6, 7, 8, 9
Round your answer to the nearest tenth.
Mean: 5
Absolute Deviations:
4, 3, 2, 1, 0, 1, 2, 3, 4
Mean Absolute Deviation: 20 divided by 9 = about 2.2
TRICK:
The mean of the data set below is 10. Find the missing score
9, 8, 13, ___, 11
The sum of the scores needs to be 50 because 50/5 scores= 10
So far, the sum is 41. That means the missing score needs to be 9.