MEAN
A student scored 70, 80, and 90 on three quizzes.
What is the average score?
80
Find the median:
2, 5, 9, 12
Which number is the outlier?
5, 6, 7, 8, 42
42
What do you remove when finding a truncated mean?
Extreme values / outliers
If data has no outliers, which measure is usually best?
Mean
Find the mean of:
4, 7, 9, 10, 15
9
Find the mode:
4, 6, 6, 8, 9, 9, 9
9
Does an outlier usually affect the mean or the median more?
Mean
Find the truncated mean after removing the highest and lowest values:
5, 6, 7, 8, 30
7
Which measure is least affected by outliers?
Median
The average of 5 numbers is 12.
The first four numbers are 8, 10, 14, and 11.
What is the fifth number?
12 × 5 = 60
8 + 10 + 14 + 11 = 43
60 − 43 = 17
Find the median:
3, 5, 7, 8, 10, 12
7.5
A class has scores:
80, 82, 84, 85, 10
Would the median or mean better describe the class performance?
10 is a very low outlier.
Mean gets pulled down.
Median better shows typical scores.
Judges give scores of 8, 8.5, 9, 6, and 9.5. Find the truncated mean.
A store sold shoe sizes:
9, 9, 9, 10, 11
Which measure helps most when restocking?
mode
The mean of 8 numbers is 15. Seven of the numbers are.
12, 13, 15, 16, 17, 18, 19
15 × 8 = 120
12 + 13 + 15 + 16 + 17 + 18 + 19 = 110
120 − 110 = 10
10, not an outlier
A data set has:
The smallest number is 4 and there are exactly 5 values.
Create one possible data set.
Range = 18
Largest = 22
Median = 12
Middle value must be 12
Build a valid set: 4, 8, 12, 15, 22
Answer: 4, 8, 12, 15, 22 or 4, 10, 12, 18, 22 or 4, 11, 12, 13, 22 or 4, 5, 12, 21, 22 or 4, 12, 12, 12, 22
Data Set A:
25, 78, 24.5, 28, 29
Data Set B:
31, 40, 50.5, 28, 34
Without calculating the mean, determine which set has the larger mean and explain.
Data A: 25 + 78 + 24.5 + 28 + 29
= 184.5
Data B: 31 + 40 + 50.5 + 28 + 34
= 183.5
Data A is larger.
A diving score uses a truncated mean.
Judges give:
9.5, 7.5, 7.5, 7.0, 8.0, 5.5
Find:
a) Mean
b) Truncated Mean
A) (5.5 + 7 + 7.5 + 7.5 + 8 + 9.5) ÷ 6
= 45 ÷ 6
= 7.5
B) Remove 5.5 and 9.5
(7 + 7.5 + 7.5 + 8) ÷ 4
= 30 ÷ 4
A basketball player scores:
0, 22, 23, 24, 25, 26, 27
Which measure best describes their typical performance?
median
Five numbers have a mean of 20.
Four numbers are:
14, 18, 22, 24
A sixth number is added and the mean stays exactly 20.
What number was added?
20 × 5 = 100
14 + 18 + 22 + 24 = 78
100 − 78 = 22
78 + 22 = 100
20 × 6 = 120
120 − 100 = 20
A set of 7 numbers has:
Mean = 10
Median = 10
Mode = 10
What is the largest possible value in the set?
A data set has 8 numbers with a mean of 42.
One number is removed from the data set, and the new mean becomes 36.
You are told the removed value is one of the following:
Which value was removed? Show working and justify your answer.
42×8=336
36×7=252
336 - 252 = 84
None of the options are correct.
Create a data set of 5 numbers where:
5, 10, 15, 20, 50
Mean:
(5 + 10 + 15 + 20 + 50)
= 100
100 ÷ 5 = 20
Truncated Mean:
Remove 5 and 50
10 + 15 + 20 = 45
45 ÷ 3 = 15
other solution: 7, 12, 15, 18, 48 or 5, 10, 20, 20, 45 or 2, 13, 14, 18, 53
Three students have the following test scores:
Student A:
72, 78, 80, 82, 88
Student B:
80, 80, 80, 80, 80
Student C:
60, 70, 80, 90, 100
Task:
So: