Download Sections 3.1 and 3.2

Chapter 3: Numerically Summarizing
Data
• Section 3.1: Measures of Central Tendency;
i.e., Where is the dataset centered?
• Section 3.2: Measures of Dispersion; i.e., How
spread out is the dataset?
• Mean
– Sample mean (“x bar”, 𝑥)
– Population mean (“mu”, μ, a parameter)
• Median
• Mode
Given the data:
2, 2, 9, 4, 8
Question 1: Mean = ?
(A)2 (B) 4 (C) 5 (D) 9
Question 2: Mode = ?
(A)2 (B) 4 (C) 5 (D) 9
Question 3: Median = ?
(A)2 (B) 4 (C) 5 (D) 9
Given the data:
2, 2, 9, 4, 8, 9
Question 1: Median = ?
(A)4 (B) 5.66 (C) 6 (D) There is no median
Question 2: Mode = ?
(A)2 (B) 6 (C) 2 & 9 (D) There is no mode
The shape of this distribution is?
(A)Symmetric
(B) Skewed Left
(C) Skewed Right
(D)Bimodal
Which one is true for these data?
(A)median = mean
(B) median < mean
(C) median > mean
(D) None are true
Why do economists typically use
median instead of mean when
discussing income or home prices?
A.
B.
C.
D.
It’s a tradition in economics.
The median uses every data point.
The median is resistant to extreme values.
The median is easier to calculate.
Which statistic is most appropriate for
qualitative data?
A.
B.
C.
D.
Mean
Median
Mode
None of the above are ever appropriate.
What can cause bimodal data?
A. Sampling data from two different symmetric
populations as though they were one
population.
B. Simple chance
C. Missing data
D. Too much data.
Common measures of dispersion
• Range
• Standard deviation (sd)
– Sample sd: s
– Population sd: σ
• Variance: 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
Given the data:
2, 2, 9, 4, 8
Range=? (A) 2 (B) 6 (C) 7 (D) 9
S = ? (A) 0 (B) 3.3 (C) 8.8 (D) 11
Using the data: 7, 7, 7, 7, 7
The standard deviation = ?
30 ± 4
A.
B.
C.
D.
34
The interval (26,34), including 26 and 34.
The interval (34,26), including 26 and 34.
Both B and C.
Suppose the mean test score on an exam for a very
large number of students was 80 with a sd of 5.
Assume the scores were distributed according to a bellshaped distribution.
Which one of the following is false?
A. About 68% of the scores were between 75
and 85.
B. About 99.7% of the scores were between 70
and 90.
C. About half the scores were below 80.
D. About 13.5% of the scores were between 85
and 90.
Empirical Rule gives us some rough
use of the SD value
•
•
•
•
Uses the “normal distribution”
68%
95%
99.7%