Lecture 4 - Measures of Spread - Range, Variance, Standard Deviation, IQR

Question 1

Relationship between Shape and Center

Answer 1

Skewed Left - Report median (Q2)

• Robust, not affected by outliers

Symmetric - typically report mean

Skewed, right - Report Q2 (median)

Question 2

Question

For the following data
2, 1, 3, 1, 1, 2, 1
which of the following is true:

A) The median is less than the mean.
B) The mode is equal to the median.
C) The shape of the data is skewed right
D) All of the above
E) None of the above

1, 1, 1, 1, 2, 2, 3

Answer 2

D) All of the above

Question 3

Measures of Spread

Range

Answer 3

Difference between the largest and smallest data values

Question 4

Sample Variance and Standard Deviation

Deviation

Answer 4

A measure of spread might be the average deviation, avg. deviation always = 0

Question 5

Sample Variance and Standard Deviation

Varience

Answer 5

Average of the squared deviations

Units² (m², kg²)

Question 6

Sample Variance and Standard Deviation

Varience Formulas

Answer 6

Question 7

Sample Variance and Standard Deviation

Sample Variance, s_x²

(or Variance)

Answer 7

s_x²

Average of the squared deviations

Question 8

Sample Variance and Standard Deviation

Standard Deviation, s_x

Answer 8

s_x=√s_x²

square root of variance

Standard deviation has the same units as the data

Question 9

Why n-1?

Answer 9

Question 10

Variance Calculation

Answer 10

Question 11

Calculate the standard deviation

Answer 11

Question 12

Quartiles

Answer 12

Question 13

Calculating Quartiles

Calculating 𝑸₁

Answer 13

1. Find the median, 𝑄₂
2. Remove all data values positionally at the median or above
3. Calculate the median of the remaining data and call it 𝑄₁

Question 14

Calculating 𝑸₃

Answer 14

1. Find the median, 𝑄₂
2. Remove all data values positionally at the median or below
3. Calculate the median of the remaining data and call it 𝑄₃

Question 15

Example

Find the third quartile for the following dataset: 2, 3, 3, 4, 7, 8

Answer 15

Question 16

Interquartile Range (IQR)

Answer 16

Question 17

Question

Which statistic(s) are considered to be robust (unaffected by
outliers)?

A) Standard deviation
B) Interquartile range
C) Median
D) Mean
E) Both B and C

Answer 17

E) Both B and C

Interquartile range and Median