Chapter #7b - 10/11/24

Question 1

what are the mean and median used to describe ?

Answer 1

the center of a distribution, but only knowing the center may be misleading

Question 2

what does measuring variability tell us ?

Answer 2

tell us how spread out the distribution is

Question 2

what percentage of observations in a distribution are greater than the first quartile ?

a) 25%
b) 50%
c) 75%

Answer 2

c) 75%

Question 2

how to calculate quartiles ?

Answer 2

• Arrange the observations in increasing order and find the median, M
• The first quartile (lower quartile), Q1, is the median of all observations (in the ordered list) below M (exclusive)
• It is one quarter of the way from the bottom of the ordered list
• The third quartile (upper quartile), Q3, is the median of all observations (in the ordered list) above M (exclusive)
• It is one quarter of the way down from the top of the ordered list

Question 3

what do the quartiles provide ?

Answer 3

a resisteant measure of varability

Question 3

define “lowest” :

Answer 3

minimum

Question 3

what are the 5 important terms in the “five-number summary display” ?

Answer 3

• lowest
• highest
• lower quartile
• upper quartile
• media

Question 4

define “highest” :

Answer 4

maximum

Question 5

define “median” :

Answer 5

number such that half of the values are at or above it and half are at or below it (middle value or average of two middle numbers in ordered list).

Question 6

define “quartiles” :

Answer 6

medians of the two halves

Question 7

how do you calculate median ?

Answer 7

value at position (n+1) / 2 = that #th value

Question 8

between mean and median which is the “average” ?

Answer 8

mean

Question 9

in an example with the following numbers what is considered the lower quartile ?

1, 2, 5, 9, 12, 15, 17, 21, 23, 25, 29

Answer 9

lower quartile or 1st quartile is the median of the values below 15. There are 5 values, so Q1 us located at (5+1) / 2 = 3th value below the median

Question 10

in an example with the following numbers what is considered the upper quartile ?

1, 2, 5, 9, 12, 15, 17, 21, 23, 25, 29

Answer 10

the upper quartile or 33rd quartile is the median of the values above 15. there are 5 values, so Q3 is located at (5+1) / 2 = 3th value above the median

Question 11

what is median ?

Answer 11

This is the middle value when all the numbers are arranged in order. If there’s an odd number of values, it’s the middle one. If there’s an even number, it’s the average of the two middle ones.

Question 12

what is mode ?

Answer 12

This is the number that appears most often. If no number repeats, there’s no mode, and if more than one number repeats the same number of times, you can have more than one mode.

Question 13

what is mean ?

Answer 13

This is the average of all numbers. Add up all the values and then divide by how many values there are.

Question 14

what does IQR stand for ?

Answer 14

Interquartile Range

Question 15

what is the IQR

Answer 15

is a measure of how spread out the middle 50% of your data is. It shows the range between the first quartile (Q1) and the third quartile (Q3) of a dataset.

• Q1 (First Quartile): The middle of the lower half of the data (25% mark).
• Q3 (Third Quartile): The middle of the upper half of the data (75% mark).

Question 16

what term is used to describe the following “ a more resistance measure of variability is given as distance the distance between the quartiles.”

Answer 16

IQR

Question 17

what is the formula for the IQR ?

Answer 17

IQR = upper quartile (Q3) - lower quartile (Q1)

Question 18

when do we call an observation an outlier ?

Answer 18

if it falls more than 1.5 xs IQR above the upper quartile to below the lower quartile

Question 19

what are boxplots ?

Answer 19

is a simple way to visually show the spread and distribution of data (5 key data)

Question 20

what are the 5 key datas boxplots show ?

Answer 20

• Minimum: The smallest value (not counting outliers).
• Q1 (First Quartile): The 25% mark.
• Median: The middle value (50% mark).
• Q3 (Third Quartile): The 75% mark.
• Maximum: The largest value (not counting outliers).

Question 21

how many steps to create a boxplot ?

Answer 21

7

Question 22

what are the 7 steps in creating a boxlpot ?

Answer 22

1. Draw horizontal (or vertical) line, label it
   with values from lowest to highest in data.
2. Draw rectangle (box) with ends at quartiles.
3. Draw line in box at value of median.
4. Compute IQR (interquartile range) = distance
   between quartiles.
5. Compute 1.5(IQR); outlier is any value more
   than this distance from closest quartile.
6. Draw line (whisker) from each end of box
   extending to farthest data value that is not an
   outlier. (If no outlier, then to min and max.)
7. Draw asterisks to indicate the outliers.

Question 23

how do you interpret boxplots ?

Answer 23

• Divide the data into fourths.
• Easily identify outliers.
• Useful for comparing two or more groups.

Question 24

define “standard deviation” :

Answer 24

represents spread or variability in the values;

Question 25

define “variance” :

Answer 25

(standard deviation) ^2

Question 26

what are the mean and standard deviation most useful for ?

Answer 26

symmetric sets of data with no outliers

Question 27

how to compute the standard deviation ?

Answer 27

1. Find the mean.
2. Find the deviation of each value from the mean. (Deviation = value – mean)
3. Square the deviations.
4. Sum the squared deviations.
5. Divide the sum by (the number of values) – 1, resulting in the variance.
6. Take the square root of the variance. The result is the standard deviation.

Question 28

what are all the values that a standard deviation can possibly take ?

a) 0 ≤ s
b) 0 ≤ s ≤ 1
c) -1 ≤ s ≤ 1

Answer 28

a) 0 ≤ s