Lecture 2 - Central Tendency, Variability, Stem & Leaf, Density Plots

Question 1

How do you calculate the Mode?

Answer 1

Find the most frequently occurring score

Question 2

How do you calculate the Median?

Answer 2

Mdn = (n+1) / 2
Median = Number of scores plus 1, divided by 2

Question 3

How do you calculate the Mean?

Answer 3

X̄ = (Σxi) / N
Mean = The sum of each individual score, divided by the number of scores

Question 4

How and why would you use a “trimmed mean”?

Answer 4

How: Cut an equal amount of scores from each end of the data set and then find the mean.

Why: To eliminate extreme values that may be distorting the data

Question 5

What is the most appropriate measure of central tendency to use for nominal data?

Answer 5

The mode

Question 6

What are the most appropriate measures of central tendency to use for ordinal data?

Answer 6

The mode or median

Question 7

What are the most appropriate measures of central tendency to use for interval/ratio data?

Answer 7

The mode, median or mean

Question 8

List 3 reasons why the Mean is useful.

Answer 8

1. It takes every score into account
2. It can be used algebraically
3. It gives stable estimates of the population mean

Question 9

When is it best to NOT use the mean?

Answer 9

When the data is skewed / there are extreme scores, because the mean is more sensitive to outliers than the mode or median.

Question 10

What is the Interquartile Range?

Answer 10

The middle 50% of scores

Question 11

What is the Range?

Answer 11

Ra = Highest Score - Lowest Score

Question 12

What is Quartile 2 also known as?

Answer 12

The Median

Question 13

How do you calculate the Interquartile Range?

Answer 13

IQR = Q3 - Q1

Question 14

How do you calculate the value for Quartile 1?

Answer 14

(n+1) / 4 = the position of the Q1 value in the range of scores

Question 15

How do you calculate the value for Quartile 3?

Answer 15

3 ( (n+1) / 4 ) = the position of the Q3 value in the range of scores

Question 16

If you calculate the deviation from the mean for every score in a sample and add them all together, what will the total always be?

Answer 16

0

Question 17

How do you calculate the sample variance of a set of scores?

Answer 17

s² = Σ(X-X̄)² / N-1

The sum of the squared deviations from the mean divided by N - 1

Question 18

How do you calculate the sample standard deviation?

Answer 18

SD = Square root of the sample variance

Question 19

Why do we use N-1 rather than just N in determining the sample variance and sample standard deviation?

Answer 19

Because this gives us the most unbiased estimation of the population parameters.

Question 20

What is a stem and leaf diagram?

Answer 20

A structured and ordered way of displaying the data where the tens column become the “stem” and the units become the “leaves”

eg. for the data 1,1,3,4,6,12,12,15,23,26,26

0 | 1,1,3,4,6
1 | 2,2,5
2 | 3,6,6

Question 21

Why is a stem and leaf diagram better than a histogram?

Answer 21

It allows us to see the individuals scores within a set of data as well as the general shape and distribution of the scores.

Question 22

What is a density plot?

Answer 22

Like a histogram but with a smooth line instead of blocks. The y axis is called density and not frequency.

Question 23

What does the area under the curve in a density plot always add up to?

Answer 23

1