Module 3, Measures of Central Tendency

Question 1

What are the 3 Measures of Central Tendency?

Answer 1

1. mode
2. median
3. mean

Question 2

Mean

Answer 2

• arithmetic average of a set of scores
• the mean can be considered a balancing point in the distribution of scores for a variable
• the average value of the variable (the most common measure of central tendency

Question 3

How to Calculate the Mean?

Answer 3

to calculate:
1. multiply each score (X) by its frequency (f)
2. sum of the products (fX)
3. divide by the total number of scores

• you need unique values for mean and thus cannot calculate from grouped frequency table (have to know what each value in the data set is)

Question 4

Score - Mean

Answer 4

if we subtract the mean from each score:
- the sum of the negative differences will always equal the sum of the positive differences
- score - mean is always going to add up to 0 in the end
* the mean as a balancing point

Question 5

Asymmetric Distributions (positive): Mean and Median

Answer 5

in a positively skewed distribution the value of the mean is usually greater than the median

Question 6

Asymmetric Distributions (negative): Mean and Median

Answer 6

in a negatively skewed distribution the mean is a smaller value than the median typically

Question 7

Mode and Modality: 1 Mode; Unimodal

Answer 7

• mode is most frequently occurring value (represented by highest bar in a histogram)
• unimodal as there is only one peak

Question 8

Mode and Modality: 2 Mode; Unimodal

Answer 8

2 bars that are of even height (2 values that have same frequency), however there is really only one peak which would mean it is still unimodal (mode and modality are distinct concepts - cannot be used interchangeably)

• even if there is a slight gap in between the modes it is not enough to create a bimodal distribution as there is not enough of a dip meaning the valley should come down all the way and go back up

Question 9

Mode and Modality: 1 Mode; Bimodal

Answer 9

• there is 1 mode, the other value is not as great - goes down and comes back up (bimodal)
  ◦ in order to assess modality you must look at HISTOGRAM (need to visually see it) - shape of distribution

Question 10

Mode

Answer 10

• most common or frequently occurring score
• score or value of a variable that appears most frequently in a set of data
  *to identify mode look down the frequency column and see what value is seen the most and we identify the tallest bar in the bar chart or histogram or the highest data point in the polygon

Question 11

What are Strengths and Weaknesses of the Mode?

Answer 11

strengths
- easy to determine
- can be used to summarize nominal data
- represents an actual value (in the data set)
- takes in account multiple modes (when it follows by bimodal for instance)
- not affected by outliers

weaknesses
- can not be used in hypotheses testing (when conducting inferential statistical analyses)
- oversimplified use of one score rather than the whole set of data

Question 12

Median

Answer 12

• the value of the variable in the center of the distribution
• the value of a variable that splits a distribution of scores in half, with the same number of scores above the median as below (arrange from lowest to highest, calculate the median score in the set of data and determine the value of the median score)
  odd number of scores: one in the middle
  even number of scores: take middle two values and average it

Question 13

What are Strength and Weaknesses of the Median?

Answer 13

strengths
- provides a more accurate measure of central tendency in skewed (asymmetric) distributions
◦ the mean is not an accurate
measure of central tendency
when it is skewed

weaknesses
- relies on only the middle one or two scores, not the whole data set (the whole data set is not represented)
- cannot be used in hypothesis testing (when conducting inferential statistics
- inaccurate for bimodal distributions (it falls in the middle of the distribution, in the valley where most of the data is not)

Question 14

Sample Mean

Answer 14

the sample mean is an example of a descriptive statistic and it describes the average score of a variable from the data we have collected

Question 15

Population Mean

Answer 15

the population mean is unknown to us but we can estimate the population mean depending on what we know for our sample data
- parameters = unknown population mean

Question 16

What are the Strength and Weaknesses of the Mean

Answer 16

strengths
- calculated from all the scores in the distribution (the scores of all the participants are represented)
- can be used in hypothesis testing (for inferential statistical analyses)

weaknesses
- affected by outliers, so inaccurate with skewed distributions (outliers pulls means away from the most frequently occurring data towards the tails of the distributions) - the mean is not accurate in describing central tendency when it is skewed
- may not describe bimodal distributions (mean often falls in between two peaks)

Question 17

If distribution is unimodal and symmetric what measure is preferred?

Answer 17

the mean, median and mode will all be same value and in the middle of the distribution (we use mean for central tendency)

Question 18

If distribution is unimodal and asymmetric what measure is preferred?

Answer 18

median is preferred as measure of central tendency because it is not affected by outliers unlike the mean is and thus lies closer to the centre of the distribution than the mean or mode

Question 19

If distribution is bimodal what measure is preferred?

Answer 19

• the median and mean are the same and there the two modes
• the mode is the most useful because only the mode can highlight the two scores with the highest frequencies