For all three variables, calculate the most appropriatemeasure of central tendency. (Please show your work) b. For each variable, explain why the measure of central tendency you calculated is the most appropriate. Respondent Marital Status Age Attitude on Abortion (high score= strong opposition) A Single 18 10 B Single 20 9 C Widowed 21 8 D Married 30 10 E married 25 7 F Married 26 7 G Divorced 19 9 H Widowed 29 6 I Divorced 31 10 J Married 55 5 K Widowed 32 4 L Married 28 3 M Divorced 23 2 N Married 24 1 O Divorced 32 9
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- For all three variables, calculate the most appropriatemeasure of
central tendency . (Please show your work)
b. For each variable, explain why the measure of central tendency you calculated is the most appropriate.
|
Respondent |
Marital Status |
Age |
Attitude on Abortion (high score= strong opposition) |
|
A |
Single |
18 |
10 |
|
B |
Single |
20 |
9 |
|
C |
Widowed |
21 |
8 |
|
D |
Married |
30 |
10 |
|
E |
married |
25 |
7 |
|
F |
Married |
26 |
7 |
|
G |
Divorced |
19 |
9 |
|
H |
Widowed |
29 |
6 |
|
I |
Divorced |
31 |
10 |
|
J |
Married |
55 |
5 |
|
K |
Widowed |
32 |
4 |
|
L |
Married |
28 |
3 |
|
M |
Divorced |
23 |
2 |
|
N |
Married |
24 |
1 |
|
O |
Divorced |
32 |
9 |
The three variables here are Marital Status (categorical), Age and Attitude on Abortion (both being numeric).
To calculate the most appropriate measure of central tendency for each of the variables and explain why the measure of central tendency is the most appropriate.
Frequency Distribution of Marital Status can be given by :
| Marital Status | Frequency |
| Single | 2 |
| Married | 6 |
| Widowed | 3 |
| Divorced | 4 |
The mode is given by the most frequent observation in the dataset, here, "married" which tells about the characteristic of the categorical data "Marital Status" mostly comprised of those who are married.
The mode is the only measure of Central tendency which can measure categorical data and gives valid information about the most common category in the dataset. Hence, the mode is being used as the most appropriate measure.
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