Question

Imagine that we were interested in studying people’s subjective well-being (i.e., feelings of general life satisfaction). We therefore administer a survey of subjective well-being (scale: 1 = extremely low, 9 = extremely high) to a sample of 14 participants. We obtain the following set of scores: 8, 2, 5, 4, 9, 5, 6, 7, 8, 5, 9, 7, 2, 1. 2.1. . Calculate the three measures of central tendency discussed in class for this set of scores (report your calculations step by step, not just the results). 2.2. Calculate the standard deviation for this set of scores using the SD-formula for a sample (report your calculations step by step, not just the results). 2.3. . Interpret the results from the survey (focus on M and SD). What can we say about the general subjective well-being experienced in our sample, and what can we say about the amount of variation in experienced well-being? 3. . Transform all 14 subjective well-being scores into z-scores (report your calculations step by step, not just the results). Explain what the highest and the lowest z-scores that you have calculated mean (i.e., how they should be interpreted)?

Answer 1

(2.1) the measures of centeral tendency are given as

mean=sum/n=78/14=	5.57
median=	5.5
mode=	5

median is middle oberservation of the distribution/series when arrange inf ascending or descending order. here data is arranged in ascending order and 7th and 8th observations are middile observatiaons and average of 7th and 8th will be median

median=(5+6)/2=5.5

mode is the most frquent observations and here 5 repeated 3 times is most repeated observation so mode is 5

(2.2) standard deviation=sqrt(sum((x-mean)²/n))=sqrt(89.43/14)=2.53

sn	x	x-mean	(x-mean)2
1	1	-4.57	20.90
2	2	-3.57	12.76
3	2	-3.57	12.76
4	4	-1.57	2.47
5	5	-0.57	0.33
6	5	-0.57	0.33
7	5	-0.57	0.33
8	6	0.43	0.18
9	7	1.43	2.04
10	7	1.43	2.04
11	8	2.43	5.90
12	8	2.43	5.90
13	9	3.43	11.76
14	9	3.43	11.76
sum=	78	3.55E-15	89.42857
n=	14	14	14

(2.3)Use the standard deviation to determine how spread out the data are from themean. A higher standard deviation value indicates greater spread in the data. ... The standard deviation can also be used to establish a benchmark for estimating the overall variation of a process.

(3)z=(x-mean)/sd

highest z=-1.8087

lowest z=1.3565

sn	x	x-mean	(x-mean)2	z=(x-mean)/sd
1	1	-4.57	20.90	-1.8087
2	2	-3.57	12.76	-1.4131
3	2	-3.57	12.76	-1.4131
4	4	-1.57	2.47	-0.6218
5	5	-0.57	0.33	-0.2261
6	5	-0.57	0.33	-0.2261
7	5	-0.57	0.33	-0.2261
8	6	0.43	0.18	0.1696
9	7	1.43	2.04	0.5652
10	7	1.43	2.04	0.5652
11	8	2.43	5.90	0.9609
12	8	2.43	5.90	0.9609
13	9	3.43	11.76	1.3565
14	9	3.43	11.76	1.3565
sum=	78	4E-15	89.43	0