1. The General Social Survey (GSS) is a survey of approximately 2000 adults cond
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Question
1. The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of more than 38,000 participants. During several years of the GSS participants were asked how many close friends they have. The mean for this variable is 7.44 friends with a standard deviation of 10.98. The median is 5.00 and the mode is 4.00.
a. Are these data for a distribution of scores or a distribution of means? Explain.
b. What do the mean and standard deviation suggest about the shape of the distribution? (Hint: compare the sizes of the mean and the standard deviation)
c. What do these three measures of central tendency suggest about the shape of the distribution?
d. Let’s say that these data represent the entire population. Pretend that you randomly selected a person from this population and asked how many close friends she or he had. Would you compare this person to a distribution of scores or to a distribution of means? Explain your answer.
e. Now pretend that you randomly selected a sample of 80 people from this population. Would you compare this sample to a distribution of scores or to a distribution of means? Explain your answer. Using symbolic notation, calculate the mean and standard error of the distribution of means. f. What is the likely shape of the distribution of means? Explain your answer.
Explanation / Answer
Soln
a) We would use a distribution of means because we are comparing a sample of a larger population to see if the average of friends differs based on the different area they live.
b) Since the Standard deviation is very large as compared to the mean of the samples mean then we can say that the data of nos of close friends are very widely distributed and Since it is of large sample data the varibles are are very far distributed from the mean.
c) The three measures of central tendency those are mean, median and mode and as we compare the three data ir shows that mean is larger than the median so it suggest that majority of date falls in the left of the mean and larger data are in the right of the mean and the distribution is skewed to the right and streching a tail towards right of the mean. Here mode is 4 that suggest that the 4 is most occuring no of friends in the data compared to any no of friends occuring.
d) If one is randomly selected then we would go for distribution of scores since the popolation is large enough and standard deviation is very large and the comparison between mean and median suggest that the majority of data lies left to the mean or less to the mean that is why we cannot directly rely on the mean of the samples mean.
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