Question

5) Where do Americans tend to fall on the conservative-liberal political spectrum? The General Social Survey asks, “I'm going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal, point 1, to extremely conservative, point 7. Where would you place yourself on this scale?”. The table shows the seven-point scale and the distribution of 1933 responses for a survey conducted in 2008. Score Category Extremely liberal Liberal Slightly liberal Moderate Slightly conservative Conservative Extremely conservative Frequency 69 240 221 740 268 327 68 (Source: Data from CSM, UC Berkeley.) This is a categorical scale with ordered categories, called an ordinal scale. Ordinal scales are often treated in a quantitative manner by assigning scores to the categories and then using numerical summaries such as the mean and standard deviation. Then evaluate the followings: a) Using the scores shown in the table, the mean for these data equals nearly 4.11. Show that you get the mean by multiplying each score by the frequency it occurred, summing up these values and then dividing the sum by the total number of observations. b) Identify the mode (or modal category). Explain why. c) In which category does the median fall? Why? Explain in detail.

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Answer 1

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Answer:

a)

Score	Frequency	xi*fi
1	69	69
2	240	480
3	221	663
4	740	2960
5	268	1340
6	327	1962
7	68	476
	Sum of xi*fi	7950
	Sum of frequency	1933
	Mean	4.11

The sum of 1933 observations can be found by multiplying each possible value by its frequency and then add those values. It implies that, x = (1x69) + (2x 240)+...+(7x68) = 7950 Since, the sample size is 1,933, the mean value is obtained as shown below: – 7,950 1,933 = 4.11

b)

Mode is the value that occurs most frequently in a set of observations. It describes that a typical observation in terms of the most common outcome. From the given data, it can be observed that the category 4 has the highest (720) frequency. So, for the given data the model (mode) category is Moderate.

c)

Median is the middle value of the ordered data of a given data set. For the 1933 sample data, the ordered sample would be 111... 222... 333... 444... 555... 666... 777...7 69 ls 240 2s 221 3 740 4s 268 5s 327 68 68 7s Since n=1933 the observations would be listed from 19 to 1,933" The middle observation of the ordered data will be (1+1933) =967th Observation. 2 However, there are 7 distinct responses among them 967th observation would be 4 which belongs to moderate category. Hence, the median falls in Moderate category.