2020-intro to statistics in sociology measures of central tendency-assignment docx PDF

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2020-intro to statistics in sociology measures of central tendency-assignment docx...

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Sociology 312 Introduction to Statistics in Sociology Professor Quan Mai Assignment 2: Measures of Central Tendency and Dispersion

1. You are the following data for 17 adults who live in Newark, NJ on the number of times they watch a movie each month. These data are as follows: 4 0 1 8 2 0 4 1 3 10 4 1 0 3 1 5 4 0 0 0 1 1 1 1 2 3 3 4 4 4 4 5 8 10 9 9 9 4 4 4 4 1 0 0 1 1 1 1 4 25 49. Mean = 7.12  take sq root of this

a) From this information, calculate and report the mean, median, mode, range, and standard deviation (that means five separate statistics) of the number of times Newark residents watch a movie each month. Mean = 3, Median = 3, Mode= 1,4, Range= 0-10, standard deviation= 2.67

b) Interpret the meaning of each one of these five measures to describe the typical tendency and the dispersion of the number of times Newark residents watch a movie each month. According to a sample of 17 adults from Newark, NJ, the average amount of times a resident watches a movie each month is 3. From the data, one can conclude 3 movies a month is also the median or right in the middle of the data. Most Newark, NJ residents in the sample either watch 1 movie a month or 4 movies a month, with 4 residents each reporting they watch a movie 1 time a month or 4. Answers reported range from residents watching 0 movies a month to as many as 10 movies a month. The standard deviation is 2.67, which means 68% of reports falls between 0.33 and 5.67 movies a month. c) Do the different measures of central tendency tell you the same thing about the number of times Newark residents watch movies each month? Please explain your answer. The measures of central tendency do say the same thing about the number of times Newark residents watch movies each month, that most of the residents watch a number of movies in a month that is close to the mean, of 3. The midrange is 2-4 and the mode centers around both 1 movie a month, and 4 movies a month. All of this data aligns with the first standard deviation. d) Do the different measures of dispersion tell you same thing about the distribution of movies watched by Newark residents? Please explain your answer. The different measures of dispersion all help explain and present the distribution of movies watched by Newark residents is mostly under 5 movies a month. 15/17, or 88%, of residents

in the sample reported they watch movies 5 times a month or under. The mode can also support this, as 8/17, 47%, of residents watched either 1 movie a month or 4 movies a month.

2. You are also given the following information about the number of times that 112 Camden residents watch movies each month. Please note that you are given a frequency distribution table below rather than a list of data.

Number of times watch

Frequency

a movie each month 0

23

1

21

2

16

3

17

4

18

5

6

6

5

7

4

8

2

a) Calculate the mean, median, and standard deviation from this information. Mean – 21 + 32 + 51 + 72 + 30 + 30 + 28 + 16 = 280 / 112 = 2.5 Median = 3 Standard deviation 012345678 6.25+2.25+0.25+0.25+2.25+6.25+12.25+20.25+30.25= 80.25/112 = 0.72 b) Interpret each of the three measures for the Camden sample. Out of a sample of 112 residents from Camden, NJ, the average number of movies watched in a month is 2.5. From the answers reported, one can conclude the median, or middle ground, of residents watching a certain number of movies per month is 2, or 2 movies per month. About 56 residents reported watching 2 or more movies per month, as well as, another 56 residents reported watching 2 or less movies per month. 68% of sample residents watch 2 or 3 movies per month as dictated by the standard deviation of 0.72 from the mean of 2.5. c) Compare how adults in Newark and Camden differ in the number and dispersion of movies they watch each month. If your conclusion is that they are similar or different, discuss why you might think that is. The samples of adults in Newark and Camden are similar but not the same. Newark residents watch about 3 movies per month while Camden residents watch about 2 per month. Newark

residents most often watch either 1 or 4 movies per month, while Camden residents most often watch either 0 or 1 movies per month. I think the sample may be more precise in the Camden sample because there are much more sample values from Camden, 112, than there are from Newark, 17. 3. Here you will be choosing a variable of your choice from the GSS using SPSS. Be sure to choose a variable for which it is appropriate to calculate all of the statistics noted. Remember that you must label the variable and put a title on your table. (You cannot use the same variable examined in the example in recitation.) a) Use SPSS to obtain a table with the mean, standard deviation, minimum, and maximum for a variable of your choice for individuals living in the United States.

b) Write a brief paragraph that interprets all four in describing your variable for individuals in the US. Out of the 1818 people who responded to the survey question, “Have you ever taken any drugs by injection with a needle?”, the majority of people, 96%, responded NO, marked by the number 2. The answer YES is marked by the number 1, therefore proving the minimum value is 1 and the maximum value is 2. The average answer for this survey is NO, as indicated by the mean value of 1.96. The mean value is much closer to NO, 2, than it is to YES, 1. The standard deviation is . 187, which means 68% of participants have a marked score range of 1.77 to 1.88. Both of these will round up to a marked label of NO, at 2....