STA 144 Week 2 Homework(1)

STA 144 Week 2 Homework Work on the following problem set from chapters 3-4 Chapter 3 1. Why is the range the most convenient measure of dispersion, yet the most imprecise measure of variability? When would you use the range? a. This is because range can determine the difference between the highest and lowest points on the data but cannot give us the differences between each score, so trying to find out how the data is separated is harder but finding out the difference between the highest and lowest is very good. We would use Range when trying to find the difference in heights, or ages. We wouldn’t use range when trying to determine the difference in categories of data sets. 2. Fill in the exclusive and inclusive ranges for the following items. Be sure to show your work below. High Score Low Score Inclusive Range Exclusive Range 7 6 2 1 89 45 45 44 34 17 18 17 15 2 14 13 1 1 1 0 2. Why would you expect more variability on a measure of personality in college freshman than you would on a measure of height? a. Because height is objective and can accurately be measured and verified and has a lower chance of having wild outliers where-as personality is extremely subjective and many people might describe personality in very different ways leading to a far more varied set of responses when compared to hard numbers. 3. Why does the standard deviation get smaller as the individuals in a group score more similarly on a test?

a. Because the variety of scores are lower so the difference between each score becomes smaller as each student is getting closer to the average score. There is less variety among the students to need to account for. 5. For the following set of scores, compute the range, the unbiased and the biased standard deviations, and the variance. Use SPSS for this question but there may be some part of it you will have to do by hand. 31, 42, 35, 55, 54, 34, 25, 44, 35 VAR00008 N Valid 9 Missing 0 Mean 39.4444 Std. Deviation 10.18714 Variance 103.778 Range 30.00 The Biased Standard Deviation is 9.6045 6. The variance for a set of scores is 25. What is the standard deviation, and what is the range? The Standard Deviation is 5 and the range is about 20

a. Create a frequency distribution and a histogram for the set. VAR00002 (Binned)

Frequen cy Percent Valid Percent Cumulative Percent 6.00 - 13.00 6 5.9 12.0 14.0 14.00 - 21.00 7 6.9 14.0 28.0 22.00 - 29.00 7 6.9 14.0 42.0 30.00 - 37.00 4 4.0 8.0 50.0 38.00 - 45.00 10 9.9 20.0 70.0 46.00 - 53.00 5 5.0 10.0 80.0 54.00 - 61.00 10 9.9 20.0 100.0 Total 50 49.5 100.0 Missin g System 51 50.5 Total 101 100.0 b. Which interval did you use? Why did you select the class interval you used? i. I used 7 as my interval because I was trying to get it as closely reflect the min and max numbers as possible. I used a Bar chart as the class because it is the sleekest looking as appears to give the best impression of the scores for anyone trying to read it. c. Is this distribution skewed? If so, to what direction? How do you know? i. The chart is skewed to the left. The formula produced -238 for skewness and looking at the chart more numbers to the left will fall below the mean 2. Using the following data, create a histogram in SPSS and paste it below Class Interval Frequency 90–100 12 80–89 14 70–79 20

b. On this incredibly crummy test, everyone received the same score This would not have a skew at all c. On the most difficult spelling test of the year, the third graders wept as the scores were delivered. This test would have a negative skew 4. Use the data available as Chapter 4 Data Set 3 (appendix) on pie preference to create a pie chart using SPSS. 5. For each of the following, indicate whether you would use a pie, line, or bar chart and why. a. The proportion of freshmen, sophomores, juniors, and seniors in a particular university A pie graph would demonstrate a better split and be more easily seen b. Change in GPA over four semesters A line graph in order to show progression or regression c. Number of applicants for four different jobs A bar graph would suit this nicely as it is separated into different categories d. Reaction time to different stimuli Bar graph because of the separated categories of stimuli e. Number of scores in each of 10 categories Bar graph again for the categories. 7. What is the purpose of a chart or graph? The purpose of a chart or graph is to more easily show the reader or whoever the intended audience is the information is a more easily read manner.