14. The scores below are from the same final exam given in a math class in two d
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Question
14. The scores below are from the same final exam given in a math class in two different years (see problem #1 at the end of Chapter 3 in this manual). Compute the mean and median (if necessary) and the range and standard deviation of these scores. Using these statistics, describe the differences in the two sets of scores.This year 35 45 65 75 87 80 69 71 53 90 99 95 70 82 73 93 67 61 57 74 72 77 71 81 83 Ten years ago 56 77 75 76 59 74 51 89 55 79 67 77 69 90 68 90 65 79 69 79 87 86 98 91 95
Answer: Given the statistics of the two sets of scores, it is apparent that while the standard deviation of this year’s scores is 14.86 and the range is 64, the standard deviation of ten years ago was 12.66 and the range was 47.
15. Some information about auto theft rates (number of auto thefts per 100,000 population) for a sample of 178 cities in two different years is summarized below. Express this statistical information in words. What changes were there in the overall shape of the distribution of this variable? In central tendency? In dispersion?
1985 2005 Mean = 150.32 125.17 Median = 117.17 123.01 Standard Deviation = 12.23 7.01
The above SPSS output summarizes data from the GSS about the size of peoples’ homes in hundreds of square feet.
16. What is the standard deviation of home size among survey respondents?
17. Why are the mean and median so different?
18. If the data maintained the same mean but were less skewed, would the standard deviation be larger or smaller
Statistics Size of Place in 1000s Valid 757 743 360.63 23.00 Missing Mean Median Mode Std. Deviation Variance Range Minimumm Maximumm Percentiles 25 1225.200 1501114 7072 7072 4.00 23.00 82.00 50 75 The above SPSS output summarizes data from the GSS about the size of peoples' homes in hundreds of square feet.
Explanation / Answer
14.
Compute the mean and median (if necessary) and the range and standard deviation of these scores.
Using these statistics, describe the differences in the two sets of scores.
The mean for this year is less than the mean ten years ago, which means that on an average there has been decrease in the marks of the students in maths by 3 numbers or approximately 4 percent.
However the range of the numbers has increased which signifies that either the minimum marks which students recieved has decreased or the maximum marks has increased.
The standard deviation is higher for the data now than for the data 10 years ago, this means have spreaded more now as compared to that of 10 years ago.
15.
Express this statistical information in words. What changes where there in overall shape of distribution of this variable? In central tendency? In dispersion?
In 1985 the mean of the variable is greater than the median and hence the distribution is skewed to the right. In 2005 the mean and median are almost same hence the distribution is almost symmetric. Hence it can be said that the shape of the distribution has changed from rightly skewed to symmetric in these 20 years.
The average theft rate has decreased from 150.32 thefts per 100,000 population in 1985 to 125.17 thefts per 100,000 population in 2005. Hence in these 20 years there have been a significant decrease in the average number of auto thefts.
The dispersion of the auto theft rates has decreased from 1985 to 2005 as it is evident from the standard deviation of data of these two years.
16. What is the standard deviation of home size among survey respondents?
The standard deviation of home size among survey respoondents is found to be 1225.200 squares feet.
17. Why are the mean and median so different?
In this case the mean is significantly higher than the median. The prresence of some data points with very high values can result in this. in our case it means that there will be some very large houses which has increased the mean of the data.
18. If the data maintained the same mean but were less skewed, would the standard deviation be larger or smaller
If the data is leess skewed then the standard deviation of the data would be smaller.
Mean Range Standard Deviation This year 73 64 14.86 Ten years ago 76 47 12.66Related Questions
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