Standard deviation - practice problems - page 4 of 6
The standard deviation, symbol sigma σ, is a statistical measure of the variability of a data set. Simply put, it tells us how spread out the values are around the mean (arithmetic mean). How far away most of them are from the mean. It is a non-negative number, defined as the square root of the variance of the data. It therefore has the same dimensions as the data.Variance in statistics is the average of the squares of the deviations from the mean (mean). Variance is also a non-negative number.
The sample standard deviation is defined as the square root of the sample variance. When calculating the sample variance, for n data, only (n-1) independent data are considered.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 114
- Germination 55283
The supplier of spruce seeds for our nursery declares a germination rate of 80% for his goods. Verify this statement based on an experiment in which only 70 seeds germinated out of 100 randomly selected seeds. - Distribution 55071
Five men drive to work together; 2 have a Škoda car, and the others have an Opel, Seat, and Hyundai. They always randomly choose which car to drive. Each of the five cars has an equal chance. The random variable X determines how many days the same charact - Suppose 4
Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be - Rich retirement Healthcare issues are receiving much attention in both academic and political arenas. A sociologist recently surveyed citizens over 60 years of age whose net worth is too high to qualify for government health care but who have no private health insurance.
- Publishing company Suppose you work for a publishing company, and before launching a new magazine targeting fashion-oriented consumers, your boss wants to hold a meeting with prospective advertisers. Assume that annual expenditures on magazine ads in this genre are normally
- Manufacturing company
A random sample of 8 manufacturing companies is selected from a population of manufacturing companies. The market values (in millions of rands) of these eight manufacturing companies are: 17 65 117 206 172 181 221 94 What is the lowest and highest market - A professor
A professor in a typing class found out that the average performance of an expert typist is 85 words per minute. A random sample of 16 students took the typing test, and we obtained an average speed of 62 words per minute with a standard deviation of 8. C - Unemployment rate
Over the last 16 years, the country's unemployment rate has changed according to the following frequency table: years of unemployment: 2 5 2 3 3 1 unemployment rate: 0.5 1 1.5 2 2.5 3 in % (percent). Determine the two-sided confidence interval for the var - Chi square
A phone battery manufacturer claims that his battery lives are approximately normally distributed with a standard deviation equal to 0.9 years. Suppose a random sample of 10 of these batteries has a standard deviation of 1.2 years. Do you think that the s
- Confidence Interval The average grade of 50 senior students in a statistics class is 85, with a standard deviation of 10.2. In comparison, 60 senior students got an average of 80 with a standard deviation of 8.9. Can the difference in the mean grade be attributed to chance,
- Performance comparing A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students was given the same test and showed an average score of 83.20. Is there evidence that this group performs le
- Three sigma rule
The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m². Determine the interval in which there will be tree heights in such a stand with a probability of 90% - A machine
A machine produces steel rods of normally distributed length, the mean length and the standard deviation being 50.0 cm and 0.5 cm, respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in - Five number summary
Find the five-number summary for these data and make a boxplot. 14,5,12,19,2,35,5,4,3,7,5,8
- Confidence interval A food testing laboratory in Abu Dhabi has been commissioned to estimate the amount of olive oil contained in 1-gallon tins purchased from a range of international olive oil producers. The manufacturers state that the standard deviation of the amount of o
- 5-number summary Given the following 5-number summary: 11, 19, 24, 30, 48, which of the statistics cannot be determined?
- Bivariate data set Here is a bivariate data set in which you believe y to be the response variable. x y 51.4 44.8 60.2 46.6 60.1 46.8 45.8 46.3 37.4 41.8 72.4 52.5 60 48.2 67.5 49.5 60.9 49.8 51.1 45.7 62.7 49.6 194.9 84.2 Make a scatter plot of this data. Which point is an
- Dataset: Dataset: 35 22 18 54 22 46 28 31 43 22 14 17 25 19 33 14. 1 Group the data into a grouped distribution using six classes of equal width. 2. Determine the mean, median, and mode using the raw data. 3. Draw an Ogive curve corresponding to the data and use i
- Statistical survey Write TRUE OR FALSE for each question: 1 Standard deviation measures central location. 2. The most frequent observation in a data set is known as the mode. 3 The most passive method of data collection is observation. 4 Access time for secondary data is sh
A mountain climber plans to buy some rope to use as a lifeline. Which of the following would be the better choice? Explain your choice. Rope A: Mean breaking strength:500lb; the standard deviation of 100lb Rope B: Mean breaking strength: 500lb; the standaDo you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
