Concept explainers
What are
a.
Define descriptive statistics
Explanation of Solution
Descriptive statistics:
If a sample is taken and some statistics or sample characteristics are obtained from the sample but no inference is made about the entire population by using this information which is available from the sample, then it is termed as descriptive statistics.
The descriptive measures have three key characteristics:
- Center
- Variability
- Shape
Measures of Center:
An individual value that attempts to describe an observation by identifying the central position of the sample data is known as measures of central tendency.
Characteristics of center:
- Mean
- Median
- Mode
- Midrange
- Geometric mean
- Trimmed mean
Variability:
The measures of variability calculate the amount of spread or deviation in the observations. If the values corresponding to the variability are high, it means that the values in the data set are spread out wide.
Characteristics of the variability:
- Range
- Sample variance
- Sample standard deviation
- Coefficient of variation
- Mean absolute deviation
Measures of shape:
The shape of the data can be predicted by having the view on the shape of the graphs like histogram or boxplots or by comparing the value of the mean and median.
b.
Explain how the descriptive measures differ from the visual displays of data.
Explanation of Solution
The statistical method helps to organize, explore and summarize the raw data in to useful information. The methods of statistics may be in visual form (Charts or graphs) or numerical form (Statistics or tables). In statistics, data visualization deals with the charts and graphs. A surveyor uses the visual form of data for clear explanation. In common, it is a practice to continue an analysis by examining graphical displays of the data set. The method of visual representation makes the people to understand the data easily.
However, the visualization has the clear logical ideas but it also needs some descriptive reports about the data. It is hard to visualize the raw data into graphical form without any descriptive measures. In order to analyze the data set, descriptive measure will give clear explanation along with graphical representation.
Want to see more full solutions like this?
Chapter 4 Solutions
Applied Statistics in Business and Economics
Additional Math Textbook Solutions
Graphical Approach To College Algebra
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Elementary Statistics: Picturing the World (7th Edition)
Introductory Statistics
Elementary & Intermediate Algebra
- A poll before the elections showed that in a given sample 79% of people vote for candidate C. How many people should be interviewed so that the pollsters can be 99% sure that from 75% to 83% of the population will vote for candidate C? Round your answer to the whole number.arrow_forwardSuppose a random sample of 459 married couples found that 307 had two or more personality preferences in common. In another random sample of 471 married couples, it was found that only 31 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common. Find a95% confidence interval for . Round your answer to three decimal places.arrow_forwardA history teacher interviewed a random sample of 80 students about their preferences in learning activities outside of school and whether they are considering watching a historical movie at the cinema. 69 answered that they would like to go to the cinema. Let p represent the proportion of students who want to watch a historical movie. Determine the maximal margin of error. Use α = 0.05. Round your answer to three decimal places. arrow_forward
- A random sample of medical files is used to estimate the proportion p of all people who have blood type B. If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 99% sure that the point estimate will be within a distance of 0.07 from p? Round your answer to the next higher whole number.arrow_forwardA clinical study is designed to assess the average length of hospital stay of patients who underwent surgery. A preliminary study of a random sample of 70 surgery patients’ records showed that the standard deviation of the lengths of stay of all surgery patients is 7.5 days. How large should a sample to estimate the desired mean to within 1 day at 95% confidence? Round your answer to the whole number.arrow_forwardA clinical study is designed to assess the average length of hospital stay of patients who underwent surgery. A preliminary study of a random sample of 70 surgery patients’ records showed that the standard deviation of the lengths of stay of all surgery patients is 7.5 days. How large should a sample to estimate the desired mean to within 1 day at 95% confidence? Round your answer to the whole number.arrow_forward
- In the experiment a sample of subjects is drawn of people who have an elbow surgery. Each of the people included in the sample was interviewed about their health status and measurements were taken before and after surgery. Are the measurements before and after the operation independent or dependent samples?arrow_forwardiid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²arrow_forward2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).arrow_forward
- matharrow_forwardCompute the median of the following data. 32, 41, 36, 42, 29, 30, 40, 22, 25, 37arrow_forwardTask Description: Read the following case study and answer the questions that follow. Ella is a 9-year-old third-grade student in an inclusive classroom. She has been diagnosed with Emotional and Behavioural Disorder (EBD). She has been struggling academically and socially due to challenges related to self-regulation, impulsivity, and emotional outbursts. Ella's behaviour includes frequent tantrums, defiance toward authority figures, and difficulty forming positive relationships with peers. Despite her challenges, Ella shows an interest in art and creative activities and demonstrates strong verbal skills when calm. Describe 2 strategies that could be implemented that could help Ella regulate her emotions in class (4 marks) Explain 2 strategies that could improve Ella’s social skills (4 marks) Identify 2 accommodations that could be implemented to support Ella academic progress and provide a rationale for your recommendation.(6 marks) Provide a detailed explanation of 2 ways…arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt