Explanation Given: The set of numbers mentioned is 75, 72, 83, 85, 77, 89 and 7.9. Formula used: Mean: Mean = sum of the data values number of data values Range: Range = largest data value − smallest data value Standard deviation: Standard deviation ( s ) = sum of ( x − x ¯ ) 2 n − 1 In the formula, x ¯ denotes the mean, ( x − x ¯ ) denotes the deviation from the mean and n is the number of values in the set. Calculation: Range: The set of numbers is 75, 72, 83, 85, 77, 89 and 7.9. In this set the smallest value is 72 and the largest value is 89. Substitute 89 for the ‘largest data value’ and 72 for the ‘smallest data value’ in the range formula. Range = 89 − 72 = 17 Thus, the value of range is 17 _ . Standard deviation: The set of numbers is 75, 72, 83, 85, 77, 89 and 79. The number of data values is 7. That is n = 7 . Add all the data values for ‘sum of data values’ and substitute 7 for ‘number of data values’ in the mean formula. Mean ( x ¯ ) = 75 + 72 + 83 + 85 + 77 + 89 + 7.9 7 = 560 7 = 80 The deviation from the mean and square of deviation is, Numbers ( x − x ¯ ) ( x − x ¯ ) 2 75 ( 75 − 80 ) = − 5

Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)

11th Edition

ISBN: 9780134756967

Author: Hal Saunders, Robert Carman

Publisher: PEARSON

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Chapter 12.3, Problem 3AE

To determine

The range and the standard deviation for set of numbers 75, 72, 83, 85, 77, 89 and 7.9.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 2AE

Chapter 12.3, Problem 4AE

Students have asked these similar questions

Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.

Module Code: MATH380202 1. (a) Define the terms "strongly stationary" and "weakly stationary". Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is weakly stationary, define the autocorrelation function (acf) Pk, for lag k. What conditions must a process {X+) satisfy for it to be white noise? (b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of the following processes {X+} are weakly stationary for t> 0? Briefly justify your answers. i. Xt for all > 0. ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0. (c) Provide an expression for estimating the autocovariance function for a sample X1,..., X believed to be from a weakly stationary process. How is the autocor- relation function Pk then estimated, and a correlogram (or acf plot) constructed? (d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where {E} is a white noise process with variance 1. Compute the population autocorre- lation function Pk for all k = 0, 1, ....

Chapter 12 Solutions

Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)

Ch. 12.1 - Solve: 0.82=x100 Ch. 12.1 - Prob. 2LC Ch. 12.1 - Automotive Trades The following bar graph shows...Ch. 12.1 - Trades Management The following graph shows the...Ch. 12.1 - General Interest The following double bar graph...Ch. 12.1 - General Interest The following stacked bar graph...Ch. 12.1 - Allied Health When Dr. Friedrich began working at...Ch. 12.1 - Automotive Trades The following line graph shows...Ch. 12.1 - Construction The following double-line graph...Ch. 12.1 - General Interest Study the circle graph at the top...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The range and the standard deviation for set of numbers 75, 72, 83, 85, 77, 89 and 7.9.

Solution Summary: The author calculates the range and standard deviation for the set of numbers 75, 72, 83, 85, and 77.

Concept explainers

Videos

The range and the standard deviation for set of numbers 75, 72, 83, 85, 77, 89 and 7.9.

Want to see the full answer?

Chapter 12 Solutions