Homework Answers
Suppose all the sample points are arranged in accending order like y1<y2<.....<yn
i.e yi where i = 1,2,3,...,n
1I Mode
we know that mode is most repeted observation in the sample if yi is most repeted obaservation then Mode = yi
hence it always lies between largest and smallest data points i.e. y1 and ynbut if i =1 or i = n then it is exactly equal to y1 or yn
2) Midpoint
midpoint is middlemost value of the data
Midpoint is always lies between largest and smallest data points because
midpoint = (largest value - smallest value)/2
but if there is only one point then it is exactly equal to y1 or yn
3)Median
median is the mid value of the given data i.e yi
therefore median is always lies between largest and smallest data points because
median = value of (n/2)th observation.
4)mean
mean is the average value of the data points hence mean is always lies between largest and smallest data points
mean = (sum of all obs) / (totale number of observation )
when there is only one point like y1 or yn then it is equal to y1 or yn
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Suppose all n data values in a data set are organized as yi < y2 <......
2. Harmonic Mean Suppose all n data values in a data set are positive, with 0...
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Flight 4581 travels daily from Pittsburgh to San Antonio. The flight is due into San Antonio at 5:07 p.m. The following list gives the Flight 4581 arrival time relative to 5:07 p.m. (in minutes) for a selection of 18 days. (A negative number means that the flight arrived early.) -8, -4,-3, -2,-1, 1, 2, 3, 4, 5, 6, 6, 7, 11, 16, 22, 28, 39 Frequency 8 6 4 2- -10 0 10 20 30 Arrival time relative to 5:07...
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I want to know the answer and
explanation of (d) and (f).
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2. Harmonic Mean Suppose all n data values in a data set are positive, with 0 < y1S n < < Use the second derivative test from calculus to show that the value of the hypothesis h that minimizes the loss function L(h) = Σ (1-1)2 h i に1 is the harmonic mean of the data, defined as
As before, suppose we have N data points of the form (21, yı), (C2, y2),..., (IN, YN). We consider the linear model Yi = Bo + Bili + Ej. Substitute into this equation the formula for Bo given at the bottom of page 2 in the “linearregression.pdf" notes. Then sum both sides from i=1 to i = N. In this way, compute the total sum of errors: What does this sum equal? (Please enter a numerical value.)
1. Suppose a population of N individuals has true (unknown) numerical measurements yi, y2, …YN (repeats allowed). The unknown population mean 1S yj One way to estimate the unknown population mean μ is to decide on a number nS N, then successively randomly select one individual at a time, observe and record the quantity of interest for that individual, put that individual back in, and repeat the process n times. Then form the mean of the recorded n observations. Prove...
A survey of 23 retirees was taken. Among other things, the retirees were asked to report the age at which they retired. Here are those 23 ages (in years). 33, 47, 49, 49, 52, 58, 59, 59, 61, 64, 64, 65, 66, 66, 67, 67, 68, 69, 71, 71, 74, 74, 76 Frequency 10 10+ 4 2+ 01A 30 40 50 60 Age (in years) 70 80 (a) For these data, which measures of central tendency take more than one...
Flight 4581 travels daily from Pittsburgh to San Antonio. The flight is due into San Antonio at 5:07 p.m. The following list gives the Flight 4581 arrival time relative to 5:07 p.m. (in minutes) for a selection of 18 days. (A negative number means that the flight arrived early.) -8, -4,-3, -2,-1, 1, 2, 3, 4, 5, 6, 6, 7, 11, 16, 22, 28, 39 Frequency 8 6 4 2- -10 0 10 20 30 Arrival time relative to 5:07...
σ2). 6. Suppose X1, Yİ, X2, Y2, , Xn, Y, are independent rv's with Xi and Y both N(μ, All parameters μί, 1-1, ,n, and σ2 are unknown. For example, Xi and Yi muay be repeated measurements on a laboratory specimen from the ith individual, with μί representing the amount of some antigen in the specimen; the measuring instrument is inaccurate, with normally distributed errors with constant variability. Let Z, X/V2. (a) Consider the estimate σ2- (b) Show that the...
I want to know the answer and
explanation of (d) and (f).
2. Percentiles and Quartiles Given a data set with n data values yvi < /2 ..S yn, define the pth percentile of the data set to be the element at index ceiling, and it means that we always round up to the next integer. For example, suppose we have a data set with n - 13 elements, and we want to calculate the 25th percentile of the data...
1. Statistical Parameters: it all the time. The data set presented in Table 1 represents a sample of stream flows in a perennial stream for a 45-day period, These stream flows were measured using a flow meter that has a precision of t0.1 Cfs. Find the following statistical parameters for the sample data given in Table 1. A perennial stream is a stream that has water flowing in a. Central Tendency i. Mean the average value of the random variable....
4. (10pts)For each of the data set below, find the mean (i) and standard (1) (4pts) 10 (2) (4pts) 20 18 16 12 14 (3) (2pts) From the results of (1) and (2), what do you think the standard deviation is for the numbers (101, 103, 105, 107, 109)? (In generol, ony S consecutive even numbers or s numbers should have exactly the same stondard deviation, since their spread are of 2 (6pts) Mean is a measure of the center...
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