Please help me. Thank you! 4. The heights of 100 studeuts at a local university

ID: 3066219 • Letter: P

Question

Please help me. Thank you!

4. The heights of 100 studeuts at a local university are given in the table below. (30 Points) Height Inchs) Class Mark Frequency 60 62 63 65 66 68 69-71 72-74 61 64 67 70 73 18 42 27 (a) Complete columns 3 through 6 in the work table below. You may enter the values directly from your caleulating our brain, or other). Include the total of each of columns 3, 5, and 6 where indicated. Finally, calculate D do it from both the device (y the average and the standard deviation, and then write your results in the spaces. For the S "r.m.s. of deviations fro calculations in the work space. n the mean" formula, and the formula which uses a?. SHOW ALL WORK for these final Average, = From r.m.s Formula) (From z2 Formula) 61 64 18 67 42 70 27 73 8 SD, Tz = _

Explanation / Answer

Question 4

Part a

Solution:

Required formulas are given as below:

Average = Xbar = f*x/f = f*x/n

f = n

SD = sqrt[f*(x - xbar)^2/(n – 1)]

SD = sqrt[(f*x^2 – ((f*x)^2/n))/(n – 1)]

f*x

x - xbar

f*x^2

f*(x - xbar)^2

305

-6.45

18605

208.0125

1152

-3.45

73728

214.245

2814

-0.45

188538

8.505

1890

2.55

132300

175.5675

584

5.55

42632

246.42

Total

100

6745

455803

852.75

From above table, we have

f = n = 100

Average = Xbar = f*x/f = f*x/n = 6745/100 = 67.45

Average = Xbar = 67.45

By using r.m.s formula,

SD = x = sqrt[f*(x - xbar)^2/(n – 1)]

x = sqrt[852.75/(100 – 1)]

x = sqrt(8.613636364)

x = 2.93489972

Now, by using x^2 formula, we have

x = sqrt[(f*x^2 – ((f*x)^2/n))/(n – 1)]

x = sqrt[(455803 – (6745^2/100))/(100 – 1)]

x = sqrt[(455803 - 454950.3)/99]

x = sqrt(852.75/99)

x = sqrt(8.613636)

x = 2.9349

f*x