27 Social Insurance Numpers e data of eat Exercise 1.70 (see data set EX0170), r

Question

27 Social Insurance Numpers e data of eat Exercise 1.70 (see data set EX0170), reprod below, show the last digit of the social number for a group of 70 students. uced 0 7342358 42 3 2002127 7 4 0099 5 3847 6 6 9 0262 95 8 quency 5 1777 8751 8 hts, Is 3 41938666 6 a. You found in Exercise 1.70 that the distribution of this data was relatively "flat," with each differeat value from 0 to 9 occurring with nearly equal frequency. Using this fact, what would be your bes estimate for the mean of the data set? 2.28 Social Insurance Numbers, continued Refer to the data set in Exercise 2.27 a. Find the percentage of measurements in the intervals x ± s, x ± 2s, and x ± 3s. ompare b. Use the range approximation to guess the value of b. How do the percentages obtained in part a compare for this set. c. Use your calculator to find the actual values of i and s. Compare and b with those given by the Empirical Rule? Should they be approximately the same? Explain. with your estimates in parts a

Explanation / Answer

Using Excel .

fiest type all data in excel.

1) best estimate for the mean of this data set is

mean = AVERAGE(A2:A71)

= 4.585714

2) using range approximatly gase the value of s.

Range = largest value - smallest value

= 9 - 0

= 9

s = range / 4 = 9 / 4 = 2.25

this is standard deviation (s) using Range.

3) Calculate X bar and s

Xbar =AVERAGE(A2:A71)

= 4.585714

s = STDEV(A2:A71)

= 2.8917

Problem 2.28

a) X bar - s = 1.693983

x bar + s =7.47446

Using normdist command

P( 1.69 < x < 7.47446) = P(X < 7.477446) - P(X < 1.69)

= 0.841345 - 0.158655

= 0.6826

So the 68 % data belongs to Xbar +s and Xbar - s  

Similarly Xbar + 2*s and Xbar- 2 *s belongs to 95 % data

and   Xbar + 3*s and Xbar- 3 *s belongs to 99.7 % data

b) comparing empirical rule we gate same result because both are same .

  

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