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Problem 30 Hard Difficulty

Earnings The table at the right shows the median weekly earnings of union and nonunion workers in various occupations.
a. Find the mean and the range of the data for union workers and for nonunion workers.
b. Find the standard deviation for each set of data.
c. Within how many standard deviations of the mean are earnings of the mean are earnings of $\$ 395$ for union workers? For nonunion workers?
d. Writing Compare the wages of union and nonunion workers. Use your results from parts (a) through (c).

Answer

a) a required value for the data set of union workers is:
Range $=279$
Mean, $\overline{x}=640.71$
a required value for the data set of non-union workers is:
Range $=317$
Mean, $\overline{x}=564.28$
b) the standard deviation for the union workers is 97.78 while for non-union workers it is 99.01
c) 6 items are within 1$\sigma$ of the mean and 7 items are within 2$\sigma$ of the mean
d) When compared the results obtained in part a, b and c of the above mentioned data, one observes that the wages of union workers is more than the non-union ones

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Video Transcript

you have the date off, we clearing off weekly earning Go Union and Non Union Workers Union. I'm non union workers off different occupation. For this given data we have to calculate mean that is expert and range where to calculate mean rate and standard deviation for both union and non union workers. So first, let us take union workers here. So for union workers, let us calculate mean for so mean is given by former Other Is X Bible because toe submission or fix that is information of the given data dared by the number off occupation that is in. So we'll get the value as summation up. This given well weekly income will because to 4 4085 dared by the number off occupation years summit. So we'll get the mean value as 6 40.7 So when we around this value, so we'll get them mean for this union workers as 6 41 So this is the answer For the first part. No second parties range where to find so range we have a formula for in that is greatest value. Greatest value in the off the income miners least value of the income. So in the income in the union working class that in union working class we can see that construction occupation is having greater sin. Cos so range will be closed toe 7 78 miners least income is from the trade that is for 99. So we'll get the range as to 79. So this is the range for the first union class now coming to standard division off Union class. That is sick month. So Sigma, the other formula is squared off. Summation off X minus X bar. The old square where expertise the mean divided by the number off occupation. So once upsetting the values will get this s square it off. 6000 69 66,022 donated by seven because number off occupation is seven. So we'll get this as 97.77 So when we around, this value will get The standard division has 98. So we got mean grains and standard deviation for union working class. Now coming to nonunion working class, that is we are to find mean again nonunion working class so mean that is ex Bible because two using the same formula that is summation off exterior by, and we'll get this asked. Permission off X is 9 3050 That is a summation off the income off the seven occupation. Do it by the total number of occupation in non union, also seven. So this will be caused to 5 64.2 So when we around this value so we'll get the mean as Fight 64 know where to find range for non union, so range will be caused to same formula that is greatest value when it's least value. So in Long Union the iest artilleries mining, which is 7 35 and the least arteries bread that is 40 80. So we'll get the Rangers 317 year. So this is the range now. The last part of the question is where to find standard deviation for non union that is standard division, the same formula. What we use previously for the union that a sig Marvel week was two square root off summation off X minus expert. The old square dirtied by the number off occupation, their expertise that mean so on sub shooting the values will get. This has 67 59,080 dared when number off occupation is seven. So we'll get decides square root off 8000 final and 16.85 So which is it close to 92.28? So that is around this value. So that is 92. So we'll get the standard deviation as 92 years. So this is the answer for this given caution.

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