Question 2 solve this problem without using minitab consider...

Question # 2: (Solve this problem without using MINITAB) Consider the following observations: 14 21 23 21 16 19 22 25 16 16 24 21 35 22 24 21 39 07 14 20 (a) [16 points] Calculate the values of the sample mean, sample median and sample standard deviation. (b) [4 points] If you remove the highest and the lowest value of the above data set which of the above measures will or will not change. Explain your answer.

Transcript

00:01 Hello students here the sample data is given 6, 8 so on till 142 so we are asked to find the q1, q3 and iqr.

00:17 So q1 is the first required tile is if you have this much of data sets here the median will lie so q1 means median of these observations so here if we divide the data into the two sets we will be having 6 at the first that will come here and the median will come here since there are 22 observations there will be two elements in the middle so that is 35 and 40 if you see the data you can find it.

01:01 So this is 142 so the q1 is the median of the first half of the observation so q1 lies over here so here you can see the middle observation here is 16.

01:18 So q1 is equal to 16 and then we ask you to find q3 which is the median of the next half observation.

01:29 So that lies here and the q3 here is 59 so q3 is 59 which is third quartile and then we have to find iqr.

01:45 Iqr means interquartile range which is q3 minus q1 which is equal to 59 minus 16 which is equal to 43.

02:00 So the correct answer is out of given options the correct answer is 16, 43, 59.

02:20 Now the next question we ask you to find how many outliers are there.

02:28 So to find the outliers the lower bound for the outliers is given by lower bound is equal to q1 minus 1 .5 into iqr.

02:43 If any observations falls beyond this value like if it takes the value less than this value it will be considered as outlier and upper bound is equal to q3 plus 1 .5 into iqr and if any value is more than this value that will be considered as outlier.

03:05 So just substitute here 16 minus 1 .5 into 43 which is equal to minus 48 .5 this is equal to 15 plus 1 .5 into 43 which is equal to 123 .5 and when we see the observation we can observe that no value is less than this lower bound but 131 and 142 are more than this value.

03:45 So these two will be considered as outliers.

03:48 So for the question using the sample data in question 1 how many outliers are identified? two outliers are identified.

04:06 Then the next question in the next question using the same information, so we have to subtract 10 from every observation...

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