Please solve the following problem and the parts being asked of it!!! For each o

Question

Please solve the following problem and the parts being asked of it!!!

For each of the following samples of scores, obtain the mean, median, mode, range, interquartile range, semi-interquartile range, sum of squares, variance, standard deviation, and unbiased estimate of population variance (i.e., variance estimate). a. 12, 11, 18, 14, 13, 14, 28, 15 b. 7, 9, 8, 10, 4, 12, 6, 5 c. 5, 5, 5, 5, 5, 5, 5, 5 Which measures of central tendency and variability would be most appropriate for the scores in part a of question #1? Why? In part b of question #1? Why?

Explanation / Answer

a) Arrange the number in ascending order

11, 12 , 13 , 14 , 14 , 15 , 18 , 28

Mean = 11 + 12 + 13 + 14 +14 + 15 + 18 + 28 = 125/8 = 15.625

median =(14 + 14)/2 = 14

mode = 14

Range = (Highest - smallest) value = ( 28 -11) = 17

Quartile 1 = (12+13) /2 = 12.5

quartle 2 = (14+14) / 2 = 14

Quartile 3 = ( 15 + 18) / 2 = 16.5

Interquartle range = Q3 - Q1 = 16.5 - 12.5 = 4

Semi quartile range = 4/2 = 2

Sum of squares = sum( x -mean)^2 = 205.875

Variance = sum( x -mean)^2 / n = 25.73438

std. deviation =sqrt(25.73438) = 5.072

b)

Arrange the number in ascending order

4 , 5 , 6 , 7 , 8 ,9 ,10 , 12

Mean = 4 + 5 + 6 + 7 +8 + 9 + 10 + 12 = 61/8 = 7.625

median =(7+8)/2 = 7.5

mode = No mode

Range = (Highest - smallest) value = ( 12 -4) = 8

Quartile 1 = (5+6) /2 = 5.5

quartle 2 = ( 7+ 8 ) / 2 = 7.5

Quartile 3 = ( 9 + 10) / 2 = 9.5

Interquartle range = Q3 - Q1 = 9.5 - 5.5 = 4

Semi quartile range = 4/2 = 2

Sum of squares = sum( x -mean)^2 = 49.875

Variance = sum( x -mean)^2 / n = 6.234375

std. deviation =sqrt(6.234375) = 2.496

c) 5,5,5,5,5,5,5,5

Mean =5+5+5+5+5+5+5+5/8 = 5

median =(5+5)/2 = 5

mode = 5

Range = (Highest - smallest) value = ( 5-5) = 0

Quartile 1 = (5+5) /2 = 5

quartle 2 = ( 5+5 ) / 2 = 5

Quartile 3 = ( 5+5) / 2 = 5

Interquartle range = Q3 - Q1 = 5 - 5 = 0

Semi quartile range = 0

Sum of squares = sum( x -mean)^2 = 0

Variance = sum( x -mean)^2 / n = 0

std. deviation =0

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