Question

Problem B: The following dataset is given: 4, 18, 18, 6, 15, 18, 9, 9, 20, 32 (8) Refer to Problem B. Calculate the median and the mode. (1) median = 16.5, and mode = 9 (3) median = 16.5, and mode = = 18 (2) median = 18, and mode = 18 (4) median = 18, and mode = 16.5 (9) Refer to Problem B. Assume that the dataset is a sample, not a population. Calculate the z-score for the value x = 16.5. (1) 3.799 (2) 0.194 (3) 0.375 (4) 0.000 (10) Refer to Problem B. Calculate the lower quartile and the upper quartile. (1) lower quartile = 2.75; upper quartile = 8.25 (2) lower quartile = 7.5; upper quartile = 18 (3) lower quartile = 8.25; upper quartile = 18.5 (4) lower quartile = 9.28; upper quartile = 16.5

Answer 1

Answers :

(8)

(3) median = 16.5 & mode=18

Explanation as below Table-1

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(9)

(2) 0.194

Explanation as per Table-1 below and Z -score calculations as below:

Given value X=	16.5
Mean=	14.9
SD=	8.2657

Z=	(X - Mean ) / SD
Z=	(16.5-14.9)/8.2657
Z=	0.194

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(10)

(3) lower quartile = 8.25 ; upper quartile = 18.5

Explanation as per below Table-1

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Note : Since no methodology was mentioned in the question, Excel was used.

Please consider this while giving your feedback.

Table-1 : Excel Output

Page Layout Bs File Home Insert & Cut En Copy Paste Format Painter Clipboard Calibri BI U Font B2 A B 1 Data 2 4 6 3 4 9 9 5 6 7 15 18 8 18 18 o O 20 32 14.9 8.2657 10 11 12 13 Mean 14 Standard Deviation (SD) 15 16 Median 17 Mode 18 19 Lower Quartile 20 Upper Quartile 21 16.5 18 8.25 18.5

Formulae in Excel as below:

<I Page Layout Formulas Da OS File Home Insert * Cut E Copy Paste Format Painter Clipboard 11 Å Calibri BIU A Font C8 А B 1 Data 2 4 3 6 4 9 5 9 6 15 7 18 8 18 9 18 10 20 11 32 12 13 Mean =AVERAGE(B2:311) 14 Standard Deviation (SD) ESTDEV.S(B2:311) 15 16 Median =MEDIAN(B2:311) 17 Mode =MODE.SNGL(B2:311) 18 19 Lower Quartile =QUARTILE.EXC(B2:B11,1) 20 Upper Quartile =QUARTILE.EXC(B2:B11,3) 21

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