Question

1. Suppose you are interested in examining the variability in current marital status by race indicated in the following data. Calculate (Step by step) by either using

   1.The Index of Qualitative Variation (IQV)

   2.The Range

   3.The Interquartile Range (IQR)

   4.The Standard Deviation (SD)

   5.The Variance

   for each racial group. At the end, provide interpretation of the calculated value for each racial group.

  

Current Marital Status	White (%)	Black (%)
Married	51.7	27.3
Widowed	8.9	8.5
Divorced	17.2	16.1
Separated	2.5	5.5
Never married	19.7	42.6

Answer 1

Statisticians use summary measures to describe the amount of variability or spread in a set of data. The most common measures of variability are the range, the interquartile range (IQR), variance, and standard deviation.

The Range :- MAXIMUM - MINIMUM

The interquartile range : Q3 - Q1  

Q3 is quartile 3

Q1 is quartile 1

variance :- σ² = Σ ( X_i - μ )² / N

Xi is sample value

μ is sample mean

N total number of sample

standard deviation = square root of the variance

white %	black %
Minimum:2.5 Maximum:51.7 range = 49.2	Minimum:5.5 Maximum:42.6 Range: = 37.1
Quartiles: Q1 --> 5.7 Q2 --> 17.2 Q3 --> 19.7 interquartile range (19.7-5.7) =14	Quartiles: Q1 --> 7 Q2 --> 16.1 Q3 --> 27.3 Interquartile Range (27.3-7) =20.3
N = 5 MEAN =20 VARIANCE = 360.6	N = 5 MEAN =20 Variance =230.4
Standard Deviation: 18.99	Standard Deviation: 15.18

INTERPRETATION :- there is huge variability in each racial group. race white marital status is are high variability than black race marital status because range, variance, and standard deviation value are higher in white race than black.according to interquartile range white race marital status distributed 14 % BETWWENQ3 AND Q1, black race marital status distribute 20.3 % distributed between Q3 and Q1.