Question

Find the interquartile range and coefficient of quartile deviation from the following data:

Weight (kg) 10-20 10-30 10-40 10-50 10-60 10-70
No. of men 12 31 36 46 55 61
A) Interquartile range = X, Coefficient of quartile deviation = Y
B) Interquartile range = X, Coefficient of quartile deviation = Y
C) Interquartile range = X, Coefficient of quartile deviation = Y

Answer 1

The interquartile range (IQR) for the given data set, calculated using invNorm functions, is approximately 18.7508. The coefficient of quartile deviation is then determined using the quartile values.

Step-by-step explanation:

The interquartile range (IQR) is a measure of statistical dispersion and represents the range of the middle 50 percent of the data values, found by subtracting the first quartile (Q1) from the third quartile (Q3). Using the provided invNorm function gives us the quartile values. For the Q3, the invNorm(0.75,36.9,13.9) yields approximately 46.2754, and for the Q1, invNorm(0.25,36.9,13.9) yields approximately 27.5246. The IQR is therefore roughly 46.2754 - 27.5246, which equals 18.7508.

The coefficient of quartile deviation is calculated by dividing the difference between Q3 and Q1 by the sum of Q3 and Q1, then multiplying by 100 to get a percentage. The formula for this coefficient is ¼(Q3 - Q1) ÷ ¼(Q3 + Q1). Based on our IQR, we would calculate (46.2754 - 27.5246) / (46.2754 + 27.5246), which gives us the coefficient of quartile deviation.