CHAPTER 3 3.2 Measures of Variability 91 The following data represent the exchan

Question

CHAPTER 3 3.2 Measures of Variability 91 The following data represent the exchange rates for the euro in terms of U.S. dollars from March 2011 until February 2013. These data can also be found in the Excel file titled Euro.xlsx. 3.9 1.40 1.44 1.43 1.44 1.43 1.43 1.38 1.37 1.36 1.32 1.29 1.32 1.32 1.32 1.28 1.25 1.23 1.24 1.29 1.30 1.28 1.31 1.33 1.35 Based on: http://www.oanda.com. a. Calculate the mean. b. Calculate the median. c. Determine the mode. d. Which of these three measurements would best describe the central tendency of the data? e. Describe the shape of this distribution. 3.10 Mark McGwire, a former Major League Baseball player

Explanation / Answer

First we arrange the data frrom smallest to largest.
1.23
1.24
1.25
1.28
1.28
1.29
1.29
1.3
1.31
1.32
1.32
1.32
1.32
1.33
1.35
1.36
1.37
1.38
1.4
1.43
1.43
1.43
1.44
1.44

n=24 which is even number,
Median = {[n/2]th +[(n/2)+1]}/2 th Observations
{[n/2]th +[(n/2)+1]}/2 = [(24/2)+(24/2)+1]/2 th Obs = (12th +13th)/2 = (1.32+1.32)/2 = 1.32

Mean=Sum(xi)/n = 32.11/24 = 1.34

Mode = Most frequent Observation = 1.32
Observe that,
Median = Mode < Mean Therefore distribution is Right tailed i.e. Positively Skewed.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---