Question

Volume of Altria Group Stock The volume of a stock is the number of shares traded on a given day. The following data, in millions, so that 3.78 represents 3,780,000 shares traded, represent the volume of Altria Group stock traded for a random sample of 35 trading days in 2004 3.78 8.74 4.35 5.02 8.40 6.06 5.75 5.34 6.92 6.23 5.32 3.25 657 7.57 6.07 3.04 5.64 5.00 7.16 4.88 10.32 3.38 725 6.52 4.43 3.38 5.53 4.74 9.70 3.56 10.96 450 797 3.01 558 With the first class having a lower class limit of 3 and a class width of 2 (a) Construct a frequency distribution. (b) Construct a relative frequency distribution. (c) Construct a frequency histogram of the data. (d) Construct a relative frequency histogram of the data. (e) Describe the shape of the distribution. (f) Repeat parts (a)-(e) using a class width of 1 (g) Which frequency distribution seems to provide a bet- ter summary of the data?

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Answer #1

a) The data must be arranged in ascending order The range of the vari able is Range - Maximum- Minimum 10.96 3.01 7.95 R - 7.95 The formula for calculating the class interval is Range Number of classes Class Interval= 7.95 4 1.9875 Class Interval =1.9875 The Computati on Table Class Interval Frequency 3-5 13 13 9-11 f 35 (b) The relative frequency distributi on Class Interval FrequencyRelative frequency 3-5 5-7 7-9 9-11 13 0.3714 0.3714 0.1714 0.0857 13

(c) The step-by-step instructions to obtain frequency histogram is obtained by using Excel2010 * Store the data Class interval, frequency in the columns of the Excel2010 worksheet Select the Entire range of the data Choose Îsert → Column → 2-D column * Select the Form at data series and series options *Reduce the Gap wi dth to zero. *Choose Design and chart layouts and then select 8th chart layout. * Click Close. The Frequency Histogram using Excel2010

The Frequency Histogram 0.4000 0.3500 0.3000 0.2500 0.2000 0.1500 0.1000 0.0500 0.0000 3-5 5-7 7-9 9-11 The class interval

Interpretation:

The frequency histogram illustrated about the data distribution, which is skewed to the right indicates that the mean is greater than the median of the data distribution. The frequency distribution of the trading days is skewed to the right.

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d) The step-by-step instructions to obtain relative frequency histogram is obtained by using Excel2010 * Store the data Class interval, Relative frequency in the columns of the Excel2010 worksheet. Entire range of the data Select the t Choose Insert -> Column -> 2- D column * Select the Form at data series and series options *Reduce the Gap wi dth to zero. * Choose Design and chart layouts and then select 8th chart layout * Click Close. The Relative Frequency Histogram using Excel2010:The Relative Frequency Histogram 0.4000 0.3500 0.3000 0.2500 0.2000 20.1500 0.1000 0.0500 0.0000 tr 5-7 The class interval 3-5 7-9 9-11

Interpretation:

The relative frequency histogram illustrated about the data distribution, which is skewed to the right indicates about the mean is greater than the median of the data distribution. The frequency distribution of the volume of trading days is right skewed.

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