Question

The first two columns of the accompanying table provide a frequency​ distribution, using limit​ grouping, for the days to maturity of 40 short-term investments. The third column shows the class marks. The raw​ days-to-maturity data are also provided. Complete parts​ (a) and​ (b) below.

Days to maturity   Frequency f   Class mark x
30-39 7    34.5
40-49 4    44.5
50-59 8    54.5
60-69    10 64.5
70-79 4    74.5
80-89 4    84.5
90-99 3    94.5

74, 69, 71, 51, 98, 65, 48, 53, 44, 30, 39, 36, 38, 49, 68, 53, 75, 38, 51, 66, 32, 64, 99, 69, 86, 87, 60, 64, 63, 70, 39, 55, 49, 86, 55, 61, 59, 56, 96, 88

A.) Use the​ grouped-data formulas to estimate the sample mean and sample standard deviation of the​ days-to-maturity data

B.) The true sample mean and sample standard deviation of the data are 61.4 and 18.3 respectively, rounded to one decimal place. Explain why the​ grouped-data formulas generally yield only approximations to the sample mean and sample standard deviation for​ non-single-value grouping. Choose the correct answer below.

A.It is the result of counting data values more than once for grouped data and only once for​ non-grouped data.

B.It is the result of using a class mark or midpoint to approximate data values rather than using the raw data..

C.It is the result of counting data values only once for grouped data and more than once for​ non-grouped data.

D.It is the result of intermediate round off error in the calculations for grouped data.

Answer 1

A)

∑f = 40 , ∑x*f = 2420 , ∑x²*f = 159170

Sample mean ( ) =   =

Sample mean ( ) = 60.5

Sample SD (s) =   =  

Sample SD (s) = 17.86

B) We calculate sample mean and sample sd for grouped data using the mid points of the class interval .

Answer : B.It is the result of using a class mark or midpoint to approximate data values rather than using the raw data..