Question

Q1. This year, the standard deviation of revenues is higher in our industry. This indicates competitors’ revenues has become more similar to each other. True or False?

Q2.

68% of these firms have ROAs that range between .23 – .04 and .23 + .04

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .04 from or adding .04 to the mean? It is because the first rule says “1 standard deviation”. Therefore, I translate the above information as follows:

Approximately (      ) firms have ROAs between ( ) and (   ).

Q3.  95% of these firms have ROAs that range between .23 – .08 and .23 + .08

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .08 from or adding .8 to the mean? It is because the first rule says “2 standard deviations”. Since one standard deviation is .04, two standard deviations will be .04+.04 = .08. Therefore, I translate the above information as follows:

Approximately, (       ) firms have ROAs between (   ) and ( ).

Q4. 99.7% of these firms have ROAs that range between .23 – .12 and .23 + .12

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .12 from or adding .12 to the mean? It is because the first rule says “3 standard deviations”. Since one standard deviation is .04, three standard deviations will be .04+.04+.04 = .12 Therefore, I translate the above information as follows:

Approximately, (     ) firms have ROAs between ( ) and (   ).

Q5.

In a sample of firms, 1^st quartile of their ROAs is 0.05 and 3^rd quartile is 0.37. Which of the following is(are) outlier(s)?

                                                -1.44      -0.88       -0.15       0.09        0.37       0.59     1.28      1.78      2.95

Answer:

Q1 = (   )          Q3=(    )       IQR = ( ) - (   )= ( )

Lower boundary = ( ) – 3 x ( )= (   )

Upper boundary = ( ) + 3 x (   )=   ( )

Therefore, any number below (   ) or above ( ) will be considered as outliers. In the above case, outlier(s) is(are) (            )

Answer 1

Result:

Q1. This year, the standard deviation of revenues is higher in our industry. This indicates competitors’ revenues has become more similar to each other. True or False?

Answer: True. (similar data values result in smaller standard deviation)

Q2. 68% of these firms have ROAs that range between .23 – .04 and .23 + .04

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .04 from or adding .04 to the mean? It is because the first rule says “1 standard deviation”. Therefore, I translate the above information as follows:

Approximately (   68%   ) firms have ROAs between ( 0.19) and ( 0.27 ).

Q3.  95% of these firms have ROAs that range between .23 – .08 and .23 + .08

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .08 from or adding .8 to the mean? It is because the first rule says “2 standard deviations”. Since one standard deviation is .04, two standard deviations will be .04+.04 = .08. Therefore, I translate the above information as follows:

Approximately, (   95%    ) firms have ROAs between (  0.15 ) and (0.31 ).

Q4. 99.7% of these firms have ROAs that range between .23 – .12 and .23 + .12

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .12 from or adding .12 to the mean? It is because the first rule says “3 standard deviations”. Since one standard deviation is .04, three standard deviations will be .04+.04+.04 = .12 Therefore, I translate the above information as follows:

Approximately, ( 99.7%    ) firms have ROAs between ( 0.11) and (  0.35 ).

Q5.

In a sample of firms, 1st quartile of their ROAs is 0.05 and 3rd quartile is 0.37. Which of the following is(are) outlier(s)?

                                                -1.44      -0.88       -0.15       0.09        0.37       0.59     1.28      1.78      2.95

Q1 = (  0.05 )          Q3=(  0.37 )       IQR = (0.37 ) - (  0.05 )= (0.32 )

Lower boundary = (0.05 ) – 3 x (0.32 )= (  -0.91 )

Upper boundary = ( 0.37) + 3 x ( 0.32 )=   (1.33 )

Therefore, any number below ( -0.91 ) or above (1.33 ) will be considered as outliers. In the above case, outlier(s) (are) (   -1.44, 1.78, 2.95   )