Business Statistics

Question 1

An accounting professor obtained a random sample of 112 final exam grades for an introductory accounting class:

(a) Consider the following Descriptive Statistics of the data generated by Excel (PHStat), comment on the parameters measuring central tendency, dispersion of accounting exam grades of 112 students.

Accounting Grades

Mean

76.08928571

Standard Error

0.971940103

Median

76.625

Mode

65.25

Standard Deviation

10.2860472

Sample Variance

105.8027671

Kurtosis

-0.807465022

Skewness

-0.111712841

Range

43.75

Minimum

53

Maximum

Sum

96.75

8522

Count

112

As measures of central tendency, the median and mean of this sample indicate an average grade of 76-77. Interestingly, the final measure of central tendency; the mode indicates that the most common score was 65.25, more than 10 points below the mean and median. In cases of such discrepancy between measures of central tendency we favour the mean and median as the mode is more of a chance finding and is therefore less robust. Because the mean and median values are very close, we can estimate that the sample data is symmetrical and follows an approximately normal distribution. This observation is further supported by very low values of skewness and kurtosis: the Kurtosis value hints a slightly flat top while the skewness indicates that its symmetry is very slightly to the left. The average difference of each observation from the mean (standard deviation) was 10.2860472. The standard error in this sample is less than one mark confirming the variation of this sample data to the population data is minimal.(b) Consider the following frequency distribution generated by Excel. What is the missing frequency value identified by asterisk?

(i) (8 / 7.14)* 20.54 = 23 (ii) (7.14 / 8)* 39 = 34.81 (iii) 34.81 + 27.68 = 62.49 (iv) 62.49 + 26.79 = 89.28 (v) 100 – 89.28 = 10.71 (vi) (8 / 7.14)* 10.71 = 12

Frequencies (Accounting Grades)

Bin Frequency Percentage Cumulative Range...