JNTU Pharm. D IV Year BIOSTATISTICS AND RESEARCH METHODOLOGY Previous Question Paper (October - 2020 - R08)

To calculate the mean and median for the grouped frequency distribution, we first determine the midpoints (x) and cumulative frequencies (cf).

1. Mean Calculation:

2. Median Calculation:

The median class is identified by the value N/2 = 89/2 = 44.5. The cumulative frequency just greater than 44.5 is 65, corresponding to the class interval 40-50.

Where L = 40, N/2 = 44.5, cf = 33 (cumulative frequency of the preceding class), f = 32 (frequency of the median class), and h = 10 (class width).

To test whether the performance of salesmen and the sales across seasons differ significantly, we perform a Two-Way ANOVA without replication. Let the null hypotheses be: H01: There is no significant difference between the performance of salesmen. H02: There is no significant difference between the sales in different seasons.

Step 1: Calculate row totals (Seasons) and column totals (Salesmen):

Step 2: Calculate Correction Factor (CF):

Step 3: Calculate Sum of Squares (SS):

Total SS = Σx² - CF = (28² + 29² + ... + 35²) - 10220.83 = 10522 - 10220.83 = 301.17

SS (Rows/Seasons) = (110² + 112² + 128²) / 4 - 10220.83 = 41088 / 4 - 10220.83 = 51.17

SS (Columns/Salesmen) = (90² + 93² + 71² + 96²) / 3 - 10220.83 = 31066 / 3 - 10220.83 = 134.50

SS (Error) = Total SS - SS(Rows) - SS(Columns) = 301.17 - 51.17 - 134.50 = 115.50

Step 4: ANOVA Table:

Step 5: Conclusion. For df(2,6), F_crit at 5% is 5.14. For df(3,6), F_crit at 5% is 4.76. Since calculated F_R (1.33) < 5.14 and F_C (2.33) < 4.76, we fail to reject H01 and H02. There is no significant difference in performance between salesmen or between seasons.