In an attempt to judge and monitor the quality of instruction, the administratio

Question

In an attempt to judge and monitor the quality of instruction, the administration of Mega-Byte Academy devised an examination to test students on the basic concepts that all should have learned. Each year, a random sample of 10 graduating students is selected for the test. The average score is used to track the quality of the educational process Test results for the past 10 years are shown in the table below. EEB Click the icon to view test scores on exit exam data. Use these data to estimate the center and standard deviation for this distribution. Then calculate the two-sigma control limits for the process average. What comments would you make to the administration of the Mega-Byte Academy? The center of the distribution is estimated as.The standard deviation is(Enter your responses rounded to one decimal place)

Explanation / Answer

1. Xbarbar = sum ( xbar values of different years ) / No. of years

= 776/10 =77.6

Standard deviation of marks among the years = [ sum ( xbar-xbarbar)2 / N]1/2

Sum ( xbarbar -xbar)2 = (85-77.6)2 + ( 83-77.6)2 +....+ ( 68.3-77.6)2

= 54.76+ 29.16+ 20.25+6.76+ 4.84+2.25+2.25+0.25+24.01+86.49

= 231.02

SD = ( 23.1)1/2 = 4.80

Central value = 77.6

2 sigma limits =

77.6 +2x 4.8 = 87.2

77.6-2x4.8 = 68

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