Question

4- Variance and Standard deviation (how far the data values lie from the mean) The mean, mode, and median do a nice job in telling where the center of the data set is, but often we are interested in more. For example, a pharmaceutical engineer develops a new drug that regulates iron in the blood. Suppose she finds out that the average sugar content after taking the medication is the optimal level. This does not mean that the drug is effective. There is a possibility that half of the patients have dangerously low sugar content while the other half have dangerously high content. Instead of the drug being an effective regulator, it is a deadly poison. What the pharmacist needs is a measure of how far the data is spread apart. This is what the variance and standard deviation do. - the variance equation: - the standard deviation equation: s=1 (x-x) n-1- 1- Calculate the mean, x. 2- Write a table that subtracts the mean from each observed value. 3- Square each of the differences. 4- Add this column (in step 3). 5. Divide by n-1 where n is the number of items in the sample. This is the variance. 6- To get the standard deviation: take the square root of the variance.

Answer 1

4. The calculation is as shown below in Excel: (X-mean) =B4-$B$14 =B5-$B$14 =B6-$B$14 =B7-$B$14 =B8-$B$14 =B9-$B$14 =B10-$B$14 =B11-$B$14 =B12-$B$14 =B13-$B$14 Mean AVERAGE(B4:B13) Sum (X-mean)^2 =C4*C4 =C5*C5 =C6*C6 =C7*07 =C8*C8 =C9*C9 =C10*C10 =C11*C11 =C12*C12 =C13*C13 =SUM(D4:013) The output is: 44 (X-mean) (X-mean)^2 -5.2 27.04 0.8 0.64 38 -11.2 125.44 46.8 2190.24 -7.2 51.84 -2.2 4.84 40 -9.2 84.64 -10.2 104.04 46 1 -3.2 10.24 50 0.8 0.64 49.2 Sum 2599.6 Mean

Now divide the sum by 10 - 1 = 9 to get the variance as shown below: 52 2599.6 = 288.8 Now take the square root of the variance to get the standard deviation as shown below: s=15 = 288.8 =16.9 Hence the standard deviation is 16.9. 5. The range of the sample is calculated as follows: Range = 24-7 = 17 The number of intervals is calculated as follows: Intervals = 20 = 4.47 Hence, the number of intervals is 5. The width of the interval is calculated as follows: Width=17 = 3.4 -3 Hence, the width of the interval is 3.

The creation of categories is as shown below: Scores Categories Frequency 7 to 10 11 to 13 14 to 17 18 to 21 21 to 24 NW The histogram is as shown below: Histogram Frequency он м о р л а тоо 7 to 10 11 to 13 18 to 21 21 to 24 14 to 17 Categories Good luck with your studies!!!