question 3 of 14 (1 point) bowl winner scores the data show the scores of the winning teams of a certain…

Explanation:

Step1: Calculate the mean

Let the data set be (x_1,x_2,\cdots,x_n). First, find the sum of the data values. (n = 20). (\sum_{i = 1}^{20}x_i=24 + 49+47+31+47+47+30+25+40+46+37+36+32+27+19+39+34+48+18+37=710) The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{710}{20}=35.5)

Step2: Calculate the squared - differences

For each data value (x_i), calculate ((x_i-\bar{x})^2). For example, when (x_1 = 24), ((24 - 35.5)^2=(- 11.5)^2 = 132.25). Do this for all 20 data values and sum them up. (\sum_{i = 1}^{20}(x_i - 35.5)^2=132.25+182.25+132.25+19.53+132.25+132.25+30.25+110.25+20.25+110.25+2.25+0.25+10.25+72.25+272.25+12.25+2.25+156.25+290.25+2.25 = 1599)

Step3: Calculate the variance

Since we assume the data is a sample, the variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}). Here, (n=20), so (s^2=\frac{1599}{19}\approx84.2)

Step4: Calculate the standard deviation

The standard deviation (s=\sqrt{s^2}), so (s=\sqrt{84.2}\approx9.2)

Answer:

The variance is (84.2) The standard deviation is (9.2)