Question

the grades for the trigonometry exam are listed below. find the range. 85, 76, 93, 82, 84, 90, 75
7
15
93
18
question 18 (3 points)
the grades for the trigonometry exam are listed below. find the standard deviation. 85, 76, 93, 82, 84, 90, 75
22.1
6.7
44.3
4.7

Explanation:

Step1: Find the maximum and minimum values

The given data set is \(85, 76, 93, 82, 84, 90, 75\). The maximum value \(max = 93\) and the minimum value \(min=75\).

Step2: Calculate the range

The formula for the range \(R\) of a data - set is \(R = max - min\). So, \(R=93 - 75=18\).

for standard deviation:

Step1: Calculate the mean

The mean \(\bar{x}=\frac{85 + 76+93+82+84+90+75}{7}=\frac{585}{7}\approx83.57\)

Step2: Calculate the squared differences

\((85 - 83.57)^2=(1.43)^2 = 2.0449\)
\((76 - 83.57)^2=(- 7.57)^2 = 57.3049\)
\((93 - 83.57)^2=(9.43)^2 = 88.9249\)
\((82 - 83.57)^2=(-1.57)^2 = 2.4649\)
\((84 - 83.57)^2=(0.43)^2 = 0.1849\)
\((90 - 83.57)^2=(6.43)^2 = 41.3449\)
\((75 - 83.57)^2=(-8.57)^2 = 73.4449\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{2.0449 + 57.3049+88.9249+2.4649+0.1849+41.3449+73.4449}{7 - 1}=\frac{265.7143}{6}\approx44.286\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{44.286}\approx6.7\)

Answer:

18