ANSWER:
Min = 17
Max = 91
Range = 74
Mean = 53.04
Standard Deviation = 23.67
STEP-BY-STEP EXPLANATION:
We have the following data set:
[tex]26,\:29,\:60,\:28,\:37,\:72,\:68,\:29,\:65,\:85,\:74,\:68,\:88,\:26,\:59,\:46,\:40,\:80,\:31,\:45,\:86,\:23,\:91,\:17[/tex]The first thing we need to do is organize the data, as follows (ascending order):
[tex]17,\:23,\:26,\:26,\:28,\:29,\:29,\:31,\:37,\:40,\:45,\:46,\:59,\:60,\:65,\:68,\:68,\:72,\:74,\:80,\:85,\:86,\:88,\:91[/tex]In this way we can determine the minimum, maximum value and the range:
[tex]\begin{gathered} Min=17 \\ \\ Max=91 \\ \\ Range=91-17=74 \end{gathered}[/tex]We calculate the mean as follows:
[tex]\begin{gathered} \mu=\frac{26+29+60+28+37+72+68+29+65+85+74+68+88+26+59+46+40+80+31+45+86+23+91+17}{24} \\ \\ \mu=\frac{1273}{24} \\ \\ \mu=53.04 \end{gathered}[/tex]Now we calculate the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt{\frac{1}{n}\sum^n(x_i-\mu)^2} \\ \\ (x_i-\mu)^2=\lparen26-53.04)^2+\left(29-53.04\right)^2+\lparen60-53.04)^2+\lparen28-53.04)^2+\lparen37-53.04)^2+\left(72-53.04\right)^2+\lparen68-53.04)^2+\lparen29-53.04)^2+\lparen65-53.04)^2+\left(85-53.04\right)^2+\lparen74-53.04)^2+\lparen68-53.04)^2+\lparen88-53.04)^2+\left(26-53.04\right)^2+\lparen59-53.04)^2+\lparen46-53.04)^2+\lparen40-53.04)^2+\left(80-53.04\right)^2+\lparen31-53.04)^2+\lparen45-53.04)^2+\lparen86-53.04)^2+\left(23-53.04\right)^2 \\ \\ (x_i-\mu)^2=13444.96 \\ \\ \frac{1}{n}\operatorname{\sum}^n(x_i-\mu)^2=\frac{13444.95}{24}=560.21 \\ \\ \sigma=\sqrt{560.21} \\ \\ \sigma=23.67 \end{gathered}[/tex]