I don't know what kind of calculator you have at your disposal, so I'll just give one way of computing the sample mean and standard deviation.
• To get the mean, add up all the data points and divide the total by the number of data:
[tex]\bar x = \displaystyle \sum_i \frac{x_i}n = \frac{1243+1264+\cdots+1275}9 \approx 1273.89 \\ \implies \boxed{\bar x \approx 1274}[/tex]
• To get the s.d. s, first compute the variance s² by adding up the squared difference between each of the data points and the sample mean, and divide the total by 1 less than the number of data:
[tex]s^2 = \displaystyle \sum_i \frac{\left(x_i-\bar x\right)^2}{n-1} = \frac{(1243-1274)^2+(1264-1274)^2+\cdots+(1275-1274)^2}8 \approx 1211.61[/tex]
The s.d. is the square root of the variance:
[tex]s^2 \approx 1211.61 \implies s \approx 34.8082 \implies \boxed{s\approx 35}[/tex]
The 90% confidence interval for the sample mean has upper and lower limits, respectively, of
[tex]\bar x \pm \dfrac{\left|Z_{\alpha/2}\right| s}{\sqrt n}[/tex]
(positive root for upper limit, negative root for lower limit)
where [tex]Z_{\alpha/2}[/tex] is the critical value for a (1 - α)×100% confidence level. By critical value, I mean
[tex]\mathrm{Pr}\left[ Z \le Z_c \right] = c[/tex]
where Z is a random variable following the standard normal distribution.
In this case, we have a 90% confidence level, so α = 0.1, and the critical value is [tex]Z_{0.05} \approx -1.64[/tex]. Then the confidence interval has upper limit
[tex]\bar x + \dfrac{\left|Z_{0.05}\right|s}{\sqrt n} = 1274 + \dfrac{1.64 \times 35}{\sqrt9} \approx 1292.97 \approx \boxed{1293}[/tex]
and lower limit
[tex]\bar x - \dfrac{\left|Z_{0.05}\right|s}{\sqrt n} = 1274 - \dfrac{1.64 \times 35}{\sqrt9} \approx 1254.8 \approx \boxed{1255}[/tex]
