Answer:
![\bar X= 33.79167](https://tex.z-dn.net/?f=%20%5Cbar%20X%3D%2033.79167)
![s= 12.06497](https://tex.z-dn.net/?f=%20s%3D%2012.06497)
![SE= \frac{s}{\sqrt{n}}= \frac{12.06497}{\sqrt{24}}=2.463](https://tex.z-dn.net/?f=%20SE%3D%20%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%3D%20%5Cfrac%7B12.06497%7D%7B%5Csqrt%7B24%7D%7D%3D2.463)
![Median= \frac{30+31}{2}= 30.5](https://tex.z-dn.net/?f=Median%3D%20%5Cfrac%7B30%2B31%7D%7B2%7D%3D%2030.5)
Step-by-step explanation:
For this case we have the following data:
23, 16, 21, 24, 34, 30, 28, 24, 26, 18, 23, 23, 36, 37, 49, 50, 51, 56, 46, 41, 54, 30, 40, and 31
We can calculate the sample mean with the following formula:
![\bar X = \frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%20%5Cbar%20X%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
And replacing we got:
![\bar X= 33.79167](https://tex.z-dn.net/?f=%20%5Cbar%20X%3D%2033.79167)
Then we can calculate the standard deviation with this formula:
![s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}](https://tex.z-dn.net/?f=%20s%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D%7D)
And replacing we got:
![s= 12.06497](https://tex.z-dn.net/?f=%20s%3D%2012.06497)
And the sample size for this case is n =24. We can calculate the standard error with this formula:
![SE= \frac{s}{\sqrt{n}}= \frac{12.06497}{\sqrt{24}}=2.463](https://tex.z-dn.net/?f=%20SE%3D%20%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%3D%20%5Cfrac%7B12.06497%7D%7B%5Csqrt%7B24%7D%7D%3D2.463)
And the median for this case since the sample size is 24 first we need to sort the data on increasing order and we got:
16 18 21 23 23 23 24 24 26 28 30 30 31 34 36 37 40 41 46 49 50 51 54 56
And for this case the median would be the average from the position 12 and 13 and we got:
![Median= \frac{30+31}{2}= 30.5](https://tex.z-dn.net/?f=Median%3D%20%5Cfrac%7B30%2B31%7D%7B2%7D%3D%2030.5)