Confidence interval,sample mean,Mode,standard deviation,Median

__Can you tell me if my answers true,and How can i obtain the confidence interval?__

**a)A samle of 10 students scored the following grades:**

**40,42,35,54,57,54,46,42,54,57**

**(i)Find the sample mean ,mode and median.**

__Sample mean:__

http://www10.0zz0.com/2009/05/28/03/985459744.jpg

http://www10.0zz0.com/2009/05/28/03/704514045.jpg

http://www10.0zz0.com/2009/05/28/03/602384295.jpg

__Sample mode:__

**mode is the most frequently ocurring value:**

**grades frequency**

**40 0**

**42 2 **

**35 0**

**54 3**

**57 2**

**46 0**

**In this example we have more than one modal (multimodal)**

**Mode=42,54,57**

__Median:__

**First we must arrange the numbers in increasing order.**

**35,40,42,42,46,54,54,54,57,57**

**Here the batch size is even,so we have 2 middle values:**

**First middle value occure at the position(n/2)=(10/2=5)**

**The first middle value is 46**

**second**** middle** **value occure at the position[(n/2) +1]=6**

**The second middle value is 54**

**Median =[(46+54)/2]=50**

**(ii)Compute the sample standard deviation**

http://www10.0zz0.com/2009/05/28/04/914408865.jpg

http://www10.0zz0.com/2009/05/28/04/698296410.jpg

**(iii)Find 90%and 95%confidence intervals for the scores**

**How can I get the confidence interval ..**

**Here the sample size is <25 (sample size=10)**

**I know how to obtain the confidence interval when the sample size >25**

**buthow to obtain the confidence interval when the sample size <25**

**(B)Suppose that the grades in a course are normally distributed with mean**** 69 and standard deviation 12.**

**(i)Determine the ranges in which 90%,95%,and 99% of grades lie.**

**Approximately 90%grades were between:**

**(µ -1.64 *σ) and (µ+1.64 *σ)**

**(69-1.64*12) and(69+1.64*12)**

**(69-19.68) and (69+19.68)**

**49.32 and 88.68**

**================================**

**Approximately 95%grades were between:**

**(µ -1.96*σ) and (µ+1.96*σ)**

**(69-1.96*12) and(69+1.96*12)**

**(69-23.52) and(69+23.52)**

**45.48 and 92.52**

**=================**

**Approximately 95%grades were between:**

**(µ -2.58*σ) and (µ+2.58*σ)**

**(69-2.58*12) and(69+2.58*12)**

**(69-30.96) and(69+30.96)**

**38.04 and 99.96**

**==============================**

**(ii)Write down the mean and the standard error of the mean of samples of size 144.**

**Since n>25**

**x=µ=69**

**http://www10.0zz0.com/2009/05/28/03/385311662.jpg**

**(iii)Find a range of values within which the means of approximately 95% of sample of size 144 lie.**

__http://www10.0zz0.com/2009/05/28/04/829750788.jpg__