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

• May 27th 2009, 09:13 PM
change_for_better
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:

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.

(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

================================
(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

=================

(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
• May 29th 2009, 03:44 AM
mr fantastic
Quote:

Originally Posted by change_for_better
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.

[snip]

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

Mode=42,54,57

[snip]

By definition the mode is 54. Why have you included 42 and 57?
• May 29th 2009, 09:10 PM
change_for_better
Quote:

Originally Posted by mr fantastic
By definition the mode is 54. Why have you included 42 and 57?

Thank you for alerting me .. I think that we must include the numbers that occure more than once

Can you help me in the following point

Quote:

(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

• May 29th 2009, 11:37 PM
matheagle
IF you are using S, then you need normality and this would be a t distribution with n-1=9 degrees of freedom.
So the 1.96 is incorrect.

And the interval is $\biggl(\bar X-t_{n-1,\alpha/2}{S\over \sqrt n} , \bar X+t_{n-1,\alpha/2}{S\over \sqrt n}\biggr)$
• May 30th 2009, 04:12 AM
mr fantastic
Quote:

Originally Posted by change_for_better
Thank you for alerting me .. I think that we must include the numbers that occure more than once Mr F says: No!

Can you help me in the following point

Read again carefully the definition you posted:

Quote:

mode is the most frequently ocurring value