# Math Help - Confidence interval,sample mean,Mode,standard deviation,Median

1. ## 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:

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

(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

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

2. 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?

3. 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

(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

4. 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 $\biggl(\bar X-t_{n-1,\alpha/2}{S\over \sqrt n} , \bar X+t_{n-1,\alpha/2}{S\over \sqrt n}\biggr)$

5. 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:

mode is the most frequently ocurring value