1. Calculate the mean and standard deviation for the numbers 1 – 20.
i.e.) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Note: The set of numbers will be considered the population.
µ = _______σ = ________
2. With your calculator, randomly generate 5 numbers from the numbers 1 – 20, 30 times.
Use:[MATH]>>>PRB #5
RandInt(1,20,5)[ENTER]Note: You cannothave the same number repeated in the group of 5.
For example: You cannot have {2,2,10,13,8} where the 2 is repeated.
After you generate your first 5 numbers, write them down in the space below, then hit [ENTER] again to generate
another 5 numbers. When you finish, you should have 30 groups of 5numbers ranging from 1 – 20.
3. Calculate the mean for each of the 30 groups and write them in the space below. You should have 30 sample means
when you finish.
4. Calculate the mean and standard deviation for the 30 sample means. Place your values in the space below and
label your values with the appropriate symbols. Note: Enter your 30 sample means into L1 in your calculator
and do 1-var stat L1 to get the mean and standard deviation.
5. Using your values from part 1 and part 4, test the 3 properties of the Distribution of Sample Means:
a.) Write the property for Mean of the Sample Means. Show the values for your means and state whether they
approximate the property.
b.) Write the property for the Standard Deviation of the Sample Means. Show the values for your standard
deviations and state whether they approximate the property.
c.) On a piece of graph paper, draw a graph (histogram) to approximate the population, then draw a 2nd
histogram to approximate the 30 sample means. ( Hint: Create a frequency distribution for each set of
data – population and sample means – then draw a histogram for each frequency distribution.)
Answer :
Mean ( ) = 10.5
standard deviation ( σ ) = 5.7663
Explanation :
( 1 )
= 210 / 20
= 10.5
Create the following table.
So mean = 10.5
data | data-mean | (data - mean)^{2} |
1 | -9.5 | 90.25 |
2 | -8.5 | 72.25 |
3 | -7.5 | 56.25 |
4 | -6.5 | 42.25 |
5 | -5.5 | 30.25 |
6 | -4.5 | 20.25 |
7 | -3.5 | 12.25 |
8 | -2.5 | 6.25 |
9 | -1.5 | 2.25 |
10 | -0.5 | 0.25 |
11 | 0.5 | 0.25 |
12 | 1.5 | 2.25 |
13 | 2.5 | 6.25 |
14 | 3.5 | 12.25 |
15 | 4.5 | 20.25 |
16 | 5.5 | 30.25 |
17 | 6.5 | 42.25 |
18 | 7.5 | 56.25 |
19 | 8.5 | 72.25 |
20 | 9.5 | 90.25 |
∑(data - mean)^{2}= 665
σ = Sqrt ( ∑(data - mean)^{2} / n )
= Sqrt ( 665 / 20 )
= Sqrt ( 33 .25 )
= 5.76628130
~ 5.7663 ( approximately)
Get Answers For Free
Most questions answered within 1 hours.