Question

Random Sample Selection 40 out of 60 students

What value is two standard deviations above the mean?
What value is 1.5 standard deviations below the mean?
Construct a histogram displaying your data.
In complete sentences, describe the shape of your graph.
Do you notice any potential outliers? If so, what values are they? Show your work in how you used the potential outlier formula to determine whether or not the values might be outliers.
Construct a box plot displaying your data.
Does the middle 50% of the data appear to be concentrated together or spread apart? Explain how you determined this.
Looking at both the histogram and the box plot, discuss the distribution of your data.

# of pencils	Frequency	Culumative Frequency	Relative Frequency	Cumulative Relative Frequency
0	5	5	0.125	0.125
1	14	19	0.35	0.475
2	10	29	0.25	0.725
3	7	36	0.175	0.90
4	1	37	0.025	0.925
5	0	37	0	0.925
6	0	37	0	0.925
7	1	38	0.025	0.95
8	1	39	0.025	0.975
9	0	39	0	0.975
10	1	40	0.025	1

Answer 1

Note : allowed to solve first four question in one post.

The method to find the mean and standard deviation is given below

Mean = 2.1
Standard devaiation = 2.09

What value is two standard deviations above the mean?

Mean + 2 std.dev = 2.1 + 2*(2.09)= 6.28

What value is 1.5 standard deviations below the mean?
Mean + 1.5 std.dev = 2.1 - 1.5*(2.09)= -1.035

Construct a histogram displaying your data.

In complete sentences, describe the shape of your graph
We see that the distribution is skewed to right, as it has some high bar on the left and a long tail on the right.