Given the following students' test scores (95, 92, 90, 90, 83, 83, 83, 74, 60, and 50), identify the mean, median, mode, range, variance, and standard deviation for the sample. Write a 500-750-word summary and analysis discussing the results of your calculations. State your results for the sample: the mean, median, mode, range, variance, and standard deviation Explain which method is best for this data set. Why? Conduct a one sample T-test and interpret the results. In what situations would this information be useful? Your homework this week has you conducting a one-sample t-test on the data. The problem with this is that we do not have enough information to conduct a one-sample t-test. We are missing the proposed population mean with which to compare our results. Since the t-test is on the rubric, I am going to give you the population mean to compare this sample to: 70! So, when you are conducting your one-sample t-test, be sure to use ‘70’ for the population mean to compare this group to. be sure to tell me whether you conducted a one-tailed or two-tailed test.

Answer:

Mean:

Also known as the average. The mean is found by adding up all of the given data and
dividing by the number of data entries.

Mean=sum/n =  (95+92+ 90+ 90+ 83+ 83+ 83+ 74+ 60+ 50)/10=80

Median:

The median is the middle number. First you arrange the numbers in order from lowest
to highest, then you find the middle number by crossing off the numbers until you reach the
middle.

As you can see we have two numbers, there is no middle number. What do we do?
It is simple; we take the two middle numbers and find the average, ( or mean ).

So median=(83+83)/2=83

Mode:

this is the number that occurs most often.

So mode is 83

All of the measures give almost similar results.So anything is good.

The variance combines all the values in a data set to produce a measure of spread. The variance (symbolized by S²) and standard deviation (the square root of the variance, symbolized by S) are the most commonly used measures of spread.

Variance (S²) = average squared deviation of values from mean

=(225+144+100+100+9+9+9+36+400+900)/10=193.2

Standard deviation (S) = square root of the variance

=sqrt(193.2)=13.9

One-Sample T-Test

The one-sample t-test is a member of the t-test family. All the tests in the t-test family compare differences in mean scores of continuous-level (interval or ratio), normally distributed data. The 1-sample t-test does compare the mean of a single sample. Unlike the other tests, the independent and dependent sample t-test it works with only one mean score.

2 tail t test

Ho:Means are equal

Ha:They are not equal

t=70-80/13.8=-0.7246

Compare it with t value at 9 degrees of freedom and(the significance level you choose) and then decide whether to

reject the null hypothesis