Question

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 (use a population mean of 70). In what situations would this information be useful? Please use SPSS.

Answer 1

Answer:

Given data in question is shown below table

	X	X-mean	(X-Mean)2
	95	15	225
	92	12	144
	90	10	100
	90	10	100
	83	3	9
	83	3	9
	83	3	9
	74	-6	36
	60	-20	400
	50	-30	900
Total	800		1932
Mean	80

Number of observations =10

Mean = (sum of observations / Number of observations )

= 800 / 10

= 80

For finding median , arrange the data in ascending order as

50, 60, 74, 83, 83 , 83, 90, 90, 92, 95

Number of observations =10 (even)

Median:

=

Mode:

A number that appears most often is the mode.

Here, 83 appears most often in the given data.

So, mode = 83

Range:

Range = highest value - minimum value

= 95 - 50

= 45

Variance :

Standard Deviation :

The mean is the arithmetic average, and it is probably the measure of central tendency that you are most familiar.

The median is the middle value. It is the value that splits the dataset in half. To find the median, order your data from smallest to largest, and then find the data point that has an equal amount of values above it and below it.

Unlike the mean, the median value doesn’t depend on all the values in the dataset. Consequently, when some of the values are more extreme, the effect on the median is smaller. Of course, with other types of changes, the median can change. When you have a skewed distribution, the median is a better measure of central tendency than the mean.

The mode is the value that occurs the most frequently in your data set. If the data have multiple values that are tied for occurring the most frequently, you have a multi model distribution. If no value repeats, the data do not have a mode.

When you have a symmetrical distribution for continuous data, the mean, median, and mode are equal. However, if you have a skewed distribution, the median is often the best measure of central tendency.

Since mean is less than the median for the given data, we can conclude the data set is skewed left.

In this case, median is the best method for this data set.

One sample t-test :

Hypothesis:

Here population mean = 70

sample mean = 80

sample standard deviation = 14.65

number of observations =10

Test statistic:

x=0.05

What this critical value means is that we would expect most values to fall under 1.833 . If our calculated t-value falls within this range, the null hypothesis is likely true.

Here

t = 2.1586 > t -table value = 1.833

so we can reject the null hypothesis. The value of 2.1586 falls into the rejection region (the left tail).