Descriptive Statistics

Using the attached DATA excel files prepare the following:

1. Determine the number of boys and girls in the class and create a bar graph or pie chart to display the information.

No.	gender	Number
1	male	14
2	female	7
	Total no of students	21

Pie chart representing the number of students represented by gender.

2. Calculate the mean, median, and mode for the Math, Reading, and Writing report card grades for the class.

	Post Project					Homework/Assignments			Report Card
No.	Name	gender	Absences	Discipline	Math	Reading	Writing	Math	Reading	Writing
1	Alex	M	6		94	92	96	B	B	B
2	Anthony	M	22		73	87	83	C	B	C
3	Brooke	M	2	X	60	50	55	C	D	D
4	Carmen	F	0		100	100	100	A	A	A
5	Christina	F	new	X	90	90	90	B	B	B
6	Douglas	M	1	X	83	92	83	B	B	B
7	Jorge	M	4	X	75	68	72	C	C	C
8	Joshua	M	5		88	88	86	B	B	B
9	Kim	M	2		99	100	100	A	A	A
10	Latisha	F	0		100	92	100	A	B	B
11	Li	M	1		100	99	100	A	A	A
12	Olga	M	new	X	33	43	58	F	F	F
13	Rachel	F	2		94	100	94	A	A	A
14	Robert	M	42		62	61	64	F	D	F
15	Rupert	M	4	X	66	62	61	C	D	D
16	Sara	F	3		91	97	97	B	A	A
17	Seth	M	0		94	92	97	B	B	B
18	Sheetal	F	0		99	98	100	A	A	A
19	Tawayna	F	16	X	78	69	73	C	C	D
20	Wayne	M	1		98	100	100	A	B	A
21	William	M	new		81	98	90	C	A	B
				MEAN	84.67	84.81	85.38	B
				MEDIAN	88	92	90	B
				MODE	92	100	100	B

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Determine if there is or is not a normal distribution for the Math, Reading, and Writing report card grades.

Statistics Results	Math	Reading	Writing
Mean	83.38095238	85.0476	86.1905
Standard Error	3.833111499	3.8788	2.89796
Median	88	92	90
Mode	92	100	100
Standard Deviation	17.56552359	17.7749	13.2801
Sample Variance	308.547619	315.948	176.362
Kurtosis	2.626160315	0.5588	-0.4531
Skewness	-1.488506551	-1.2094	-0.8656
Range	69	60	42
Minimum	31	40	58
Maximum	100	100	100
Sum	1751	1786	1810
Count	21	21	21
Confidence Level (95.0%)	7.995730453	8.09104	6.04504

From the Descriptive, statistics results shown in the table below, the data provided does not have normal distribution. The Math, Reading and Writing report cards data have a high standard errors of 3.83, 3.87 and 2.89 respectively, indicating a high variation in the data. The sample variance is also high 308.5, 315.9, and 176.3 respectively. Variance is the measure of relative mean of the data, showing how far the data is a measure of dispersion. In this case, high variance is an indication that the data is random and is much spread over a large area. On the other hand, if the variance were low it would indicate that the data is closely related. Therefore, high variance of the data is an indication that the data is highly skewed. Furthermore, the data also has a high standard deviation, indicating that the data is significantly a bias. This is because standard deviation is a measure of how on average the data falls away from the mean. It has similar interpretation as the high variance as it is computable from calculation of the square root of variance, therefore, since it has its square rooted, it is less susceptible to outliers.

Create a scatter plot diagram illustrating the Reading scores for the class.

Analyze the purpose of the descriptive statistics used.

The descriptive statistics used to analyze this data summarizes the data to a more meaningful manner, with reference to the students marks. The descriptive statistics determine the patterns arising from the data, but the patterns are only restricted to drawing conclusions from the data and not beyond the data. With raw data, it is difficult to visualize the inference of the data, but with the use of descriptive statistics, it is possible to interpret and visualize the data in a more meaningful manner. In this case, descriptive statistics gives the chance to present the data in a more meaningful way, giving the chance for simpler interpretation of the data. For example, from the data, there are 21 students, and the interest is in the overall performance of the students in different subjects. The interest could rely on the overall distribution of the marks in different subjects. With the use of descriptive statistics it is possible to [resent the data in graphical form making it easier to interpret the data. descriptive statistics was used in the data as a measure of central tendency of the data. it was used to simply describe the patterns of the marks scored by the class in different subjects form the lowest to the highest.

The median, mode and the mean was used as the measures of the central tendencies. It was used also to summarize the data by describing the spread of the score. For example, from the mean of the students results, used to measure the general performance of the students in different subjects. The measures of spread aid in summarizing the spread of the score, including the range, standard deviations and variance of the data. In a quantitative study, there are many manageable forms of data needing description, as it reduces the data into simpler form. Describing the large set of observations with a singular indicator to run the data makes the interpretation of the data distorted losing the significance of the data. Calculating the average of the data does not give the overall interpretation of the data. Therefore, with the use of these statistics, it is possible to interpret the data in more than form. This is because descriptive statistics provide powerful summary and interpretation of the data enabling the possibility of comparison of the data in many forms.

With the use of univariate analysis, it is possible to determine distribution of the data, the central tendency, and the dispersion of the data. Distribution of the data is the frequency of individual values for a given variable, in this case, the scores of the students with reference to different subjects. There is a direct relationship between student absences and Math grades as the students absent for more times performed badly. The student with the least grade of F in Math was absent from class for forty-two lessons, while the students that did not miss the classes performed well.

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