Question

The following data shown are the Test scores from our first Test .

63        70        93        80        90        82        75        75        48        92        97        70

56        79        34        67        48        66        60        90        95        89        76        82

   

    61      96         60        93         54        88       59         71       92        55        70         57

   

59        69        80        45         74       75        68        57        100    86       79         59 *

1. Construct the Histogram and Calculate Statistics from data for the first test.

2. If minimum averages have been established for each of these grades:

A         93%                 B83%              C73%              D63%              F< 60%  

                                                                                                                                                                                                                                                                                               

Construct a Pie Graph and Bar Chart for the data

3. Construct a Box plot

4. Calculate the z-score for your first test score.

5. Compute the percentile score for your first test score.

6. What value corresponds to the 40^th percentile?

7. Check the data for outliers. Does your score belong to outliers?

8. From Histogram determine if the data are approximately normally distributed .

9. Using Chebyshev’s theorem at least what percentage will fall between B and C grade.

10. If I curve the scores by10% how will the standard deviation be affected.

Answer 1

a) The data has the following statistics

N	Max	Min	Mean S.D
48	100	34	72.58 15.83

The data has been arranged in to following interval data

Histogram
Marks	Frequency
33-43	1
43-53	4
53-63	11
63-73	9
73-83	11
83-93	7
93-103	6

b) the barchart and pie chart are as fellow

c) the boxplot is as fellow

5.- the Z score and percentle scores are as fellow

marks	Z-Score	Percentile Rank
63	-0.605	32%
70	-0.163	43%
93	1.29	89%
80	0.468	66%
90	1.1	81%
82	0.595	70%
75	0.153	53%
75	0.153	53%
48	-1.553	4%
92	1.226	85%
97	1.542	98%
70	-0.163	43%
56	-1.047	13%
79	0.405	62%
34	-2.437	0%
67	-0.353	36%
48	-1.553	4%
66	-0.416	34%
60	-0.795	26%
90	1.1	81%
95	1.416	94%
89	1.037	79%
76	0.216	60%
82	0.595	70%
61	-0.732	30%
96	1.479	96%
60	-0.795	26%
93	1.29	89%
54	-1.174	9%
88	0.974	77%
59	-0.858	19%
71	-0.1	49%
92	1.226	85%
55	-1.111	11%
70	-0.163	43%
57	-0.984	15%
59	-0.858	19%
69	-0.226	40%
80	0.468	66%
45	-1.742	2%
74	0.089	51%
75	0.153	53%
68	-0.289	38%
57	-0.984	15%
100	1.732	100%
86	0.847	74%
79	0.405	62%
59	-0.858	19%

7. the value corresponds to 40th percentile is 69

8. Yes the data is positively skewed but is not completely normal.

9. about 23% of the data.

10. Standard deviation will alter.