 # Statistics Questions

Subject Mathematics General Statistics

## Question

Complete the following questions:

I. Frequency Distributions
The following are 50 scores on a History examination.
37 39 42 30 38 20 17 16 15 6
25 22 15 25 31 18 21 13 5 11
27 26 26 22 31 15 16 22 17 6
22 27 27 32 17 32 14 12 23 18
28 29 33 28 19 19 34 20 21 29

From these scores, construct a frequency distribution table.
Use nine classes, with the first class 0–4, and the last 40–44
Class Interval tally frequency
40-44        1. (_____)_
35-39        2. (_____)_
30-34        3. (_____)_
25-29        4. (_____)_
20-24        5. (_____)_
15-19        6. (_____)_
10-14        7. (_____)_
5-9           8. (_____)_
0-4           9. (_____)_

II. From the following scores on two tests, calculate the following values:
Test 1 (X): 29, 28, 25, 25, 22, 22, 21, 20, 19, 19
Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24
Mean of Test 1 (X)
Mx= (_____)
Mean of Test 2 (Y)
My= (____)
Summation of squared deviations scores for Test 1
Σx2= (______)
Summation of squared deviations scores for Test 2
Σy2 = (______)
Summation of the product of deviation scores for Test 1 and Test 2
Σxy = (______)

Correlation Coefficient:
r = (_____)

III. Twenty students received the following scores on a short quiz:
23, 20, 20, 19, 19, 19, 18, 18, 18, 18,
17, 17, 17, 15, 14, 13, 13, 12, 12, 18.
Calculate the following:
Mean=   (______)
Median = (______)
Mode =   (______)
SD =       (______)

If this small sample is normally distributed, 68% of the scores should fall between what two values? ______________and___________________.

IV. A student takes examinations in a History course and an English course.
The following information is taken from the two tests:
History                                  English
Student Score                                           64                                          80
Mean                                                         54                                           70
SD                                                               4                                           10

What is the z-score for History? (_______)
What is the z-score for English? (_______)
What is the T-score for History? (_______)
What is the T-score for English? (_______)

V. Use the following data to answer the following questions (*indicates the correct answer).
ITEM 1: A B C D*
UPPER: 2 4 2 4
LOWER: 6 1 3 2

ITEM 2: A B C* D
UPPER: 0 5 5 5
LOWER: 0 3 11 1
Circle the letter of the correct answer.

What is the difficulty level of item 1?
What is the difficulty level of item 2?
a. 4/12 a. 5/15
b. 6/12 b. 6/15
c. 2/24 c. 5/30
d. 4/24 d. 6/30
e. 6/24 e. 16/30

What is the discrimination index of item 1?
What is item 2’s discrimination index?
a. 2/12 a. 6/15
b. 6/12 b. 4/15
c. 2/24 c. -6/15
d. 6/24 d. -6/30

Which distractor on Item 1 needs revision or elimination?
a. 1-A
b. 1-B
c. 1-C
d. None of these

Which of the following is indicated by Item 2?
a. Ambiguous
b. Guessing
c. Miskeyed
d. Too difficult

The majority of Mr. Smith’s students made very high scores on this test. The curve of the distribution of scores on this test would most likely be
a. normal
b. symmetrical
c. positively skewed
d. negatively skewed

Which of the following r’s have the least predictive value?
a. 0.91
b. 0.50
c. 0.17
d. 0.23
e. -1.00

The reliability procedure that involves correlation of partial scores from one administration of one test is
a. test-retest
b. parallel forms
c. split half
d. none of the above

Total: _____ x 3+1 =_______/100

## Solution Preview

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For normal distributions, 68% represents one standard deviation from the mean in both directions. So the values would fall between [17-2.88,17+2.88]=[14.12,19.88]

E. To calculate the difficulty level for a question, you divide the number of students who got the answer correct by the number of students, so: (4+2)/(2+4+2+4+6+1+3+2)=6/24.

E. To calculate the difficulty level for a question, you divide the number of students who got the answer correct by the number of students, so: (5+11)/(5+5+5+3+11+1)=16/30

A. To calculate the discrimination index for a question, you subtract the students who chose the correct answer from the Lower group from the students who chose the correct answer from the Upper group, then divide by the number of students from each group. For item 1, we would calculate: (4-2)/12=2/12....

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