# Summation Notation – Statistic Final Exam

### Summation Notation, Measure of Central Tendency, Sample, Statistic Exam

The key terms in these Statistic chapters include Measure Of Central Tendency, Mean, Summation Notation, Sample, Median, Standard Deviation, Data, Sums of Squares, Frequency Distribution, Biased Statistic, Population, Set of Scores, Mode, Distribution, Summation Notation – Statistic Exam.

You are instructed to subtract four points from each score and find the sum of the resulting values. How would this set of instructions be expressed in summation notation?
a. EX-4
b. E(X-4)
c. 4-EX
d. E(4-X)

A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students. However, one of the participants fails to solve the problems so the researcher has an undetermined score. What is the best measure of central tendency of these data?
a. the mean
b. the median
c. the mode
d. central tendency cannot be determined for these data

Which set of scores has the smallest standard deviation?
a. 11, 17, 31, 53
b. 5, 11, 42, 22
c. 145, 143, 145, 147
d. 27, 105, 10, 80

What is the value of the Sums of Square (SS) for the following set of scores? Scores: 8, 3,1
a. 26
b. 29
c. 74
d. 144

For the following frequency distribution of quiz scores, how many individuals took the quiz?
(x- 5, 4, 3, 2, 1  f – 6, 5, 5, 3, 2)

a. n = 5
b. n = 15
c. n = 21
d. cannot be determined

What is the mode for the population of scores shown in the frequency distribution tables?
(x – 5, 4, 3, 2, 1    f – 1, 2, 3, 4, 2)

#### a. 2 – correctb. 3c. 3.5d. 4

For the distribution in the following graph, what is the value of EX?
(number 7 not test)
a. 15
b. 21
c. 30
d. cannot determine

A researcher measures eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements?

a. mean
b. median
c. mode
d. any of the three measures could be used

You are instructed to subtract four points from each score and find the sum of the resulting values. How would this set of instructions be expressed in summation notation?
a. EX-4
b. E(X-4)
c. 4-EX
d. E(4-X)

A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students. However, one of the participants fails to solve the problems so the researcher has an undetermined score. What is the best measure of central tendency of these data?
a. the mean
b. the median
c. the mode
d. central tendency cannot be determined for these data

Which set of scores has the smallest standard deviation?
a. 11, 17, 31, 53
b. 5, 11, 42, 22
c. 145, 143, 145, 147
d. 27, 105, 10, 80

What is the value of the Sums of Square (SS) for the following set of scores? Scores: 8, 3,1
a. 26
b. 29
c. 74
d. 144

A sample of n = 25 scores has M = 20 and s^2 = 9. What is the sample standard deviation?

a. 3
b. 4.5
c. 9
d. 81

##### Explanation

(s^2 = variance)  3^2 = 9

A sample of n = 5 scores has a standard deviation of s = 5. What is the value of SS, the sum of the squared deviations for this sample?

#### 100

Which of the following statements is correct regarding a biased statistic?

A biased statistic occurs when the average value of a statistic either underestimates or overestimates the corresponding population parameter.

Which response option below is the standard deviation of the sample of n = 11 scores depicted below? (2, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10)

#### 2.61

Which of the following values for the population standard deviation would cause a score located above the mean average to have the most extreme position in the distribution?

#### σ = 1

A sample of n = 15 scores has M = 20 and s 2 = 9. What is the sample standard deviation?

#### 3

One sample has n = 4 and M = 10. A second sample has n = 6 scores and M = 5. If the two samples are combined, then what is the mean for the combined sample?

a. 70/4 = 17.5
b. 70/6 = 11.67
c. 70/10 = 7
d. cannot be determined with the information given

##### Explanation(40+30 = 70/10 = 7)

A sample of n = 6 has a mean of M = 5. One person with a score of X = 12 is added to the distribution. What is the mean for the new set of scores?

a. M = 5
b. M = 6
c. M = 7
d. M = 8

What is the shape for the distribution shown in the following graph? (number 12 on test)

a. positively skewed
b. negatively skewed
c. symmetrical
d. normal

What is the mean for the population of scores shown in the frequency distribution table?
(x- 5, 4, 3, 2, 1     f – 1, 2, 3, 4, 2)

a. 15/5 = 3
b. 15/12 = 1.25
c. 32/5 = 6.60
d. 32/12 = 2.67

Which of the following symbols identifies the sample variance?

a. s
b. s^2
c. sigma (weird o)
d. sigma^2

A population with a mean of mu= 6 has a EX = 42. How many scores are in the population?

a. N = 7
b. N =252
c. 6/42 = 1/7
d. cannot be determined from the information given

Describe the sequence of mathematical operations that would be used to evaluate each of the following expressions:
a. (EX)^2
b. EX^2
c. E(X-2)^2

a. 1. Add all the score together, 2. square sum total
b. 1. Square each score, 2. add squared scores together
c. 1. Subtract 2 from each score. 2. square new scores, 3. add scores together

A professor grades a sample of 10 statistics exams (n = 10) and records the following number of errors on each exam: 0, 4, 2, 8, 2, 3, 1, 0, 5, and 7.

a. What is the most appropriate measure of central tendency? Explain
b. Compute the SS, the variance, and the standard deviation

a. mean because the data is ration and no outliers
b. ss = 69.6
s^2 = 7.73
SD = 2.78

Which response option below is consistent with the standard deviation for the population of N = 10 scores depicted below?

a. 2.67

b. 3.16

c. 3.00

d. 2.53

On an exam with a mean of µ = 80, a person scores X = 90. Which of the following values for the standard deviation would position this person highest within the class?

#### σ = 2

One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2. Which set of sample statistics would present the clearest picture of a real difference between the two treatments?

M1 = 36, M2 = 40, and both variances = 6

A sample of n = 5 scores has a standard deviation of s = 5. What is the value of SS, the sum of the squared deviations for this sample?

#### 100

Which of the following statements is correct regarding a biased statistic?

A biased statistic occurs when the average value of a statistic either underestimates or overestimates the corresponding population parameter.

Which response option below is the standard deviation of the sample of n = 11 scores depicted below? (2, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10)

#### 2.61

Which of the following values for the population standard deviation would cause a score located above the mean average to have the most extreme position in the distribution?

#### σ = 1

A sample of n = 15 scores has M = 20 and s 2 = 9. What is the sample standard deviation?

#### 3

One sample has n = 4 and M = 10. A second sample has n = 6 scores and M = 5. If the two samples are combined, then what is the mean for the combined sample?

a. 70/4 = 17.5
b. 70/6 = 11.67
c. 70/10 = 7
d. cannot be determined with the information given

##### Explanation(40+30 = 70/10 = 7)

A sample of n = 6 has a mean of M = 5. One person with a score of X = 12 is added to the distribution. What is the mean for the new set of scores?

a. M = 5
b. M = 6
c. M = 7
d. M = 8

You are instructed to subtract four points from each score and find the sum of the resulting values. How would this set of instructions be expressed in summation notation?
a. EX-4
b. E(X-4)
c. 4-EX
d. E(4-X)

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