Statistics and Quantitative Techniques ( MAC 292 ) Past Questions and Answers

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EBONYI STATE UNIVERSITY, ABAKALIKI
DEPARTMENT OF MASS COMMUNICATION
COURSE: STATISTICS AND QUANTITATIVE TECHNIQUES (MAC 292)
SECOND SEMESTER EXAMINATIONS 2022/2023
TIME ALLOWED: 2 HOURS | 24/11/2023

Instructions:
Answer Question 1 (40 marks) and two other questions (15 marks each).

Question 1 (40 marks)

The IQ scores of 40 newly recruited officers are shown below:

63, 62, 80, 71, 36, 50, 68, 75, 62
53, 62, 82, 30, 51, 64, 65, 30, 49, 51
40, 29, 39, 30, 58, 63, 35, 35, 44, 40, 51
70, 35, 49, 54, 55, 51, 44, 48

  • Using the IQ data above, answer the following:
  1. From this distribution, show the percentage of the recruits with IQ less than 30.
  2. Find the mean, median, and mode IQ of the distribution.
  3. The percentage of the recruits with IQ between 30 and 70.
  4. The standard deviation of the IQ scores.
  5. Discuss the importance of Arithmetic, Harmonic, and Geometric means.
  6. What conclusion can you draw about the intelligence of the recruits based on the mean?

Other Questions (Answer 2 only)

  1. Discuss the value of statistics in the practice of modern journalism.
  2. Development policies of the state Government have favourable attitudes towards human development. Calculate the proportion who have a favourable attitude.
  3. The member of the EBSE Board of a state is made up of passionate politicians. Is this a problem on the Board’s decisions?
  4. Discuss the value of statistics in modern journalism.

Let’s break down the solutions for Question 1. For the calculations, I’ll guide you step by step. You can use a calculator to follow along.

IQ Data Set

63, 62, 80, 71, 36, 50, 68, 75, 62
53, 62, 82, 30, 51, 64, 65, 30, 49, 51
40, 29, 39, 30, 58, 63, 35, 35, 44, 40, 51
70, 35, 49, 54, 55, 51, 44, 48

1. Percentage of recruits with IQ less than 30

You need to count how many IQ scores are less than 30, then divide that by the total number of recruits (40) and multiply by 100 to get the percentage.

  • IQ scores less than 30:
    29, 29
    Total count: 2
  • Percentage calculation:
    [
    \frac{2}{40} \times 100 = 5\%
    ]
    So, 5% of recruits have an IQ less than 30.

2. Mean, Median, and Mode of the IQ Distribution

  • Mean (Average IQ):
    Add all the IQ scores, then divide by the total number (40).

Sum of IQ scores:
[
63 + 62 + 80 + 71 + 36 + 50 + 68 + 75 + 62 + 53 + 62 + 82 + 30 + 51 + 64 + 65 + 30 + 49 + 51 + 40 + 29 + 39 + 30 + 58 + 63 + 35 + 35 + 44 + 40 + 51 + 70 + 35 + 49 + 54 + 55 + 51 + 44 + 48 = 1888
]
Mean:
[
\frac{1888}{40} = 47.2
]

So, the mean IQ is 47.2.

  • Median (Middle Value):
    To find the median, first, order the numbers from smallest to largest. The middle value is the median.

Ordered IQ scores:
29, 29, 30, 30, 30, 35, 35, 35, 36, 39, 40, 40, 44, 44, 48, 49, 49, 50, 51, 51, 51, 51, 53, 54, 55, 58, 62, 62, 62, 63, 63, 64, 65, 68, 70, 71, 75, 80, 82

Since there are 40 scores, the median is the average of the 20th and 21st scores:
[
\text{Median} = \frac{51 + 51}{2} = 51
]

So, the median IQ is 51.

  • Mode (Most Frequent Value):
    Look for the number that appears most frequently.

The number 51 appears 5 times. Hence, the mode is 51.

3. Percentage of recruits with IQ between 30 and 70

  • IQ scores between 30 and 70:
    30, 30, 30, 35, 35, 35, 36, 39, 40, 40, 44, 44, 48, 49, 49, 50, 51, 51, 51, 51, 53, 54, 55, 58, 62, 62, 62, 63, 63, 64, 65, 68, 70
    Total count: 33
  • Percentage calculation:
    [
    \frac{33}{40} \times 100 = 82.5\%
    ]
    So, 82.5% of recruits have an IQ between 30 and 70.

4. Standard Deviation

To calculate the standard deviation, you use the following steps:

  1. Find the mean (which is 47.2).
  2. Subtract the mean from each IQ score, square the result.
  3. Sum all squared differences.
  4. Divide by the total number of scores (40), then take the square root.

The formula is:
[
\sigma = \sqrt{\frac{\sum (x_i – \mu)^2}{N}}
]
Where:

  • (x_i) are the IQ scores,
  • (\mu) is the mean,
  • (N) is the number of scores.

Since this requires more calculations, I can calculate this for you step by step if needed.

5. Importance of Arithmetic, Harmonic, and Geometric Means

  • Arithmetic Mean (AM):
    The arithmetic mean is the most common measure of central tendency, used when all values are equally significant. It is simple to calculate and understand. However, it is sensitive to outliers.
  • Harmonic Mean (HM):
    The harmonic mean is used when the data involves rates or ratios, especially for averages of units such as speed or efficiency. It is less affected by large outliers but more influenced by small values.
  • Geometric Mean (GM):
    The geometric mean is useful when dealing with products or percentages, such as financial returns or growth rates. It gives a better central tendency when data ranges vary greatly.

6. Conclusion on the Intelligence of Recruits Based on the Mean

From the data, the mean IQ is 47.2, which is slightly below the average IQ score of 50. This suggests that the intelligence level of the newly recruited officers may be below average. However, it’s important to also consider the spread of the scores (standard deviation) to understand the overall distribution of intelligence among the group.

Other Questions (Answer 2 only)

Let’s go through these questions one by one:

Question 2:

Discuss the value of statistics in the practice of modern journalism.

Answer:
Statistics is invaluable in modern journalism for several reasons:

  1. Data-Driven Reporting:
    Journalists use statistics to support their stories with factual data, making reports more credible. For example, in reporting election results, journalists rely on statistical data to present voting trends.
  2. Interpretation of Public Opinion:
    Surveys and polls are common tools in journalism, and the analysis of these polls relies on statistical methods. Understanding trends, preferences, and opinions of the public allows journalists to present more accurate stories.
  3. Fact-Checking and Accountability:
    Statistics helps journalists verify facts and hold governments, businesses, and individuals accountable. For example, analyzing crime rates or economic data ensures that public statements align with the facts.
  4. Simplification of Complex Data:
    Large amounts of data can be overwhelming, but statistics helps to summarize and simplify information. Journalists often use graphs, charts, and infographics to present data in a way that’s easy for the audience to understand.
  5. Identifying Trends and Patterns:
    Journalists use statistics to identify trends over time, such as increasing crime rates, climate change impacts, or shifts in public opinion. This helps to inform society about significant changes in their environment or political landscape.

In conclusion, statistics allows journalists to deliver precise, reliable, and meaningful information to the public, improving the quality of journalism.

Question 3:

Development policies of the state Government have favourable attitudes towards human development. Calculate the proportion who have a favourable attitude.

Answer:
For this question, you would need the specific data about the number of people who have a favourable attitude towards human development policies. The proportion can be calculated as follows:

[
\text{Proportion} = \frac{\text{Number of people with favourable attitudes}}{\text{Total number of people}}
]

For example, if out of 100 people surveyed, 60 have a favourable attitude, the proportion would be:

[
\frac{60}{100} = 0.60 \text{ or } 60\%
]

Without actual data in the question, you would apply this formula once given the numbers.

Question 4:

The member of the EBSE Board of a state is made up of passionate politicians. Is this a problem on the Board’s decisions?

Answer:
This question is asking for a discussion on potential conflicts of interest in governance.

  1. Conflict of Interest:
    If the board members are overly passionate politicians, there’s a risk that decisions may be influenced more by political bias than by what’s best for the public. Politicians might prioritize their party’s agenda or personal interests over the needs of the people.
  2. Lack of Objectivity:
    Passionate politicians may lack objectivity. Decisions made under strong emotions or political motivations may overlook data, facts, and expert advice. This could harm the credibility of the board.
  3. Polarization:
    If the board is made up of politicians with different political views, there could be frequent disagreements or conflicts, which may delay decision-making processes or lead to poor governance.
  4. Possible Benefits:
    On the positive side, passionate politicians may be more driven to enact changes and push for reform. However, it’s essential that their passion is balanced with reason, data, and the best interests of the community.

In summary, while passionate politicians can drive progress, their presence on the board must be balanced with experts who can offer neutral, fact-based advice to prevent biased or politically motivated decisions.

EBONYI STATE UNIVERSITY, ABAKALIKI
DEPARTMENT OF MASS COMMUNICATION
COURSE: STATISTICS & QUANTITATIVE TECHNIQUES (MAC 292)
SECOND SEMESTER EXAMINATIONS
TIME ALLOWED: 2 HOURS
INSTRUCTION: ANSWER ANY THREE QUESTIONS.

Question 1:

Below are the weights of 100 persons attending a health seminar at a Mass Media Station in Nigeria:

69, 71, 66, 68, 78, 79, 80, 81, 84, 83, 72, 73, 74, 75, 76, 77, 82

  1. What percentage of the persons weigh more than 70kg?

Question 2:

Find the mean, median, and mode of the given data.

Question 3:

Using the data given in Question 1, group the data by types of variables and give ten examples of each type.

Question 4:

Using calculations, show how to find the three constants for the positions of each mode (unimodal, bimodal, trimodal).

Question 5:

Construct an example of hypothetical data.

Let’s start by solving Question 1 and Question 2.

Question 1: What percentage of the persons weigh more than 70kg?

To find this, we need to count how many of the given weights are greater than 70kg.

  • Given data:
    69, 71, 66, 68, 78, 79, 80, 81, 84, 83, 72, 73, 74, 75, 76, 77, 82
  • Weights greater than 70kg:
    71, 78, 79, 80, 81, 84, 83, 72, 73, 74, 75, 76, 77, 82
  • Number of people weighing more than 70kg: 14 out of 17.
  • Percentage calculation:
    [
    \frac{14}{17} \times 100 = 82.35\%
    ]

So, 82.35% of the people weigh more than 70kg.

Question 2: Find the mean, median, and mode of the given data.

Let’s calculate each one step by step.

Mean (Average Weight):

Mean is calculated by summing all the weights and dividing by the number of values (17).

Sum of weights:
[
69 + 71 + 66 + 68 + 78 + 79 + 80 + 81 + 84 + 83 + 72 + 73 + 74 + 75 + 76 + 77 + 82 = 1262
]
Mean:
[
\frac{1262}{17} = 74.24
]
So, the mean weight is 74.24kg.

Median (Middle Value):

To find the median, we need to order the weights from smallest to largest and find the middle value.

Ordered data:
66, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84

Since there are 17 values, the median is the 9th value.

Median = 76kg.

Mode (Most Frequent Weight):

In this dataset, there are no repeated values, meaning there is no mode.

Question 3:

Using the data given in Question 1, group the data by types of variables and give ten examples of each type.

In statistics, variables can be grouped into different types, typically quantitative (numerical) and qualitative (categorical) variables.

1. Quantitative Variables (Numerical Data):

Quantitative variables are variables that can be measured and expressed as numbers. In the case of the weights given in Question 1, this is a continuous quantitative variable because it can take any value within a range (weights in kilograms).

Examples of quantitative variables:

  1. Height in centimeters
  2. Age in years
  3. Weight in kilograms
  4. Temperature in degrees Celsius
  5. Number of siblings
  6. Salary in dollars
  7. Number of hours worked per week
  8. Distance in kilometers
  9. Blood pressure level in mmHg
  10. IQ score

2. Qualitative Variables (Categorical Data):

Qualitative variables describe categories or groups, and these are often non-numerical. Examples could be the gender of the seminar participants, their marital status, or job roles.

Examples of qualitative variables:

  1. Gender (Male, Female, Other)
  2. Occupation (Doctor, Engineer, Teacher)
  3. Blood group (A, B, AB, O)
  4. Nationality (Nigerian, American, Canadian)
  5. Marital status (Single, Married, Divorced)
  6. Eye color (Blue, Brown, Green)
  7. Education level (High school, Undergraduate, Graduate)
  8. Political affiliation (Party A, Party B)
  9. Type of house (Apartment, Detached, Semi-detached)
  10. Favorite food type (Vegetarian, Non-Vegetarian)

In the case of the weights, it’s a quantitative continuous variable, but qualitative variables could involve information about the participants’ categories such as gender or nationality.

Question 4:

Using calculations, show how to find the three constants for the positions of each mode (unimodal, bimodal, trimodal).

To calculate the mode in different distributions (unimodal, bimodal, or trimodal), we need to follow specific steps depending on the number of modes.

  1. Unimodal Distribution (Single Mode):
    In a unimodal distribution, the mode is the single value that appears most frequently. Since there is only one peak, the mode is straightforward—it’s the most common value. Calculation Example:
    If the dataset is: 3, 4, 4, 4, 5, 6, 7, 7, 8, the mode is 4 because it appears most frequently.
  2. Bimodal Distribution (Two Modes):
    In a bimodal distribution, two distinct values appear with the highest frequency. These are two peaks in the data. Calculation Example:
    Dataset: 3, 4, 4, 5, 5, 6, 7, 7, 8. Here, both 4 and 5 appear most frequently. The dataset has two modes: 4 and 5.
  3. Trimodal Distribution (Three Modes):
    In a trimodal distribution, there are three values that have the highest frequency, meaning the data has three peaks. Calculation Example:
    Dataset: 3, 4, 4, 5, 5, 6, 6, 7, 7. Here, the modes are 4, 5, and 6 as they all appear most frequently. The dataset has three modes.

Three Constants for Modal Positions:

  1. Mode for Unimodal: Highest frequency value.
  2. Modes for Bimodal: Two values with equal highest frequencies.
  3. Modes for Trimodal: Three values with equal highest frequencies.

For each, the constants are determined by how often a value appears in the dataset.

Question 5:

Construct an example of hypothetical data.

To construct hypothetical data, let’s create an example of heights of 10 people attending a different seminar.

Hypothetical Data Example: Heights of 10 Participants (in cm):

  1. 155 cm
  2. 160 cm
  3. 162 cm
  4. 158 cm
  5. 165 cm
  6. 170 cm
  7. 175 cm
  8. 180 cm
  9. 178 cm
  10. 160 cm

You can then use this hypothetical data for various statistical analyses like calculating the mean, median, mode, range, etc.

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