Concept Review - Module 3: Data Management

1. In a frequency distribution, why do we use class boundaries instead of just class limits?

• To increase the frequency of each class
  

• To eliminate gaps between intervals

• To make the data symmetrical

• To change the class size

Answer explanation

Answer: To eliminate gaps between intervals
Class boundaries are used to avoid gaps in data intervals. For example, a class of 10–19 and 20–29 would overlap without boundaries like 9.5–19.5 and 19.5–29.5.

2. What does the highest frequency in a distribution represent?

• The class with the widest interval

• The class containing the most observations

• The midpoint of the lowest class

• The average of all scores

Answer explanation

Answer: The class containing the most observations
The highest frequency identifies the class where most data values fall, often called the “modal class.”

3. In a cumulative frequency table, the “less than” column helps to:

• Identify the number of cases above a certain value

• Locate the total range of scores

• Identify the number of cases below a certain value

• Determine the standard deviation

Answer explanation

Answer: Identify the number of cases below a certain value
The “less than cumulative frequency” column shows how many values fall below a certain upper boundary.

4. 4. Which measure of central tendency is least affected by extreme values?

• Mean

• Median

• Mode

• Range

Answer explanation

Answer: Median
The median is resistant to extreme values (outliers), unlike the mean, which can be heavily influenced by very high or very low scores. Mode is not affected by extreme values either, but it’s limited in use:

• - It only considers the most frequent value(s).

• - It may not exist (if all values occur only once).

• - It may not be unique (if the dataset is multimodal).

• - It does not reflect the overall “balance” of the dataset.

5. 5. If the correlation coefficient between study time and test scores is +0.85, this indicates:

• A weak relationship between the two variables

• A strong positive relationship

• No relationship

• A negative relationship

Answer explanation

Answer: A strong positive relationship
A correlation of +0.85 means as one variable increases, the other tends to increase strongly in a linear way.

6. What does it mean if two variables are positively correlated?

• As one increases, the other decreases

• All data lies on the trendline

• As one increases, the other also increases

• The relationship is random

Answer explanation

Answer: As one increases, the other also increases
Positive correlation means variables move in the same direction (e.g., more study hours, higher grades).

7. 7. In regression analysis, what does the slope represent?

• 7. The predicted value of the dependent variable

• 7. The strength of correlation

• 7. The rate of change in the dependent variable for each unit increase in the independent variable

• 7. The constant value added to predictions

Answer explanation

Answer: The rate of change in the dependent variable for each unit increase in the independent variable
In regression, the slope tells how much the dependent variable (Y) changes when the independent variable (X) increases by one unit.

8. 8. If R² = 0.90 in a regression model, what does this mean?

• 8. 90% of the data values are correct

• 8. 90% of the variation in the dependent variable is explained by the independent variable

• 8. The correlation coefficient is 0.90

• 8. The model has no error

Answer explanation

Answer: 90% of the variation in the dependent variable is explained by the independent variable
R2=0.90R^2 = 0.90R2=0.90 means the regression model accounts for 90% of the changes in Y based on X, which indicates a very strong fit.

9. 9. Why do we prefer grouped data when dealing with large datasets?
   
   
   

• 9. To reduce the number of observations

• 9. To simplify and summarize information

• 9. To eliminate outliers

• 9. To increase accuracy

Answer explanation

Answer: To simplify and summarize information
Grouped data makes large datasets easier to read and analyze because it condenses many observations into classes/intervals.

10. 10. Which measure of central tendency is most appropriate for nominal data?

• Mean

• Median

• Mode

• Range

Answer explanation

Answer: Mode
Nominal data (like gender, color, brand) are categories without numerical meaning. The only central tendency measure that applies is the mode (the most frequent category).