NBT Data Interpretation & Analysis 1 — Questions and Answers
Question 1: What does a bar graph represent?
- Categories of data.
- Relationships between variables.
- Trends over time.
- Data comparison across different categories. (Correct answer)
Correct answer: Data comparison across different categories.
A bar graph uses rectangular bars of varying heights or lengths to represent and compare data among different categories. Each bar corresponds to a specific category, and its length or height indicates the value or frequency for that category. This visual representation makes it easy to see differences and similarities between distinct groups of data.
Question 2: What is the median of the following data set: 1, 3, 3, 6, 7, 8, 9?
- 5.
- 6. (Correct answer)
- 7.
- 8.
Correct answer: 6.
The median is the middle value in a data set when the values are arranged in ascending or descending order. For the given ordered data set (1, 3, 3, 6, 7, 8, 9), there are 7 values. The middle value is the (7+1)/2 = 4th term. Counting from either end, the 4th term is 6, which is the median.
Question 3: What is the mode of the following data set: 1, 2, 3, 3, 4, 5, 6?
- 2.
- 3. (Correct answer)
- 4.
- 5.
Correct answer: 3.
The mode of a data set is the value that appears most frequently. In the given data set (1, 2, 3, 3, 4, 5, 6), the number 3 appears twice, which is more often than any other number. Therefore, 3 is the mode of this data set.
Question 4: How is the mean of a data set calculated?
- Multiply all values and divide by the total number of values.
- Add all values and divide by the total number of values. (Correct answer)
- Add all values and divide by two.
- Find the middle value of the data set.
Correct answer: Add all values and divide by the total number of values.
The mean, also known as the average, is calculated by summing all the individual values in a data set and then dividing that sum by the total count of values in the set. This method provides a central tendency measure that represents the typical value of the data.
Question 5: Which of the following graphs is best suited for showing trends over time?
- Bar graph.
- Pie chart.
- Line graph. (Correct answer)
- Histogram.
Correct answer: Line graph.
A line graph is particularly effective for illustrating how data changes or trends over a continuous period, such as time. It connects data points with lines, making it easy to visualize increases, decreases, or stability in a variable over time. This makes it ideal for showing trends.
Question 6: What is the range of the following data set: 4, 8, 15, 16, 23, 42?
- 38. (Correct answer)
- 23.
- 16.
- 42.
Correct answer: 38.
The range of a data set is the difference between the highest and lowest values. In the given data set (4, 8, 15, 16, 23, 42), the highest value is 42 and the lowest value is 4. Subtracting the lowest from the highest (42 - 4) gives a range of 38.
Question 7: What does a pie chart represent?
- Trends over time.
- Comparison of categories.
- Parts of a whole. (Correct answer)
- Distribution of data.
Correct answer: Parts of a whole.
A pie chart is a circular graph divided into sectors, where each sector represents a proportional part of the whole. The size of each slice corresponds to the percentage or fraction that category contributes to the total. This makes pie charts ideal for showing how different components make up a complete set.
Question 8: If a data set has an outlier, what effect does it have on the mean?
- The mean remains unaffected.
- The mean is skewed by the outlier. (Correct answer)
- The mean becomes the median.
- The mean is replaced by the mode.
Correct answer: The mean is skewed by the outlier.
An outlier is an extreme value in a data set that is significantly different from other values. When an outlier is present, it can disproportionately pull the mean towards itself, either increasing or decreasing it significantly. This 'skewing' effect means the mean may no longer accurately represent the central tendency of the majority of the data.
Question 9: What is a histogram used for?
- Show trends over time.
- Display categorical data.
- Show frequency distribution of numerical data. (Correct answer)
- Represent parts of a whole.
Correct answer: Show frequency distribution of numerical data.
A histogram is a graphical representation that displays the frequency distribution of numerical data using bars. Each bar represents a range of values (a bin or interval), and its height indicates how many data points fall within that specific range. This helps visualize the shape, spread, and central tendency of continuous data.
NBT Data Interpretation & Analysis 1
What does a bar graph represent?