Connecting the Dots…
1. What is a statistical question? Give one example from daily life.
Answer:
A statistical question is a question that can be answered by collecting and analyzing data. The answers usually vary from person to person or situation to situation.
Example:
“How tall are the students of Class 7?”
Explanation: Different students have different heights. We need to collect data from many students and then analyze it. Therefore, it is a statistical question.
2. Why is the question “Do you like reading?” not a statistical question?
Answer:
It is not a statistical question because it is asked to one person and gives only one answer.
Explanation: Statistical questions require data from many observations with varying answers. The question “Do you like reading?” gives a single response (Yes or No) from one person, so it is not statistical.
3. A player scored 18, 22, 15, 25 and 20 runs in five matches. Find the average runs scored per match.
Answer:
Average = Total runs ÷ Number of matches
= (18 + 22 + 15 + 25 + 20) ÷ 5
= 100 ÷ 5
= 20
Average runs = 20 runs per match
Explanation: The average represents the equal share of runs across all matches. If the player had scored the same number of runs in every match, it would have been 20 runs.
4. Explain the average as a fair-share concept.
Answer:
Average can be understood as an equal or fair share given to every member of a group.
Explanation: If all collected items are shared equally among all members, the share received by each member is the average. It balances high and low values and distributes the total equally.
5. The number of flowers blooming over five days is 4, 6, 8, 3 and 9. Find the average number of flowers blooming per day.
Answer:
Average = (4 + 6 + 8 + 3 + 9) ÷ 5
= 30 ÷ 5
= 6
Average = 6 flowers per day
Explanation: Although the number of flowers changed each day, the average tells us that the garden bloomed as if 6 flowers appeared every day.
6. The enrollment of a school over six years was 1400, 1500, 1600, 1700, 1800 and 1900. Find the mean enrollment.
Answer:
Mean = (1400 + 1500 + 1600 + 1700 + 1800 + 1900) ÷ 6
= 9900 ÷ 6
= 1650
Mean enrollment = 1650 students
Explanation: The mean represents the typical enrollment of the school during these six years.
7. Name four ways in which data can be compared.
Answer:
Data can be compared using:
Minimum value
Maximum value
Average (Mean)
Total of all values
Explanation: These measures help us understand the characteristics of a data set and compare different groups of data effectively.
7. Name four ways in which data can be compared.
Answer:
Data can be compared using:
Minimum value
Maximum value
Average (Mean)
Total of all values
Explanation: These measures help us understand the characteristics of a data set and compare different groups of data effectively.
8. What is a dot plot? State one advantage of using it.
Answer:
A dot plot is a graph in which each data value is represented by a dot on a number line.
Explanation: Dot plots make it easy to see how data is spread out, where values are clustered, and which values occur most frequently.
9. Find the mean of the data: 12, 15, 18, 20, 25.
Answer:
Mean = (12 + 15 + 18 + 20 + 25) ÷ 5
= 90 ÷ 5
= 18
Mean = 18
Explanation: The mean is obtained by dividing the sum of all values by the number of values.
10. What is the median? How is it found?
Answer:
The median is the middle value in a sorted data set.
Explanation:
Arrange the data in ascending order.
If the number of values is odd, the middle value is the median.
If the number of values is even, the average of the two middle values is the median.
11. Find the median of 5, 8, 10, 12, 15.
Answer:
The data is already arranged.
5, 8, 10, 12, 15
Median = 10
Explanation: There are five values, so the third value is the middle value and hence the median.
12. Find the median of 7, 9, 12, 15, 18, 21.
Answer:
Middle values = 12 and 15
Median = (12 + 15) ÷ 2
= 27 ÷ 2
= 13.5
Median = 13.5
Explanation: Since there are six values (an even number), the median is the average of the two middle numbers.
13. What is an outlier?
Answer:
An outlier is a value that is very different from the rest of the data.
Explanation: It lies far away from the other values and can strongly affect the average of the data.
14. Why is the median often better than the mean when outliers are present?
Answer:
The median is less affected by extremely high or low values.
Explanation: Outliers can change the mean significantly because the mean uses every value. The median depends only on the position of values, so it remains more stable.
15. Find the mean and median of 4, 5, 6, 7, 30.
Answer:
Mean = (4 + 5 + 6 + 7 + 30) ÷ 5
= 52 ÷ 5
= 10.4
Median = 6
Explanation: The value 30 is an outlier. It pulls the mean upward, but the median remains 6 and better represents the center of the data.
16. What are measures of central tendency?
Answer:
Mean and median are called measures of central tendency.
Explanation: They help identify the central or representative value around which the data is grouped.
17. A player scored 45, 30, 0, 60 and did not play one match. How many matches should be used when calculating the average?
Answer:
Only the matches actually played should be counted.
Number of matches played = 4
Average = (45 + 30 + 0 + 60) ÷ 4
= 135 ÷ 4
= 33.75
Average = 33.75 runs
Explanation: A score of 0 means the player played but scored no runs. A match not played should not be included in the calculation.
18. What information can a clustered (double) bar graph show?
Answer:
A clustered bar graph compares two or more groups of data side by side.
Explanation: It helps compare values across categories or across time more easily than separate graphs.
19. While interpreting a graph, what are the two important steps suggested in the chapter?
Answer:
Identify what is given.
Infer from what is given.
Explanation: First understand the scale, labels, and data shown. Then analyze patterns and draw conclusions from the graph.
20. A class has heights (in cm): 140, 142, 145, 148, 150. Find the mean and median.
Answer:
Mean = (140 + 142 + 145 + 148 + 150) ÷ 5
= 725 ÷ 5
= 145
Median = 145
Mean = 145 cm
Median = 145 cm
Explanation: The data is balanced and has no outlier. Therefore, the mean and median are equal and both represent the center of the data well.
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