CBSE Class 7 Mathematics Connecting the Dots Worksheet Set 01

Very Short Answer Questions

Question 1. What is a statistical question? Give one example of your own.
Answer:
A statistical question is one that can be answered only by collecting and analysing data, because the answer is expected to vary. Example: “How many glasses of water do the students of my class drink in a day?”

Teacher's Note:
1. The answer must vary from case to case.
2. A question with one fixed answer is not statistical.

Question 2. What is meant by a statistical statement?
Answer:
A statistical statement is a claim or summary about some happening, given in terms of numbers, proportions, chances or predictions, for example “David spends about 7 hours daily in school”.

Teacher's Note:
1. Words like 'about', 'usually' and 'on average' often appear in such statements.
2. It sums up many values in one sentence.

Question 3. Write the formula used to find the arithmetic mean of a data set.
Answer:
Mean = (Sum of all the values in the data) ÷ (Number of values in the data).

Teacher's Note:
1. The mean is also called the average.
2. It is the fair share of the total.

Question 4. Define the median of a data set.
Answer:
The median is the middle value of the data after it has been sorted. If the number of values is even, it is the average of the two middle values.

Teacher's Note:
1. Always sort the data first.
2. Half the values lie on each side of the median.

Question 5. What is an outlier in a data set?
Answer:
An outlier is a value that differs greatly from the rest of the data, such as 118 cm among heights of 165 cm, 170 cm, 173 cm and 175 cm.

Teacher's Note:
1. An outlier can be at the high end or the low end.
2. It pulls the mean towards itself.

Question 6. Name the two measures of central tendency studied in this chapter.
Answer:
The arithmetic mean (average) and the median.

Teacher's Note:
1. Both give a central value of the data.
2. The range is a measure of spread, not of centre.

Question 7. Write any two things about a data set that a dot plot helps us to see at a glance.
Answer:
A dot plot shows (1) the smallest and largest values of the data, and (2) where the values cluster together or spread out, including the values that repeat.

Teacher's Note:
1. Repeated values form taller piles of dots.
2. An outlier stands apart from the other dots.

Question 8. By what other name is a clustered column graph known?
Answer:
It is also called a double bar graph, because each cluster has two bars drawn side by side.

Teacher's Note:
1. One bar of each cluster belongs to each group.
2. A key shows which bar is which.

Question 9. Find the mean of 8, 5, 11, 4 and 7.
Answer:
Sum = 8 + 5 + 11 + 4 + 7 = 35; there are 5 values. Mean = 35 ÷ 5 = 7.

Teacher's Note:
1. Count the values carefully.
2. The mean 7 lies between 4 and 11, as it should.

Question 10. Find the median of 14, 9, 21, 17 and 12.
Answer:
Sorted: 9, 12, 14, 17, 21. The middle (3rd) value is 14, so the median is 14.

Teacher's Note:
1. Five values, so the 3rd is the middle.
2. Sort before picking the middle.

Question 11. What is meant by the range of a data set? Find the range of 12, 30, 7 and 25.
Answer:
The range is the maximum value minus the minimum value. Here, range = 30 − 7 = 23.

Teacher's Note:
1. Range tells how spread out the data is.
2. Pick the largest and smallest values first.

Question 12. Write any one term that was used for the arithmetic mean in ancient Indian mathematics.
Answer:
Samamiti (“mean measure”), used by Bhaskaracharya. (Samarajju, samikarana and samya are other such terms.)

Teacher's Note:
1. All these words carry the idea of 'equal' or 'levelling'.
2. Indian mathematicians used the mean long ago.

Question 13. Five children collected 7, 4, 9, 6 and 4 seashells. If they share all the shells equally, how many will each child get?
Answer:
Total = 7 + 4 + 9 + 6 + 4 = 30 shells. Each child gets 30 ÷ 5 = 6 shells, which is the mean.

Teacher's Note:
1. Equal sharing of the total gives the mean.
2. The total stays the same after sharing.

Question 14. Find the median of 24, 31, 18, 27, 35 and 22.
Answer:
Sorted: 18, 22, 24, 27, 31, 35. There are 6 values, so median = (24 + 27) ÷ 2 = 25.5.

Teacher's Note:
1. Even count: average the two middle values.
2. The median here is not one of the data values.

Question 15. A batter scored 45, 0, 62 and 38 runs in four matches of a series and did not play the fifth match. By which number must the total be divided to find the mean runs per match, and why?
Answer:
By 4, because the batter played in only 4 matches. The 0 is a real score and is counted, but the match not played has no value at all.

Teacher's Note:
1. Zero is a value; 'did not play' is no value.
2. Mean here = 145 ÷ 4 = 36.25 runs.

Question 16. Group A has 5 members who scored 60 marks in all; Group B has 4 members who scored 52 marks in all. Which group has the higher mean score?
Answer:
Mean of A = 60 ÷ 5 = 12; mean of B = 52 ÷ 4 = 13. So Group B has the higher mean, even though its total is smaller.

Teacher's Note:
1. Totals are unfair when group sizes differ.
2. Compare means, not totals.

Question 17. On a bar graph the scale is 1 unit length = 5 hours. What value is shown by a bar that is 3 units long?
Answer:
Each unit stands for 5 hours, so 3 units show 3 × 5 = 15 hours.

Teacher's Note:
1. Value = number of units × scale.
2. Always read the scale first.

Question 18. A data set contains one outlier at the higher end. Will its mean be greater than or less than its median?
Answer:
Greater. A very large value raises the sum and pulls the mean up, while the median hardly moves.

Teacher's Note:
1. The mean moves towards the outlier.
2. A low outlier would make the mean smaller than the median.

Question 19. The heights of the five members of a family are 168 cm, 172 cm, 160 cm, 166 cm and 174 cm. Find their mean height.
Answer:
Sum = 168 + 172 + 160 + 166 + 174 = 840 cm. Mean = 840 ÷ 5 = 168 cm.

Teacher's Note:
1. Add carefully before dividing.
2. The mean lies between 160 cm and 174 cm.

Question 20. Which useful piece of information about data is lost when the data is shown on a dot plot?
Answer:
The original order of the values is lost. For example, after plotting monthly onion prices we can no longer tell which price belonged to January.

Teacher's Note:
1. A dot plot sorts the data.
2. Keep the table if the order matters.

Question 21. Why are dots or slanted lines sometimes drawn inside the bars of a bar graph?
Answer:
They help readers who find it difficult to tell colours apart, and they keep the groups separate when the graph is printed in black-and-white.

Teacher's Note:
1. Patterns work even without colour.
2. The key shows the same pattern as the bars.

Question 22. Write the two steps suggested in the chapter for making sense of the data shown in a graph.
Answer:
Step 1: Identify what is given (how the graph is organised, what the axes show, the scale and the patterns). Step 2: Infer from what is given (analyse the observations and write summary statements).

Teacher's Note:
1. First read, then interpret.
2. Never infer before checking the scale and axes.

Question 23. In one town the monthly onion prices lay between ₹24 and ₹59, and in another town between ₹17 and ₹60. In which town were the prices more spread out?
Answer:
Range of the first town = 59 − 24 = 35; range of the second town = 60 − 17 = 43. So prices were more spread out in the second town.

Teacher's Note:
1. A larger range means more spread.
2. Range = maximum − minimum.

Question 24. In the double bar graph showing runs scored per over in a cricket match, what do the small circles drawn above some bars tell us?
Answer:
A small circle above a bar shows that a wicket fell in that over.

Teacher's Note:
1. Extra marks on a graph can carry extra information.
2. Always read the key of a graph.

Question 25. The mean of five numbers is 24. Four of the numbers are 20, 31, 18 and 27. Find the fifth number.
Answer:
Sum of five numbers = 5 × 24 = 120. Sum of the four = 20 + 31 + 18 + 27 = 96. Fifth number = 120 − 96 = 24.

Teacher's Note:
1. Total = mean × number of values.
2. Check: 120 ÷ 5 = 24.

Question 26. Can the mean of a data set be smaller than the smallest value of that data set? Give a reason.
Answer:
No. The mean is a fair share of the total, so it always lies between the smallest and the largest value. If it were below the smallest value, every value would have to be below the smallest value, which is impossible.

Teacher's Note:
1. The mean lies between the minimum and maximum.
2. The same is true for the median.

Question 27. For the data 11, 13, 12, 14 and 70, find the mean and the median, and state which of the two represents this data better.
Answer:
Sum = 120, so mean = 120 ÷ 5 = 24. Sorted: 11, 12, 13, 14, 70, so median = 13. The median (13) represents the data better, because the outlier 70 pulls the mean above four of the five values.

Teacher's Note:
1. An outlier distorts the mean.
2. Prefer the median when there is an outlier.

Question 28. In a bar graph of average heights, the vertical axis begins at 145 cm instead of 0. Why can such a graph mislead a reader?
Answer:
The bars then show only how much each value is above 145 cm. A small real difference looks like a huge difference in bar length, so the bar lengths must not be compared as ratios.

Teacher's Note:
1. Always check where the axis starts.
2. Such a graph is a zoomed-in view.

Question 29. In an innings a team scored 407 runs for the loss of 10 wickets, and yet the median of the runs scored by its 11 players was 0. Explain briefly how this is possible.
Answer:
With 11 players the median is the 6th sorted score, so a median of 0 means at least 6 players scored 0. The 407 runs came from a few players who scored heavily, together with extras.

Teacher's Note:
1. The median ignores how large the big values are.
2. A few large values can make a big total.

Question 30. The mean marks of a group of 5 students is 60. A sixth student who scored 72 marks joins the group. Find the new mean.
Answer:
Total of 5 students = 5 × 60 = 300. New total = 300 + 72 = 372 for 6 students. New mean = 372 ÷ 6 = 62.

Teacher's Note:
1. Work with totals when a value is added.
2. A value above the mean raises the mean.