CBSE Class 7 Mathematics Connecting the Dots MCQs Set 11

Answer: (b) How many hours do the Grade 7 students of our school sleep at night?

Explanation:
1. A statistical question is one whose answer can be found only by collecting data, because the answer varies from case to case.
2. Sleeping hours are different for different students, so we must collect and study data to answer it.
3. The other three questions have one fixed answer each, so the statistical question is (b).

Teacher's Note:
1. Ask yourself: will the answer vary from person to person or day to day?
2. One fixed answer means the question is not statistical.

Answer: (c) dividing the sum of all the values by the number of values

Explanation:
1. Mean = (sum of all the values) ÷ (number of values).
2. Option (a) describes the range and option (b) describes the median.
3. So the mean is found by dividing the sum of all the values by the number of values.

Teacher's Note:
1. Mean, median and range are three different numbers; keep their rules apart.
2. The mean is the fair share of the total.

Answer: (a) arrange all the values in increasing or decreasing order

Explanation:
1. The median is the middle value of the data after it has been sorted.
2. So we must first arrange the values in order; only then can we pick out the middle value.

Teacher's Note:
1. Never pick the middle value of unsorted data.
2. Adding and dividing are steps for the mean, not the median.

Answer: (d) an outlier

Explanation:
1. A value that lies far away from all the other values of the data is called an outlier.
2. For example, a height of 118 cm among heights of 165, 170, 173 and 175 cm is an outlier.

Teacher's Note:
1. An outlier can be very large or very small.
2. Outliers pull the mean towards themselves.

Answer: (c) shows the extremes and how the data values cluster or spread out

Explanation:
1. A dot plot puts one dot for each value above a number line, piling up dots for repeated values.
2. So we can see at once the smallest and largest values and where the values crowd together or spread out.
3. It sorts the values, so the order of collection is lost, and it does not give the mean directly. The answer is (c).

Teacher's Note:
1. Repeated values show up as taller piles of dots.
2. A dot plot loses the original order of the data.

Answer: (a) a clustered column graph

Explanation:
1. When two bars, one for each group, stand side by side for every category, the graph is a clustered column graph.
2. It is also called a double bar graph.

Teacher's Note:
1. Each cluster holds one bar for each group.
2. A key tells which bar belongs to which group.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A is true: the mean and the median are the two measures of central tendency in this chapter.
2. R is true: each of them gives a central value around which the data gathers.
3. This is exactly the reason for the name, so R is the correct explanation of A.

Teacher's Note:
1. 'Central tendency' means the tendency of data to gather around a centre.
2. Range is not a measure of central tendency; it measures spread.

Answer: (d) A is false, but R is true.

Explanation:
1. Sorting the data gives 2, 4, 5, 7, 9. The middle (3rd) value is 5, so the median is 5, not 2. A is false.
2. R correctly gives the meaning of the median, so R is true.
3. So A is false but R is true.

Teacher's Note:
1. 2 is the middle value of the unsorted list, which is a common mistake.
2. Always sort first.

Answer: (a) Only Statement I is true.

Explanation:
1. Statement I is the meaning of statistics given in the chapter, so it is true.
2. Statement II is false: the mean of 4 and 7 is (4 + 7) ÷ 2 = 5.5, which is not one of the values.
3. So only Statement I is true.

Teacher's Note:
1. A mean can even be a decimal when all the data are whole numbers.
2. One counter-example is enough to show a statement is false.

Answer: (b) Only Statement II is true.

Explanation:
1. A dot plot places values along a number line, which sorts them, so the order of collection is lost. Statement I is false.
2. The leftmost and rightmost dots show the smallest and largest values at once, so Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. After plotting monthly prices, we can no longer tell which price was for which month.
2. The extremes are the first and last dots.

Answer: (b) 6

Explanation:
1. Total books = 4 + 6 + 9 + 5 + 6 = 30.
2. Number of friends = 5.
3. Mean = 30 ÷ 5 = 6 books. (30 is the total, not the mean.)

Teacher's Note:
1. Do not stop at the total; divide by the number of values.
2. Check: the mean lies between the smallest (4) and largest (9) values.

Answer: (b) (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r)

Explanation:
1. Mean = sum of the values ÷ number of values, so (i)-(q).
2. Median = middle value of the sorted data, so (ii)-(p).
3. Outlier = a value far away from the rest, so (iii)-(s).
4. Range = maximum − minimum, so (iv)-(r). The answer is (b).

Teacher's Note:
1. Learn each term with a tiny example.
2. Range measures spread; mean and median measure the centre.

Answer: (c) The mean

Explanation:
1. A very large value increases the sum a lot, so the mean goes up noticeably.
2. The median depends only on the position of the middle value, so it shifts very little.
3. The minimum does not change and the number of values grows only by 1. So the mean changes the most.

Teacher's Note:
1. The mean is sensitive to outliers; the median is not.
2. This is why the median is preferred when there is an outlier.

Answer: (b) 6

Explanation:
1. A score of 0 is a real score from a match he played, so that match is counted.
2. The match he did not play has no value at all and is not counted.
3. So the total is divided by the number of matches played, 6.

Teacher's Note:
1. Zero is a value; 'not played' is no value.
2. Never count a match in which the player did not take part.

Answer: (d) the scale of the graph

Explanation:
1. A statement that tells how much one unit of length on an axis stands for is the scale of the graph.
2. Here one unit of length stands for 20 rockets.

Teacher's Note:
1. Always read the scale before reading values from a graph.
2. The scale is chosen so that all values fit on the graph.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. R is true: a very small value lowers the total and so pulls the mean down, while the middle value of the sorted list barely changes.
2. This is exactly why the mean falls below the median, so A is true.
3. So both are true and R correctly explains A.

Teacher's Note:
1. Example: 118, 165, 170, 173, 175 has mean 160.2 and median 170.
2. The mean is pulled towards the outlier.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A is true: with no outlier, nothing pulls the mean away from the middle, so mean and median are close.
2. R is true, but it only gives the definition of the mean.
3. R does not explain why the mean and the median come close, so both are true but R is not the correct explanation.

Teacher's Note:
1. A true definition is not always the reason for a statement.
2. Ask: does R tell us WHY A happens?

Answer: (c) A is true, but R is false.

Explanation:
1. A is true: the median of 20, 22, 24, 26 is (22 + 24) ÷ 2 = 23, which is not a data value.
2. R is false: for an even number of values, the median is the average of the two middle values, not the larger one.
3. So A is true but R is false.

Teacher's Note:
1. With an even count, add the two middle values and halve the sum.
2. The median then lies between two data values.

Answer: (a) Only Statement I is true.

Explanation:
1. A high outlier increases the sum and pulls the mean above the median, so Statement I is true.
2. A low outlier pulls the mean down, below the median, so Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. The mean moves towards the outlier.
2. High outlier: mean > median; low outlier: mean < median.

Answer: (c) Both the statements are true.

Explanation:
1. Both bars of a cluster stand on the same vertical axis, so they are read with the same scale. Statement I is true.
2. Patterns inside the bars help colour-blind readers and keep the groups apart in greyscale printing. Statement II is true.
3. So both the statements are true.

Teacher's Note:
1. One graph has one scale for all its bars.
2. Patterns make a graph readable without colour.

Answer: (d) 11.5 mm

Explanation:
1. Sorted: 7, 9, 11, 12, 15, 20.
2. There are 6 values (even), so the median is the average of the 3rd and 4th values, 11 and 12.
3. Median = (11 + 12) ÷ 2 = 11.5 mm.

Teacher's Note:
1. An even count needs the average of two middle values.
2. Sort before choosing the middle values.

Answer: (a) (i)-(r), (ii)-(q), (iii)-(s), (iv)-(p)

Explanation:
1. (i) (5 + 9 + 7) ÷ 3 = 21 ÷ 3 = 7, so (r).
2. (ii) (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5, so (q).
3. (iii) (10 + 20 + 30 + 40 + 50) ÷ 5 = 150 ÷ 5 = 30, so (s).
4. (iv) (1 + 1 + 4) ÷ 3 = 6 ÷ 3 = 2, so (p). The answer is (a).

Teacher's Note:
1. Count the values in each set before dividing.
2. The mean always lies between the smallest and largest values.

Answer: (d) April

Explanation:
1. Compare the two bars in each month: January 20 and 30, February 35 and 25, March 25 and 45, April 40 and 40.
2. Only in April do both bars reach the same height, 40 cycles.
3. So the shops sold an equal number of cycles in April.

Teacher's Note:
1. Equal sales means the two bars of a cluster have the same height.
2. Read each bar against the gridlines and the scale.

Answer: (b) Grade 7, by 6 students

Explanation:
1. Grade 6: 18 + 12 + 9 + 15 = 54 students.
2. Grade 7: 24 + 10 + 14 + 12 = 60 students.
3. 60 − 54 = 6, so Grade 7 had 6 more students.

Teacher's Note:
1. Add all the bars of one colour to get a group's total.
2. The scale here is 1 unit = 3 students.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. R is true: the mean of a group uses only the values of that group.
2. So the mean of one section tells us nothing about the heights of the other section; A is true.
3. R is exactly why A holds, so R is the correct explanation of A.

Teacher's Note:
1. Equal group sizes do not mean equal means.
2. To find a group's mean we need that group's own data.

Answer: (d) Only Statement II is true.

Explanation:
1. Data from just two schools cannot be stretched into a claim about every school in the country, so Statement I is false.
2. Statement II correctly states this limitation, so it is true.
3. So only Statement II is true.

Teacher's Note:
1. Do not generalise from a small amount of data.
2. In another school the boys may be taller on average.

Answer: (c) 46

Explanation:
1. Total marks of 6 students = 6 × 38 = 228.
2. Sum of the five known marks = 30 + 45 + 36 + 42 + 29 = 182.
3. Sixth student's marks = 228 − 182 = 46.

Teacher's Note:
1. Total = mean × number of values.
2. Check: (182 + 46) ÷ 6 = 38.

Answer: (d) The mean becomes smaller, while the median stays the same.

Explanation:
1. With 60: sum = 156, mean = 156 ÷ 7 ≈ 22.3; sorted 14, 15, 16, 16, 17, 18, 60, so median = 16.
2. Without 60: sum = 96, mean = 96 ÷ 6 = 16; sorted 14, 15, 16, 16, 17, 18, so median = (16 + 16) ÷ 2 = 16.
3. So the mean becomes smaller, while the median stays the same.

Teacher's Note:
1. Removing an outlier changes the mean a lot.
2. The median depends only on the middle position.

Answer: (c) (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)

Explanation:
1. (i) Mean = 75 ÷ 5 = 15, so (q).
2. (ii) Six values; median = (15 + 20) ÷ 2 = 17.5, so (r).
3. (iii) Range = 25 − 5 = 20, so (s).
4. (iv) Sorted 5, 7, 12; median = 7, so (p). The answer is (c).

Teacher's Note:
1. Sort 12, 7, 5 before choosing the middle value.
2. Range is a difference, not an average.

Answer: (b) Ravi is wrong, because the vertical axis starts at 145 cm and not at 0, so the bar lengths cannot be compared as a ratio; the two averages differ by only 8 cm.

Explanation:
1. The vertical axis starts at 145 cm, so each bar shows only how much the height is above 145 cm.
2. Team A's average is 150 cm and Team D's is 158 cm, a difference of just 8 cm.
3. 158 cm is nowhere near two and a half times 150 cm, so Ravi is wrong, for the reason given in (b).

Teacher's Note:
1. Always check where the vertical axis begins.
2. A cut axis gives a zoomed-in view; bar lengths cannot be compared as ratios.