Data Handling — Mental Maths

Fill in the blanks:

(i) Bar graphs are ..... representation of ungrouped data.

(ii) In a grouped frequency distribution, the difference between lower limit and upper limit of a class is called ......

(iii) The mid point of the class interval is called ......

(iv) Bar graphs of grouped data are called .....

(v) The circle graphs are commonly called ......

(vi) An experiment which has more than one possible outcomes and it is not possible to predict the outcome in advance is called ......

(vii) The outcomes which ensures the occurrence of an event are called ......

(viii) An event which never happens is called ......

Answer

(i) Bar graphs are visual representation of ungrouped data.

(ii) In a grouped frequency distribution, the difference between lower limit and upper limit of a class is called class size or class width.

(iii) The mid point of the class interval is called class mark.

(iv) Bar graphs of grouped data are called histograms.

(v) The circle graphs are commonly called pie charts or pie graphs.

(vi) An experiment which has more than one possible outcomes and it is not possible to predict the outcome in advance is called random experiment.

(vii) The outcomes which ensures the occurrence of an event are called favourable outcomes.

(viii) An event which never happens is called an impossible event.

State whether the following statements are true (T) or false (F):

(i) The data arranged in ascending or descending order of size is called data array.

(ii) The lower limit of class 10-20 is 20.

(iii) The class size of class 20-30 is 10.

(iv) The class mark of 25-35 is 30.

(v) There is no difference between bar graphs and histograms.

(vi) In histograms the breadth of a rectangle is meaningless.

(vii) In histograms, there is no gap between two adjacent rectangles.

(viii) In a pie chart, size of each sector is proportional to the value of item represented by it.

(ix) In a pie chart, angle of sector = $\dfrac{\text{value of item}}{\text{sum of values of all items}} \times 180°$

(x) In tossing a coin getting head or tail are equally likely events

(xi) Probability of an event E satisfies 0 ≤ P(E) ≤ 1

(xii) P(occurrence of an event) = P(non-occurrence of an event)

Answer

(i) The data arranged in ascending or descending order of size is called data array.

Hence, the given statement is true.

(ii) In the class 10-20, the smaller number 10 is the lower limit and the larger number 20 is the upper limit.

Hence, the given statement is false.

(iii) Class size = Upper limit - Lower limit

⇒ Class size = 30 - 20

⇒ Class size = 10

Hence, the given statement is true.

(iv) Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

⇒ Class mark = $\dfrac{35 + 25}{2}$

⇒ Class mark = $\dfrac{60}{2}$

⇒ Class mark = 30

Hence, the given statement is true.

(v) Bar graphs are used for ungrouped data and there are gaps between the bars, whereas histograms are used for grouped data and there is no gap between adjacent rectangles.

Hence, the given statement is false.

(vi) In a histogram the breadth of a rectangle is meaningful as it represents the class size.

Hence, the given statement is false.

(vii) In histograms, there is no gap between two adjacent rectangles as there is no gap between the class intervals.

Hence, the given statement is true.

(viii) In a pie chart, the whole circle is divided into sectors and the size of each sector is proportional to the value of the item represented by it.

Hence, the given statement is true.

(ix) As the angle about the centre of a circle is 360°, in a pie chart angle of sector = $\dfrac{\text{value of item}}{\text{sum of values of all items}} \times 360\degree$ and not 180°.

Hence, the given statement is false.

(x) On tossing a coin there is no reason for a head to occur in preference to a tail, so getting a head or a tail are equally likely events.

Hence, the given statement is true.

(xi) The number of outcomes favourable to an event E is greater than or equal to 0 and is less than or equal to the total number of outcomes, so 0 ≤ P(E) ≤ 1.

Hence, the given statement is true.

(xii) P(occurrence of an event) and P(non-occurrence of an event) are equal only when the number of favourable outcomes is half of the total number of outcomes, which is not true for every event.

For example, when a die is thrown, P(getting the number 5) = $\dfrac{1}{6}$ whereas P(not getting the number 5) = $\dfrac{5}{6}$.

Hence, the given statement is false.