Data Handling(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

DATA HANDLING MCQs

Total Questions : 114 | Page 4 of 12 pages

Question 31. Find the arithmetic mean of the following data : [2 MARKS]
(a) 2, 3, 4, 5, 6, 7, 8, 9
(b) 12,13,14,15,16,17,18,19, 20

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Each part: 1 Mark
The arithmetic mean is,

Mean = \frac{Sum of all observations}{Total number of observations}

(a)

Mean = \frac{2 + 3 + 4 + 5 + 6 + 7 + 8 + 9}{8}

\Rightarrow Mean = \frac{44}{8} = 5.5

(b)

Mean = \frac{12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20}{8}

\Rightarrow Mean = \frac{144}{9} = 16

Question 32. Marks obtained by students out of 20 in a class test are written on the board. What is the range of the marks?
12 ,14 , (-1), (-6), 15, 0, 8, 2. [2 MARKS]

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Formula: 1 Mark
Result:1 Mark
Range is defined as the difference between the highest and the lowest observation.
Here, after arranging marks inascending order : ( -6 ),( -1 ) , 0 , 2, 8 , 12 , 14 , 15.
Lowest observation: (-6)
Highest observation: 15
Range = Highest observation -Lowest observation
Range = 15 - (-6) = 21

Question 33. Find the mean of 9, 10, 8, 9, 12, 10. [2 MARKS]

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Formula: 1 Mark
Result:1 Mark

M e a n = \frac{Sum of all observation}{Total number of observation}

M e a n = \frac{9 + 10 + 8 + 9 + 12 + 10}{6} = 9.66

.
The mean is 9.66.

Question 34. The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

\begin{matrix} D a y & M o n & T u e & W e d & T h u r s & F r i & S a t & S u n R a i n f a l l & 0.0 & 12.2 & 2.1 & 0.0 & 20.5 & 5.5 & 1.0 (i n m m) \end{matrix}

(i) Find the range of the rainfall in the above data.
(ii) Find the mean rainfall for the week.
(iii) On how many days was the rainfall less than the mean rainfall? [4 MARKS]

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Range: 1 Mark
Mean: 2 Marks
Answer: 1 Mark
(i) Range = Highest observation -Lowest observation
Range = 20.5 - 0.0 = 20.5
(ii)

M e a n = \frac{S u m o f a l l o b s e r v a t i o n}{T o t a l n u m b e r o f o b s e r v a t i o n}

M e a n = \frac{0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0}{7}

M e a n = \frac{41.3}{7} = 5.9

(iii) On Mon, Wed, Thurs, Sat, and Sun the rainfall was less than mean rainfall i.e. 5.9 mm.

\Rightarrow

On 5 daysthe rainfall was less than the mean rainfall.

Question 35. Following cards are facing down: [3 MARKS]

Following Cards Are Facing Down: [3 MARKS]Find The Probabil...

Find the probability of drawing:
1. Vowel
2. Consonant

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Formula: 1 Mark
Application: 1 Mark
Calculation: 1 Mark
Here, we have 8 cardsA, E, I,O,U,B, G, H
Vowels = A, E, I, O, U

\Rightarrow

Number of vowel cards = 5
So, probability of drawing vowel

P (E) = \frac{No.of vowels}{Total number of cards} = \frac{5}{8}

Consonants = B, G, H

\Rightarrow

Number ofConsonant cards = 3
Probability of drawing consonant:

P (E) = \frac{No.of consonants}{Total number of cards} = \frac{3}{8}

Question 36. The runs scored by 11 players in a cricket match are 12, 32, 43, 32, 12, 32, 12, 32, 36, 54,11. Find the mode of the runs scored by the players. [2 MARKS]

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Steps: 1 Mark
Result:1 Mark
Given runs are,12, 32, 43, 32, 12, 32, 12, 32, 36, 54,11.
Arranging the numbers in ascending order:
11, 12, 12, 12, 32, 32, 32, 32, 36, 43, 54.
Mode of a set of observations is the observation which occurs most often.
Clearly, here, 32 runs are scored by most of the batsman.
So, the mode of the observation is32.

Question 37. The ages in years of 10 teachers of a school are:
34, 43, 31, 56, 37, 28, 25, 35, 40, 42
(i) What is the range of the ages of the teachers?
(ii) What is the mean age of these teachers? [3 MARKS]

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Formulas: 1 Mark
Each part: 1 Mark
(i) Arranging the ages in ascending order, we get:
25, 28, 30, 34, 35, 37, 40, 42, 43, 56
We find that the age of the oldest teacher is 56 years and the age of the youngest teacher is 25 years.
Range of the ages of the teachers = (56 - 25) years = 31 years
(ii) Mean age of the teachers:

= \frac{25 + 28 + 30 + 34 + 35 + 37 + 40 + 42 + 43 + 56}{10} y e a r s

= \frac{370}{10} y e a r s = 37 y e a r s

Question 38. Given below are the weights of 9 different students of class 10^th: 54 kg , 56 kg , 54 kg , 57 kg , 54 kg , 52 kg , 54 kg , 55 kg , 59 kg. Find the mode and median of the given observations. [3 MARKS]

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Steps: 2 Marks
Result: 1 Mark
Given,
Weights of 9 different students : 54kg, 56kg , 54kg , 57kg , 54kg , 52kg , 54kg , 55kg , 59kg
Arranging the data in ascending order,
52kg,54kg,54kg,54kg,54kg,55kg,56kg,57kg,59kg
Median is the middle most observationof the given observations

\Rightarrow

Median = 54kg
Mode is the most repeatedobservationof the given observations
Clearly, 54kg is the mostrepeated observation

\Rightarrow

Mode = 54kg

Question 39. (a) The number of boys taking part in different extracurricular activities is shown in the table given below. Represent the data on a bar graph. [4 MARKS]

\begin{matrix} Activities & No. of boys Scouts & 25 Debate & 13 Science Club & 7 Inst. Music & 30 S.U.P.W & 15 \end{matrix}

(b) What is the difference between the number of mangoes sold on Sunday and the number of custard apples sold on Wednesday?

(a) The Number Of Boys Taking Part In Different Extracurricu...

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(a) Scale: 1 Mark
Bar graph: 1 Mark
(b) Solution: 2 Marks
(a) Scale: x axis - extracurricular activities
y axis - Number of boys; 1 cm = 5 units

(b) Number of mangoes sold on Sunday = 85
Number of custard apples sold on Wednesday = 20
Difference = 65

Question 40. In the following table, the number of villains caught by BATMAN and SUPERMAN during a week is given. Whose daily average is more and how much is it?