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Bar graphs are better indicative as they show exact numerical value. Also, to indicate negative values and positive values, it looks easier in a bar graph.

Since, Histogram is a graphical representation of data, if data represented in manner of class-interval. Therefore, for case (b) and (d), we would use a histogram to show the data, because in these cases, data can be divided into class-intervals. In case (b), a group of competitions having different heights in an athletics meet. In case (d), the number of passengers boarding trains in an interval of one hour at a station.

(i) Range of numbers = Highest number – Lowest number = 62 – 42 = 20

(ii) 9 numbers are greater than 50

(iii) 6 numbers are between 40 and 50 Ans

(c) 5 : 14

Mode = 3 Median – 2 Mean

∴ Mode : Median = 7 : 4

∴ Let, Mode = 7x and Median = 4x

∴ 7x = 3 × 4x – 2 Mean 

⇒ 7x = 12x – 2 Mean 

⇒ 2 Mean = 5x ⇒ Mean = \(\frac52x\)

∴ Mean : Mode = \(\frac52x\) : 7x = 5x : 14x

= 5 : 14

Given data.

7x, 5x, 3x, 2x, x (x > 0) and Range = 12. 

Maximum value = 7x; Minimum value = x 

Range = Maximum value – Minimum value 

= 7x – x – 12 

⇒ 6x = 12 

⇒ 6x/6 = 12/6

∴ x = 12

(d) 2.66

Arranged in ascending order, the values are

  \(\frac{x}{6},\) \(\frac{x}{2},\) \(\frac{x}{4},\) \(\frac{3x}{5}\) and \(\frac{7x}{10}\) 

∴ Median value = \((\frac{5+1}{2})\)th value

= 3rd value = \(\frac{x}{2}\)

Given \(\frac{x}{2}\) = 3 ⇒ x = 6

∴ The values are \(\frac{6}{6},\) \(\frac{6}{4},\) \(\frac{6}{2},\) \(\frac{3\times6}{5},\) \(\frac{7\times6}{10},\)

i.e., 1, 1.5, 3, 3.6 and 4.2

∴ Mean = \(\frac{1+1.5+3+3.6+4.2}{5}\)

= \(\frac{13.3}{5}\) = 2.66

(d) \(\overline{x} + (a-b)\)

Given, \(\frac{x_1 + x_2+x_3+.....+x_n}{n}=\overline{x}\)

∴ \(\frac{x_1 +(a-b) +x_2+(a - b)+x_3+(a-b)+.....+x_n+(a-b)}{n}\)

= \(\frac{x_1 + x_2+x_3+.....+x_n}{n} + \frac{n(a-b)}{n}\)

= \(\overline{x} + (a-b)\)

(a) 15

The seven boys who failed the test scored the marks less than these given marks. Let the marks be x₁ , x₂ , x₃ , x₄ , x₅ , x₆ , x₇ 

Then the marks arranged in ascending order are x₁ , x₂ , x₃ , x₄ , x₅ , x₆ , x₇ , 12, 15, 15, 15, 16, 17, 17, 18,18, 19, 19, 19

∴ Median score = \((\frac{19+1}{2})\)th item

= 10th item = 15.

(d) \(\frac{4}{3}\)\(\overline{x}\)

Mean of the combined data = \(\frac{n\times2\overline{x}+2n\times\overline{x}}{n+2n}\)

= \(\frac{2n\overline{x}+2n\overline{x}}{3n}\) = \(\frac{4n\overline{x}}{3n}=\frac43\overline{x}\)

(c) 3

m = \(\frac{1+7+5+3+4+4}{6}=\frac{24}{6}=4\)

Now mean of 3, 2, 4, 2, 3, 3 and p is (4 –1) = 3

∴ \(\frac{3+2+4+2+3+3+p}{7}=3\)

⇒ \(\frac{17+p}{7}\) = 3 ⇒ 17 + p = 21 ⇒ p = 4

∴ The observations are 3, 2, 4, 2, 3, 3 and 4.

Arranged in ascending order, the numbers are 2, 2, 3, 3, 3, 4, 4.

Median = \((\frac{7+1}{2})\)th value = 4th value = 3

Median is one of the observations in the data if number of observations is Odd.

Correct option is : (ii) 35

Correct option is : (iii) 21

frequency

The number of times an observation occurs in a given data, is called its frequency.

Required frequency table for given data is:

(i) 60 families have 2 children each.

(ii) Zero

(iii) The percentage of families having 4 children = 60/300 x 100 = 20%

(d) Data represented using circles is known as pie chart.

Note Bar graph Data using bars of different heights in a graphical display is known as bar graph (bar chart).

Histogram Grouped data can be represented by a histogram.

Pictograph Data using pictures and symbols to represent the statistical information is known as pictograph.

Correct option is C) 13 Y

(a) In year 2002, maximum wheat produced. 

(b) In year 1998, minimum wheat produced.

(a) This bar graph shows the number of shirts sold from Monday to Saturday. 

(b) To show number of shirts on vertical line, scale 1 unit = 5 shirts. 

(c) Maximum shirts sold on Saturday, number of shirts = 60. 

(d) Minimum number of shirts sold on Tuesday. 

(e) 35 shirts sold on Thursday

(a) Scale – 1 unit length = 10 students 

(b) New admission every year = 10 × 10 = 100 

(c) Number of students in year 2003 = 60 × 10 = 600 

And number of students in year 2000 = 30 × 10 = 300 

Yes, number of students in year 2003 are double of number of students in year 2000.

(i) Age group 15-20 has the highest number of literate female.

(ii) Class width = 5 years 

(iii) Lowest frequency = 320 

(iv) Class marks of classes = average of class intervals = 17.5, 25, 32.5, 40, 47.5, 55 

(v) Age group of 10-15 has the lowest literate females.

Arranging the heights in ascending order, we get

128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154

(a) Height of the tallest boy is 154 cm.

(b) Height of the shortest boy is 128 cm.

(c) Range = Highest value – Lowest value = (154 – 128) cm = 26 cm

(d) Since, observations are odd in number

∴ Median height = Middle most height = 142 cm

(i) Class mark for the class interval 40 – 45:

Class mark = (40+45) / 2 = 85/2 = 42.5

(ii) Range of the above weights:

Range = Highest value – Lowest value

Range = 74 – 30 = 44

(iii) Number of classes = 9

The frequency distribution table is shown below:

The frequency table shows the weekly wages of 15 workers in a factory:

(i) The range of wages (in Rs) is 350-150 i.e. 200.

(ii) From the frequency table, we can see that the number of workers earning Rs 350 is 1.

(iii) Here, the minimum wage is 150. Hence, the number of workers earning the minimum wage is 3.

False.

The difference between the highest and lowest observations in a given data is called its Range.

In the figure data is: 

S, A, H, S, A, M, S, T, M, T, H, % A, T, S, M, H, M, A, S, T, M, A, T, S, T, H, M. 

By arranging the letters, of same type together. 

A, A, A, A, A, H, H, H, H, M, M, M, M/M, M, S, S, S, S, S, S, T, T, T, T, T, T, T.

As T occurs most frequently in the data. 

∴ Mode = T Data having only one mode is known as unimodal data. 

So, given data is unimodal data.

The given data is arranged in ascending order.
12, 12, 13, 13, 14, 14, 14, 16, 19
∴ The middle number is median = 14
∴ The mode is highest frequency score = 14

True.

Mode is the observation that occurs most frequently in the data.

The frequency table with class intervals 0 – 5, 5 – 10, 10 – 15, . . . , 45 – 50 is shown below:

The frequency table of the scores is shown below:

(i) The mode is always one of the numbers in a data.  True

(ii) The mean is one of the numbers in a data.  False

(iii) The median is always one of the numbers in a data.  True

(iv) The data 6, 4, 3, 8, 9,12,13, 9 has mean 9.  False

1. Number 3 appeared maximum times (7 times) on dice. 

2. Number 5 appeared minimum times (2 times) on dice. 

3. Difference between the number of times odd numbers have appeared and number of times even numbers have appeared is zero. 

⇒ Frequency of even number occurred ~ Frequency of odd number occurred 

= Frequency of 2, 4, 6 ~ Frequency of 1, 3, 5 

= (4 + 6 + 5) ~ (6 + 7 + 2) = 15 ~ 15 = 0

(i) Range of Wages = 350 – 150 

(ii) Workers getting Rs.350 = 1. 

(iii) Workers getting minimum wages = 3.

Correct option is C) 6

(i) From the figure, the highest rectangle corresponds to the largest number of workers. The required interval is Rs 950−1000. There are 8 workers in this interval.

(ii) The lowest rectangle corresponds to the least number of workers. The required interval is Rs 900−950. There are 2 workers in this interval.

(iii) The total number of workers is the sum of workers in all the intervals. It can be calculated as follows:

Total workers = 3 + 7 + 5 + 4 + 2 + 8 + 6 + 5 = 40 workers

(iv) The factory intervals are 750−800, 800−850, .. 1050−100. Hence, the factory size is 50.

(i) Wage-group 950-1000 has the largest numbers of workers and their number is 8.

(ii) Wages 900-950 is getting the least number of workers. The number of such workers is 2.

(iii) Total number of workers = total no. of frequencies = 3+7+5+4+2+8+6+5 = 40

(iv) Factory size = 50

The frequency table of the daily minimum temperatures is shown below:

(d) decreased by 1.5

From the question,

Khilona earned scores in3 exam = 97, 73, 88

Then, Mean = (97 + 73 + 88 +)/3

Mean = 86 marks

Khilona earned scores in 4 exam = 97, 73, 88, 80

Then, Mean = (97 + 73 + 88 + 80)/4

Mean = 84.5 marks

Then, her average score will be 86 – 84.5 = 1.5, decreased by 1.5

(i) Cat is the most popular pet.

(ii) Eight(8) students have dog as a pet.

Correct option is  B) Median

(a) Since, no number is less than 1 on a die.

∴ Getting a number less than 1 on throwing a die is impossible to happen.

(b) When a coin is tossed two outcomes are possible i.e., Head or Tail.

∴ Getting head when a coin is tossed may or may not happen.

(c) A team winning the match may or may not happen because a team can lose the match.

(d) Christmas will be on 25 December is certain to happen.

(e) Since, moon always revolves around the earth.

∴ Today moon will not revolve around the earth is impossible to happen.

(f) A ball thrown up in the air will fall down after some time is certain to happen due to gravity of earth.

(d) 4, 3, 4, 3, 4, 6, 4

Mean of the given data = (4 + 3 + 4 + 3 + 4 + 6 + 4)/7

= 4

Mode is the observation that occurs most frequently in the data i.e. 4.

When the given data is arranged in ascending (or descending) order, then the middle most observation is the median of the data.

Arranging the given data, 3, 3, 4, 4, 4, 4, 6.

So, the median is 4.

The probability of an event which is impossible to happen is 0.

(i) Yes, it is certain to happen.

(ii) It can happen but not certain

(iii) It is impossible.

(iv) It can happen but not certain.

(v) It can happen but not certain.

The frequency table of the monthly wages of 28 laborers working in a factory is shown below: