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1.	The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:(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.
Answer» 1)Range=H-L=20.5-0=20.5 2)Mean=`(0+0+1+2.1+5.5+12.2+20.5)/7` Mean=5.9 mm 3)5 days.

2.	A coin is flipped to decide which team starts the game. What is the probability that your team will start?
Answer» We know, Probability(P) = Number of favorable outcomes/Total number of outcomes When a coin is flipped, there can be total `2` outcomes head and tail. And we can select `1` option between Head or tail. So, the probability that our team start `= 1/2`.

3.	Draw a pie chart showing the following information. The table shows the colours preferred by a group of people. Colours Nubers of people Blue `18,` Green `9,` Red `6,` Yellow `3,` and Tatal `36`
Answer» Given above is the video Showing how to make pie chart from given data.

4.	Find the difference between the place value and face value of 9 in 309,812.
Answer» face value=9 Place value=9*1000=9000 difference=9000-9=8991.

5.	The weekly wages (in Rs) of 30 workers in a factory are.830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840Using tally marks make a frequency table with intervals as 800–810, 810–820 and so on.
Answer» We can see minimum value in the given data is `804` and the maximum value is `898`. So, the class interval can be,`800-810,810-820,820-830,830-840,840-850,850-860,860-870,870-880,880-890,890-900`. Now, we can map given weekly wages according to their class interval. Please refer to video for complete frequency table using tally marks.

6.	Observe this bar graph which shows the marks obtained by Aziz in half-yearly examination in different subjects.
Answer» a)Information about the marks obtained in subject by aziz in half year exams. b)Hindi c)Social science d)Hindi=80 marks english=60 marks Maths=70 marks Science=50 marks social science=40 marks

7.	A survey was carried out on 30 students of class VI in a school. Data about the different modes of transport used by them to travel to school was displayed as pictograph. What can you conclude from the pictograph?
Answer» 4 students uses private car as mode of transportation. 5 students uses school bus as mod of transportation. mode of transportation used by most of the students is school bus mode of transporation used by least number of students is cycle.

8.	In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.(a) Find how many students obtained marks equal to or more than 7.(b) How many students obtained marks below 4?
Answer» Please refer to video for constructing a table using tally marks. From the table, (a) Number of students who obtained marks equal to or more than 7 ` = 5+4+3 = 12` (b) Number of students who obtained marks below 4 ` = 2+3+3 = 8`

9.	A cricketer scores the following runs in eight innings:58, 76, 40, 35, 46, 45, 0, 100.Find the mean score.
Answer» Mean=sum of runs/total innings Mean=`(58+76+40+35+46+45+0+100)/8` mean=400/8=50 runs.

10.	Total number of students of a school in different years is shown in the following table
Answer» A) a) 6 b)5 complete symbols and 1 incomplete symbols B) B is more informative.

11.	The ages in years of 10 teachers of a school are:32, 41, 28, 54, 35, 26, 23, 33, 38, 40(i) What is the age of the oldest teacher and that of the youngest teacher?(ii) What is the range of the ages of the teachers?(iii) What is the mean age of these teachers?
Answer» 1) age of the oldest teacher=54 years age of the youngest teacher=23 years 2)Range=54-23=31 years 3)mean=sum of ages/number of people mean=`(32+41+28+54+35+26+23+33+38+40)/10` mean=350/10=35 years.

12.	Let X be a continuous random variable with p.d.f. f(x) = kx(1-x), 0b).. find k and determine anumber b such that `P(X le b) ` = `P (X ge b)`
Answer» `kint_0^1(x(1-x))dx=1` `k[int_0^1xdx-int_0^1x^2dx]=1` `k[x^2/2--x^3/3]_0^1` `k[1/2-1/3]=1` `k=6` `P(0,b)=P(b,1)` `6int_0^b(x-x^2)dx=1/2` `6[x^2/2-x^3/3]_0^b=1/2` `b^2/2-b^3/3=1/12` `4b^3-6b^2+1=0` `When b=1/2` `4/8-6/4+1=0` `4b^3-6b^2+1=(2b-1)(2b^2-2b-1)` `2b-1=0` `b=1/2` or `2b^2-2b-1=0` `b=(2pmsqrt12)/4` `=1/2pmsqrt3/2` Which is not possible so, `1/2+sqrt3/2>1,1/2-sqrt3/2<0`.

13.	Find the median of the data: 24, 36, 46, 17, 18, 25, 35
Answer» First arrange the data in ascending order=>`17,18,24,25,35,36,46` Median of the data is 25.