Median from data = x+ 2
or 21 = x + 2
x = 21-2
x = 19

Frequency distribution of scores:

(a) Red colour of the car liked by people =15
    Black colour of the car liked by people = 20
    White colour of the car liked by people = 17
    Silver colour of the car liked by people = 12
    Other colour of the car liked by people = 9
    Hence, black colour of the car is the most liked.
(b) Mode concept used in (a).

Given heights (in ern) of 6 girls in a group are
142,150,146,154, x and 148.
Sum of heights =142 + 150 + 146 + 154 + x + 148
=740 + x
\(Mean/Average\frac { sum\quad of\quad observatins }{ number\quad of\quad observations } \)
\(\Rightarrow\)  \(147=\frac { 740+x }{ 6 } \Rightarrow 147\times 6=740+x\)
\(\Rightarrow\) 882 = 740 + \(\Rightarrow\) x = 882 - 740 = 142

[HH, HT, TH, TT],\(\frac { 3 }{ 4 } \)

Out of 6 marbles, one can be drawn in 6 ways
\(\therefore\) Total number of possible outcomes = 6
A probability of drawing marble with number 2, P(2) = \(\frac{1}{6}\)

A die when rossed shall land up with 8 on top, it is impossible

55

On arranging the data in ascending order, we get 128,132,135,139,141,143,146,149,150,151
From ascending order, we get
Highest value = 151
Lowest value = 128
Range of the data = Highest value - Lowest value
= 151-128
= 23

Given, marks obtained by a group of students in a Science test
85,76,90,85,39,48,56,95,81,75
On rearranging the marks in ascending order, we get
39,48,56,75,76,81,85,85,90,95
Range of the marks obtained = Highest marks - Lowest marks
= 95 - 39 = 56

Given data are 35,32, 35, 42, 38, 32 and 34.
For median of the given data, we first arrange the given data in ascending order, we get
Here, n = 7, which is odd
\(\left( \frac { n+1 }{ 2 } \right) ^{ th }\) data will be the median i.e. \(\frac { 7+1 }{ 2 } =\frac { 8 }{ 2 } \)=4th observation
Hence, 4th observation, i.e. 35 is the median of the given data

2

ClassVIII

From part (i), it is clear that the child has improved his performance the least in S. Science, i.e. 2 marks.

(i) We have, 6,15,120,50,100,80,10,15,8,10,15
On arranging the data in ascending order, we get 6,8,10,10,15,15,15,50,80,100,120 Now, sum of the runs
= 6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120
= 429
Number of players = 11
\(\therefore\)  \(Mean=\frac { sum\quad of\quad the\quad runs }{ NUmber\quad of\quad players } =\frac { 429 }{ 11 } =39\)
(ii) From part (i), ascending order of runs is as follows:
6,8,10,10,15, 15, 15,50,80,100,120
Here, 15 occurs more frequently i.e. 3 times.
\(\therefore\)  Mode =15
(iii) The value of the middle observation is 15.
\(\therefore\)  Median =15
No, mean, mode and median are not same.​​​​​​​

On arranging the adjacent data in descending order, we get

From the above table, it is clear that highest rainfall was on Friday i.e. 20.5 mm and lowest rainfall was on Monday and Thursday i.e. 0.0 mm.
\(\therefore\)   Range of rainfall = Highest rainfall - Lowest rainfall = Rainfall on Friday - Rainfall on Monday or Thursday
= 20.5- 0.0= 20.5

To find the mean number of points per game for C, we divide the total points by 3, because C did not play 3rd game.

We know that, there are seven days in a week. Let the sleeping hours during a week are as follows:

Now, sum of the sleeping hours of one week
=8+7+6+7+6+7+8=49h
and number of days in a week = 7
Mean = \(\frac { total\ sleeping\ hours }{ total\ number\ of\ days } =\frac { 49 }{ 7 } =7h\)
Hence, the mean of your sleeping hours during Cine week is 7 h.