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Chapters
1: Rational and Irrational Numbers
Unit 2: Commercial Mathematics
2: Compound Interest (Stage 1) [Basic Concepts]
3: Compound Interest (Stage 2) [Applications]
Unit 3: Algebra
4: Expansions
5: Factorisation
6: Simultaneous (Linear) Equations [Including Problems]
7: Indices [Exponents]
8: Logarithms
Unit 4: Geometry
9: Triangles [Congruency in Triangles]
10: Isosceles Triangles [Including Inequalities]
11: Mid-point Theorem and Its Converse [Including Intercept Theorem]
12: Pythagoras Theorem [Proof and Simple Applications with Converse]
13: Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
14: Construction of Polygons (Using ruler and compass only)
15: Area Theorems [Proof and Use]
16: Circle
Unit 5: Statistics and Graph Work
17: Statistics
▶ 18: Mean and Median [For Ungrouped Data Only]
Unit 6: Mensuration
19: Area and Perimeter of Plane Figures
20: Solids [Surface Area and Volume of 3-D Solids]
Unit 7: Trigonometry
21: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]
22: Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]
Unit 8: Co-Ordinate
23: Co-ordinate Geometry
24: Graphical Solution [Solution of Simultaneous Linear Equations, Graphically]
25: Distance Formula
![Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 18 - Mean and Median [For Ungrouped Data Only] - Shaalaa.com](/images/concise-mathematics-english-class-9-icse_6:e09935b48e334a1e8f06ebb2011509f8.jpg "Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 18 - Mean and Median [For Ungrouped Data Only]")
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Solutions for Chapter 18: Mean and Median [For Ungrouped Data Only]
Below listed, you can find solutions for Chapter 18 of CISCE Selina for Concise Mathematics [English] Class 9 ICSE.
Selina solutions for Concise Mathematics [English] Class 9 ICSE 18 Mean and Median [For Ungrouped Data Only] Exercise 18 (A) [Pages 264 - 265]
Multiple Choice Typе: Choose the correct answer from the options given below.
The mean of x − 2, x, x + 2, x + 4 is ______.
x + 1
x
4x + 4
x + 2
Mean of 10 observations (numbers) is 20. If one number is included, the mean becomes 21, the included number is ______.
431
31
231
131
Mean of 20 observations (numbers) is 30. If one number is excluded, the mean of remaining numbers becomes 28. The excluded number is ______.
532
1132
68
572
If each observation of the data is decreased by 15; then the mean ______.
remains same
is increased by 15
is decreased by 15
is multiplied by 15
If the mean of x1, and x2, is 12.5 and mean of x1, x2 and x3 is 16. The value of x3 is ______.
32
3.5
285
23
Find the mean of 43, 51, 50, 57 and 54.
Find the mean of the first six natural numbers.
Find the mean of the first ten odd natural numbers.
Find the mean of all factors of 10.
Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.
If different values of variable x are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5 and 11.1;
find
(i) the mean ` barx `
(ii) the value of ` sum (x_i - barx)`
The mean of 15 observations is 32. Find the resulting mean, if the observation is: Increased by 3
The mean of 15 observations is 32. Find the resulting mean, if the observation is: Decreased by 7
The mean of 15 observations is 32. Find the resulting mean, if each observation is: Multiplied by 2
The mean of 15 observations is 32. Find the resulting mean, if the observation is: Divided by 0.5
The mean of 15 observations is 32. Find the resulting mean, if the observation is: Increased by 60%
The mean of 15 observations is 32. Find the resulting mean, if the observation is: Decreased by 20%
The mean of 5 numbers is 18. If one number is excluded, the mean of the remaining number becomes 16. Find the excluded number.
If the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11, find the value of x.
Selina solutions for Concise Mathematics [English] Class 9 ICSE 18 Mean and Median [For Ungrouped Data Only] Exercise 18 (B) [Page 267]
Multiple Choice Tyрe: Choose the correct answer from the options given below.
12 observations in a data are written in ascending order. If the last (12th) observation is doubled, the median will increase by ______.
12
24
0
6
12 observations in a data are written in descending order. If the first observation is doubled, the median will ______.
remain same
increase by 12
decrease by 12
change by 12
Median of numbers 10, 12, 9, 8, 10, 12, 10, 6 and 4 is ______.
12
10
6
9
The median of 80 observations is 60. If each observation is doubled, the resulting median will be ______.
60
20
140
120
If each observation in a data is decreased by two, their ______.
mean decreases by 2, but median remains same.
mean remains same, but median decreases, by 2.
mean and median both decrease by 2.
mean and median both remain the same.
Find the median of: 25, 16, 26, 16, 32, 31, 19, 28 and 35
Find the median of:
241, 243, 347, 350, 327, 299, 261, 292, 271, 258 and 257
Find the median of:
63, 17, 50, 9, 25, 43, 21, 50, 14 and 34
Find the median of:
233, 173, 189, 208, 194, 204, 194, 185, 200 and 220.
The following data have been arranged in ascending order. If their median is 63, find the value of x.
34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.
In 10 numbers, arranged in increasing order, the 7th number is increased by 8, how much will the median be changed?
Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 and 40. Find the median score of the whole group.
The median of observations 10, 11, 13, 17, x + 5, 20, 22, 24 and 53 (arranged in ascending order) is 18; find the value of x.
Selina solutions for Concise Mathematics [English] Class 9 ICSE 18 Mean and Median [For Ungrouped Data Only] TEST YOURSELF [Pages 267 - 269]
Multiple Choice Type: Choose the correct answer from the options given below.
If each observation of a given set of data is increased by 5, their mean ______.
remains the same
becomes five times
is decreased by 5
is increased by 5
The median of observations (written in ascending order) 26, 29, 42, 53, x, x + 2, 70, 75, 82, 83 and 100 is 65; then ______.
x = 65
x + 2 = 65
`(x + (x + 2))/2 = 6`
none of these
The mean of x − 5, x − 3, х − 1 and x + 1 is ______.
4x − 8
`(4x - 8)/4`
`(x - 3 + x - 1)/2`
none of these
26, x + 4, x + 2 and 18 are in descending order of their values and their median is 20, then the value of x is ______.
19
17
15
13
Statement (1): For n number of data in a set, median = `(n/2)^(th)` term.
Statement (2): If n is even, median = `1/2[(n/2)^(th) "term" + (n/2 + 1)^(th) "term"]`.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Statement (1): The mean of 100 observations is 50 and one of these observations is increased by 150, the sum of resulting observations is 100 × 50 + 150.
Statement (2): The sum of resulting observations = 100 × 50 + 100.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A): The mean of x1, x2 and x3 is m. Then the value of (x1 − m) + (x2 − m) + (x3 − m) = 0.
Reason (R): x1 + x2 + x3 = 3m ⇒ (x1 − m) + (x2 − m) + (x3 − m) = (x1 + x2 + x3) − 3m.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
Assertion (A): Mean of n observations is x and mean of another set of n observations is y, the combined mean of all the observations is `(x + y)/2`.
Reason (R): Total of all the observations = nx + ny ∴ Mean of all the observations = `(nx + ny)/(2n)`.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
The mean of 100 observations is 40. It is found that an observation 53 was misread as 83.
Find the correct mean.
The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88.
Find the correct mean.
Find the mean of 75 numbers, if the mean of 45 of them is 18 and the mean of the remaining ones is 13.
The mean weight of 120 students of a school is 52.75 kg. If the mean weight of 50 of them is 51 kg,
find the mean weight of the remaining students.
The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 72.25, find the ratio of the number of boys to the number of girls.
Find x if 9, x, 14, 18 x, x, 8, 10 and 4 have a mean of 11.
In a series of tests, A appeared for 8 tests. Each test was marked out of 30 and averages 25. However, while checking his files, A could only find 7 of the 8 tests. For these, he scored 29, 26, 18, 20, 27, 24 and 29.
Determine how many marks he scored for the eighth test.
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if the observations, given above, be: multiplied by 3.
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if the observations, given above, be: divided by 2.
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if the observations, given above, be: multiplied by 3 and then divided by 2.
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if each of the observations, given above, be: increased by 25%
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if each of the observations, given above, be: decreased by 40%
The mean of 18, 24, 15, 2x + 1 and 12 is 21. Find the value of x.
The mean of 6 numbers is 42. If one number is excluded, the mean of the remaining number is 45. Find the excluded number.
The mean of 10 numbers is 24. If one number is included, the new mean is 25. Find the included number.
The following observations have been arranged in ascending order. If the median of the data is 78, find the value of x.
44, 47, 63, 65, x + 13, 87, 93, 99, 110.
The following observations have been arranged in ascending order. If the median of these observations is 58, find the value of x.
24, 27, 43, 48, x - 1, x + 3, 68, 73, 80, 90
Find the mean of the following data: 30, 32, 24, 34, 26, 28, 30, 35, 33, 25
(i) Show that the sum of the deviations of all the given observations from the mean is zero.
(ii) Find the median of the given data.
Find the mean and median of the data: 35, 48, 92, 76, 64, 52, 51, 63 and 71.
If 51 is replaced by 66, what will be the new median?
The mean of x, x + 2, x + 4, x + 6 and x + 8 is 11, find the mean of the first three observations.
Find the mean and median of all the positive factors of 72.
The mean weight of 60 students in a class is 40 kg. The mean weight of boys is 50 kg while that of girls is 30 kg. Find the number of boys and girls in the class.
The average of n numbers x1, x2, x3 ….. xn is A. If x1 is replaced by ( x+ α )x1, x2, is replaced by ( x+ α )x2 and so on.
Find the new average.
The heights (in cm) of the volleyball players from team A and team B were recorded as:
Team A: 180, 178, 176, 181, 190, 175, 187
Team B: 174, 175, 190, 179, 178, 185, 177
Which team had a greater average height?
Find the median of team A and team B.
The Mean of the following arrayed data, 5, 8, (3x − 1), (4x + 1), (3x + 7), is equal to its Median. Find the value of x.
Case-Study Based Question
The data representing the number of people in municipalities in different towns is shown by the bar graph given below.
- What is the number of people living in municipality F?
- What is the total number of people living in municipalities A to C?
- What is the total population of all the municipalities under consideration?
- What the average (mean) of people living in municipalities B to E?
The Frequency Polygon shown depicts the monthly rainfall in the Kathmandu (Nepal).
Answer the following:
- Which month had the highest rainfall?
- How many months had rainfall above 200 mm?
- How many months had rainfall below 100 mm?
- Calculate the Mean rainfall in the months from June to September.
Solutions for 18: Mean and Median [For Ungrouped Data Only]
Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 18 - Mean and Median [For Ungrouped Data Only]
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