7th Maths : Term 3 Unit 5 : Statistics : Miscellaneous Practice problems, Challenge Problems, Text Book Back Exercises Questions with Answers, Solution

**Exercise
5.4**

** **

__Miscellaneous
Practice problems__

** **

**1. Arithmetic mean of 15 observations
was calculated as 85. In doing so an observation was wrongly taken as 73 for 28.
What would be correct mean?**

**Solution: **

Arithmetic mean = Sum of
all observations / Number of observations

85 = Sum of 15 observation / 15

85 × 15 = sum of 15 observations

1275 = sum of 15 observations

Wrong observation = 73

Correct observation = 28

∴ Correct Mean = [Sum – Wrong value + Correct value] / Number of
obervation

= [1275 – 73 + 28] / 15 = [1202 + 28] / 15 = 1230 / 15 = 82

Correct Mean = 82

** **

**2. Find the median of 25, 16, 15, 10,
8, 30.**

**Solution: **

Arranging the data
in ascending order: 8, 10, 15, 16, 25, 30

Here *n* = 6, even

∴ Median = 1/2 {(*n* / 2)* ^{th}* term + (

= 1/2 {(6 / 2)* ^{th}*
term + (6/2 + 1)

= 1/2 {3^{th} term + 4^{th} term}

= 1/2 {15 + 16} = 1/2 (31)

∴ Median = 15.5

** **

**3. Find the mode of 2, 5, 5, 1, 3, 2,
2, 1, 3, 5, 3.**

**Solution: **

Arranging the data in
ascending order: 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5

Here 2, 3 and 5 occurs 3 times each.

Which is the maximum number of times.

∴ Mode is 2, 3 and 5.

** **

**4. The marks scored by the students in
social test out of 20 marks are as follows: 12, 10, 8, 18, 14, 16. Find the mean
and median?**

**Solution:**

Arranging the given data in ascending order: 8, 10, 12, 14, 16,
18.

Mean = Sum of all observations / Number of observations

= [ 8 +10 + 12 + 14 + 16 + 18 ] / 6 = 78 / 6

Mean = 13

There are* n* = 6
observations, which is even

∴ Median = 1/2 {(*n* / 2)* ^{th}* term + (

= 1/2 {(6/2)* ^{th}*
term + (6/2 + 1)

= 1/2 {3^{th} term + 4^{th} term}

= 1/2 {8+18} = 1/2 (26) =13

∴ Median = 13

** **

**5. The number of goals scored by a football
team is given below. Find the mode and median for the data of 2, 3, 2, 4, 6, 1,
3, 2, 4, 1, 6.**

**Solution:**

Arranging the given data in ascending order: 1, 1, 2, 2, 2, 3,
3, 4, 4, 6, 6

Clearly 2 occurs at the maximum of 3 times and so mode = 2

Here number of data of data n = 11, odd.

∴ Median = ([*n* + 1] / 2)* ^{th}* term

= ([11+ 1] / 2)* ^{th}*
term = (12 / 2)

= 6^{th} term

Median = 3

** **

**6.
Find the mean and mode of 6, 11, 13, 12, 4, 2.**

**Solution:**

Arranging is ascending order : 2, 4, 6, 11, 12, 13

Mean = Sum of all observations / Number of observations = [ 2 + 4
+ 6 + 11 + 12 + 13] / 6

Mean = 48 / 6 = 8

All observation occurs only once and so there is no mode for
this date.

** **

__Challenge
Problems__

** **

**7.
The average marks of six students is 8. One more student mark is added and the mean
is still 8. Find the student mark that has been added.**

**Solution: **

Average = Sum of all observations / Number of observations

8 = Sum of observation / 6

Sum of observation = 6 × 8

= 48

If one more mark is added then number of observations = 6 + 1 = 7

Let the number be *x*

Still average = 8

∴ 8 = [48 + *x* ] / 7

48 + *x* = 7 × 8

48 + *x = *56

48 + *x = *56 – 48

*x = *8

∴ The number that is added = 8

** **

**8.
Calculate the mean, mode and median for the following data: 22, 15, 10, 10, 24,
21. **

**Solution:**

Arranging in ascending order: 10, 10, 15, 21, 22, 24

Mean = Sum of all observations / Number of observations

= [ 10 + 10 + 15 + 21 + 22 + 24 ] / 6

= 102 / 6 = 17

Here *n* = 6, even

∴ Median = 1/2 {(*n* / 2)* ^{th}* term + (

= 1/2 {(6/2)* ^{th}*
term + (6/2 + 1)

= 1/2 {3^{th} term + 4^{th} term}

= 1/2 {15 + 21} = 1/2 (36)

∴ Median = 18

Clearly the data 10 occurs maximum number of times and so 10 is
the mode.

∴ Mode = 10

** **

**9.
Find the median of the given data: 14, −3, 0, −2, −8, 13, −1, 7. **

**Solution:**

Arranging in ascending order: –8, –3, –2, –1, 0, 7, 13, 14

Here number of data *n*
= 8, even

∴ Median = 1/2 {(*n* / 2)* ^{th}* term + ([

= 1/2 {(8 / 2)* ^{th}*
term + ([8/2] + 1)

= 1/2 {4^{th} term + 5^{th} term}

= 1/2 {–1 + 0} = 1/2 (–1) = – 0.5

∴ Median = – 0.5

** **

**10.
Find the mean of first 10 prime numbers and first 10 composite numbers.**

**Solution:**

First 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Mean = Sum of all data / number of data

= [ 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 +29 ] / 10

= 129 / 10

Mean = 12.9

Mean of first 10 prime numbers = 12.9

First 10 prime numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Mean = [ 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 ] / 10

= 112 / 10

= 11.2

Mean of first 10 prime numbers = 11.2

** **

__ANSWERS:__

** Exercise 5.4**

1. 82

2. 15.5

3. 2, 3 and 5

4. 13;13

5. 2;3

6. 8; No mode.

**Challenge Problems**

7. 8

8. 17; 10 ; 18

9. –0.5

10. 12.9 ; 11.2

Tags : Questions with Answers, Solution | Statistics | Term 3 Chapter 5 | 7th Maths , 7th Maths : Term 3 Unit 5 : Statistics

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7th Maths : Term 3 Unit 5 : Statistics : Exercise 5.4 | Questions with Answers, Solution | Statistics | Term 3 Chapter 5 | 7th Maths

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