**Exercise 23.1**

**Question :1. Ashish studies for 4 hours, 5 hours and 3 hours on three consecutive days. How many hours does he study daily on an average?**

**Solution 1:**

**Question :2. A cricketer scores the following runs in 8 innings: 58, 76, 40, 35, 48, 45, 0, 100.**

**Find the mean score.**

**Solution 2:**

**Question :3. The marks (out of 100) obtained by a group of students in science test are 85, 76, 90, 84, 39, 48, 56, 95, 81 and 75. Find the**

**(i) Highest and the lowest marks obtained by the students.**

**(ii) Range of marks obtained.**

**(iii) Mean marks obtained by the group.**

**Solution 3:**

**Question :4. The enrolment of a school during six consecutive years was as follows:**

**1555, 1670, 1750, 2019, 2540, 2820**

**Find the mean enrolment of the school for this period.**

**Solution 4:**

**Question :5. 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 from the above data.**

**(ii) Find the mean rainfall for the week.**

**(iii) On how many days was the rainfall less than the mean rainfall.**

**Solution 5:**

**Question :6. If the heights of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively, find the mean height.**

**Solution 6:**

**Question :7. Find the mean of 994, 996, 998, 1002 and 1000.**

**Solution 7:**

**Question :8. Find the mean of first five natural numbers.**

**Solution 8:**

**Question :9. Find the mean of all factors of 10.**

**Solution 9:**

**Question :10. Find the mean of first 10 even natural numbers.**

**Solution 10:**

**Question :11. Find the mean of x, x + 2, x + 4, x + 6, x + 8**

**Solution 11:**

**Question :12. Find the mean of first five multiples of 3.**

**Solution 12:**

**Question :13. Following are the weights (in kg) of 10 new born babies in a hospital on a particular day: 3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6 Find the mean X¯**

**Solution 13:**

**Question :14. The percentage of marks obtained by students of a class in mathematics are:**

**64, 36, 47, 23, 0, 19, 81, 93, 72, 35, 3, 1 Find their mean.**

**Solution 14:**

**Question :15. The numbers of children in 10 families of a locality are:**

**2, 4, 3, 4, 2, 3, 5, 1, 1, 5 Find the mean number of children per family.**

**Solution 15:**

**Question :16. The mean of marks scored by 100 students was found to be 40. Later on it was discovered that a score of 53 was misread as 83. Find the correct mean.**

**Solution 16:**

**Question :17. The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number.**

**Solution 17:**

**Question :18. The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.**

**Solution 18:**

**Question :19. The mean weight of 8 numbers is 15 kg. If each number is multiplied by 2, what will be the new mean?**

**Solution 19:**

_{1}, x

_{2}, x

_{3}…x

_{8}be the eight numbers whose mean is 15 kg.

_{1}+ x

_{2}+ x

_{3}+⋯…+ x

_{8})/8

_{1}+ x

_{2}+ x

_{3}+ …+ x

_{8}= 15 × 8

_{1}+ x

_{2}+ x

_{3}+…+ x

_{8}= 120

_{1}, 2x

_{2}, 2x

_{3}…2x

_{8}.

_{1}+ 2x

_{2}+ 2x

_{3}+⋯+ 2x

_{8})/8

_{1}+ x

_{2}+ x

_{3}+ …+ x

_{8}))/8

**Question :20. The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.**

**Solution 20:**

_{1}, x

_{2}, x

_{3}, x

_{4}and x

_{5}be 5 numbers whose mean is 18.

**Question :21. The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.**

**Solution 21:**

**Question :22. The mean of 5 numbers is 27. If one more number is included, then the mean is 25. Find the included number.**

**Solution 22:**

**Question :23. The mean of 75 numbers is 35. If each number is multiplied by 4, find the new mean.**

**Solution 23:**

_{1}, x

_{2}, x

_{3}…x

_{75}be 75 numbers with their mean equal to 35. Then,

_{1}+ x

_{2}+ x

_{3}+ …..+ x

_{75})/75

_{1}+ x

_{2}+ x

_{3}+ …..+ x

_{75}= 35 × 75

_{1}+ x

_{2}+ x

_{3}+ …..x x

_{75}= 2625

_{1}+ 4x

_{2}+ 4x

_{3}+⋯+ 4 x

_{75})/75

_{1}+ x

_{2}+ x

_{3}+ …+ x

_{75}))/75

**Exercise 23.2**

**Question :1. A die was thrown 20 times and the following scores were recorded:**

**5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1**

**Prepare the frequency table of the scores on the upper face of the die and find the mean score.**

**Solution 1:**

**Question :2. The daily wages (in Rs) of 15 workers in a factory are given below:**

**200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180**

**Prepare the frequency table and find the mean wage.**

**Solution 2:**

**Question :3. The following table shows the weights (in kg) of 15 workers in a factory:**

**Calculate the mean weight.**

**Solution 3:**

**Question :4. The ages (in years) of 50 students of a class in a school are given below:**

**Solution 4:**

**Question :5. Calculate the mean for the following distribution:**

**Solution 5:**

**Question :6. Find the mean of the following data:**

**Solution 6:**

**Question :7. The mean of the following data is 20.6. Find the value of p.**

**Solution 7:**

**Question :8. If the mean of the following data is 15, find p.**

**Solution 8:**

**Question :9. Find the value of p for the following distribution whose mean is 16.6**

**Solution 9:**

**Question :10. Find the missing value of p for the following distribution whose mean is 12.58**

**Solution 10:**

**Question :11. Find the missing frequency (p) for the following distribution whose mean is 7.68**

**Solution 11:**

**Question :12. Find the value of p, if the mean of the following distribution is 20**

**Solution 12:**

^{2}= 300 – 295

^{2}= 5

^{2}= 1

**Exercise 23.3**

**Find the median of the following data (1 – 8)**

**Question :1. 83, 37, 70, 29, 45, 63, 41, 70, 34, 54**

**Solution 1:**

^{th}term + (((n+1))/2)

^{th}term

**Question :2. 133, 73, 89, 108, 94,104, 94, 85, 100, 120**

**Solution 2:**

^{th}term + (((n+1))/2)

^{th}term

**Question :3. 31, 38, 27, 28, 36, 25, 35, 40**

**Solution 3:**

^{th}term + (((n+1))/2)

^{th}term

**Question :4. 15, 6, 16, 8, 22, 21, 9, 18, 25**

**Solution 4:**

^{th}term

**Question :5. 41, 43,127, 99, 71, 92, 71, 58, 57**

**Solution 5:**

^{th}term

**Question :6. 25, 34, 31, 23, 22, 26, 35, 29, 20, 32**

**Solution 6:**

^{th}term + (((n+1))/2)

^{th}term

**Question :7. 12, 17, 3, 14, 5, 8, 7, 15**

**Solution 7:**

^{th}term + (((n+1))/2)

^{th}term

**Question :8. 92, 35, 67, 85, 72, 81, 56, 51, 42, 69**

**Solution 8:**

^{th}term + (((n+1))/2)

^{th}term

**Question :9. Numbers 50, 42, 35, 2x +10, 2x – 8, 12, 11, 8, 6 are written in descending order and their median is 25, find x.**

**Solution 9:**

**Question :10. Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?**

**Solution 10:**

^{th}term

**Question :11. Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57, If 58 is replaced by 85, what will be the new median?**

**Solution 11:**

^{th}term

**Question :12. The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.**

**Solution 12:**

^{th}term

**Question :13. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95**

**Solution 13:**

^{th}term + (((n+1))/2)

^{th}term

**Exercise 23.4**

**Question :1. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14**

**By using the empirical relation also find the mean.**

**Solution 1:**

^{th}term

**Question :2. Find the median and mode of the data: 35, 32, 35, 42, 38, 32, 34**

**Solution 2:**

**Question :3. Find the mode of the data: 2, 6, 5, 3, 0, 3, 4, 3, 2, 4, 5, 2, 4**

**Solution 3:**

**Question :4. The runs scored in a cricket match by 11 players are as follows:**

**6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 10**

**Find the mean, mode and median of this data.**

**Solution 4:**

Arrange the data in ascending order such that similar values are grouped together, as follows:

6, 8, 10, 10, 15, 15, 50, 80, 100, 120

The number of observations n is 11. Since n is odd,

Thus, median = (((n+1))/2)^{th} term

Median = value of 6th term

= 15

Here, 10 occur three times. Therefore, 10 is the mode of the given data.

Now,

Mode = 3 Median – 2 Mean

10 = 3 x 15 – 2 Mean

2 Mean = 45 – 10 = 35

Mean = 35/2 = 17.5

The value of mean: 17.5

Mode: 10

Median: 15

**Question :5. Find the mode of the following data:**

**12, 14, 16, 12, 14, 14, 16, 14, 10, 14, 18, 14**

**Solution 5:**

**Question :6. Heights of 25 children (in cm) in a school are as given below:**

**168, 165, 163, 160, 163, 161, 162, 164, 163, 162, 164, 163, 160, 163, 163, 164, 163, 160, 165, 163, 162**

**What is the mode of heights?**

**Also, find the mean and median.**

**Solution 6:**

^{th}term

**Question :7. The scores in mathematics test (out of 25) of 15 students are as follows:**

**19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20**

**Find the mode and median of this data. Are they same?**

**Solution 7:**

**Question :8. Calculate the mean and median for the following data:**

**Using empirical formula, find its mode.**

**Solution 8:**

^{th}term

**Question :9. The following table shows the weights of 12 persons.**

**Find the median and mean weights. Using empirical relation, calculate its mode.**

**Solution 9:**

^{th}term + (((n+1))/2)

^{th}term