Exercise 7.1

1. Maximum day time temperatures of Hyderabad in a week (from 26th February to 4th March, 2011) are recorded as 26°C, 27°C, 30°C, 30°C, 32°C, 33°C and 32°C.

(i)

(i) What is the maximum temperature of the week?

Solution:

°C

(ii)

(ii) What is the average temperatures of the week?

Solution:

Average Temperature = Number of daysSum of all temperatures

Given temperatures: 26°C, 27°C, °C, 30°C, °C, °C and 32°C

Sum of temperatures

26+27+30+30+32+33+32 =

Number of days=

Calculate the average: 2107=

The average temperature of the week is 30°C.

2. Rice consumed in a school under the mid-day meal program for 5 consecutive days is 15.75 kg, 14.850 kg, 16.500 kg, 14.700 kg, and 17.700 kg. Find the average rice consumption for the 5 days.

Solution:

To find the average rice consumption, we use the formula:

Average Consumption= Total Rice ConsumedNumber of Days

Given rice consumption (in kg): 15.75, 14.850, 16.500, 14.700, 17.700

Sum of rice consumption: 15.75 + 14.850 + 16.500 + 14.700 + 17.700

Let's calculate:

15.75+14.850=

30.600+16.500=

47.100+14.700=

61.800+17.700=

Divide by the number of days = 79.55 =

The average rice consumption over 5 days is 15.90 kg.

3. In a village three different crops are cultivated in four successive years. The profit (in rupees) on the crops, per acre is shown in the table below -

Crop/Year	Ground nuts	Jawar	Millets
2005	7000	6000	9500
2006	8000	1000	5000
2007	7500	8000	3000
2008	7500	1000	4000

(i)

(i) Calculate the mean profit for each crop over the 4 years.

Solution:

The mean profit for each crop over the 4 years using the formula:

Mean = Sum of values over 4 years4

Groundnuts: 7000+8000+7500+75004

=300004

Jawar: 6000+1000+8000+10004

=160004 =

Millets: 9000+5000+3000+40004

=210004

(ii)

(ii) Based on your answers, which crop should be cultivated in the next year?

Solution:

Since Groundnuts have the highest mean profit (7500) over the 4 years, they should be cultivated in the next year for better profitability.

4. The number of passengers who travelled in APSRTC bus from Adilabad to Nirmal in 4 trips in a day are 39, 30, 45 and 54. What is the occupancy ratio(average number of passengers travelling per trip) of the bus for the day?

Solution:

To find the occupancy ratio (average number of passengers per trip), we use the formula:

Average = Total number of passengersNumber of trips

Given data:

Number of passengers in 4 trips: 39, , 45,

Number of trips:

Sum of passengers: 39 + 30 + 45 + 54 =

Calculate the average: 1684 =

The occupancy ratio (average number of passengers per trip) is 42 passengers per trip.

5. The following table shows themarks scored by Anju, Neelesh and Lekhya in four unit tests of English.

Name of the student	Unit Test I	Unit Test II	Unit Test III	Unit Test IV
Anju	Absent	19	23	21
Neelesh	0	20	22	24
Lekhya	20	24	24	24

(i)

(i) Find the average marks obtained by Lekhya.

Solution:

The formula for average marks:

Average= Total MarksNumber of Tests

Marks obtained by Lekhya: 20, , 24, 24

Total Marks: 20+24+24+24 =

Average: 924 =

Lekhya's average marks = 23

(ii)

(ii) Find the average marks secured by Anju. Will you divide the total marks by 3 or 4? Why?

Solution:

Marks obtained by Anju:(Absent), 19, 23,

Since Anju missed one test, we divide the sum by 3, not .

Total Marks: 19 + 23 + 21 =

Average: 633 =

Anju's average marks =

Dividing by 3 because Anju did not appear in the first test.

(iii)

(iii) Neelesh has given all four tests. Find the average marks secured by him. Will you divide the total marks by 3 or 4? Why?

Solution:

Marks obtained by Neelesh: 0, 20, 22,

Since Neelesh attempted all four tests, we divide by 4, even though one score is 0.

Total Marks: 0 + 20 + 22 + 24 =

Average: 664 =

Neelesh's average marks = 16.5

Dividing by 4 because he appeared in all four tests, even though one score is 0.

(iv)

(iv) Who performed best in the English?

Solution:

Comparing average marks:

Lekhya:

Anju:

Neelesh:

Lekhya performed best in English as she had the highest average marks (23).

6. Three friends went to a hotel and had breakfast to their taste, paying ₹ 16, ₹ 17 and ₹ 21 respectively

(i)

(i) Find their mean expenditure.

Solution:

Given, 3 friends expenditure.

We have to find their mean expenditure.

Mean expenditure = (₹ 16 + ₹ 17 + ₹ 21) 3

Mean expenditure =

Mean expenditure = ₹

(ii)

(ii)If they have spent 3 times the amount that they have already spent, what would their mean expenditure be?

Solution:

If they have spent 3 times the amount that they have already spent.

i.e. ₹ 16 x 3 =

₹ 17 x 3 =

₹ 21 x 3 =

Mean expenditure = ₹ 48+51+633

Mean expenditure = ₹

(iii)

(iii) If the hotel manager offers 50% discount, what would their mean expenditure be?

Solution:

Given that,the hotel manager offers % discount

Then their mean expenditure is Each one pay half amount.

Mean expenditure = ₹ 8+8.5+10.53

Mean expenditure = ₹ 273

Mean expenditure = ₹

(iv)

(iv) Do you notice any relationship between the change in expenditure and the change in mean expenditure.

Solution:

From above result, there is relationship between the change in expenditure and the change in mean expenditure.

Change in expenditure is directly proportional to the change in mean expenditure.

7. Find the mean of the first ten natural numbers.

Solution:

We have to find the mean of the first ten natural numbers.

1st 10 natural numbers are 1, 2, , 4, , 6, , 8, and 10

Mean of the first ten natural numbers = Sum of first ten natural numbersTotal number of natural numbers

Mean of the first ten natural numbers = 1+2+3+4+5+6+7+8+9+1010

Mean of the first ten natural numbers =

8. Find the mean of the first five prime numbers.

Solution:

We have to find the mean of the firstfive prime numbers.

First five prime numbers are 2, ,5, and .

Mean of the first five prime numbers = 2+3+5+7+115

Mean of the first five prime numbers = 285

Mean of the first five prime numbers =

9. In a set of four integers, the average of the two smallest integers is 102, the average of the three smallest integers is 103, the average of all four is 104. Which is the greatest of these integers?

Solution:

Given that,

The average of the two smallest integers is

The average of the three smallest integers is

The average of all four is .

We have to find greatest of these integers.

We know,

Average of the two smallest integers = Sum of two smallest integers2

102 = Sum of two smallest integers2

Sum of two smallest integers =

Now,

We know,

Average of the 3 smallest integers = Sum of 3 smallest integers3

= Sum of 3 smallest integers3

Sum of 3 smallest integers =

But sum of two smallest integers =

Sum of two smallest integers + 3rd integer = 309

3rd integer = 309 – 204

3rd integer =

Now,

We know,

Average of the 4 smallest integers = Sum of 4 smallest integers4

104 = Sum of 4 smallest integers4

Sum of 4 smallest integers =

But sum of 3 smallest integers =

Sum of 3 smallest integers + 4th integer = 416

4th integer = 416 – 309

4th integer =

From above,

Greatest integer is 107.

10.Write question to find the mean, giving suitable data.

Solution:

Students in class 1 to 5 are 34, , 45, and 35.

We have to mean.

Mean = Sum of students in class 1 to 5total number of class

Mean = 34 + 35 + 45 + 36 + 355

Mean = 1855

Mean =

Data Handling

Glossary

Exercise 7.1

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Data Handling

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Glossary

Exercise 7.1

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