For a certain locality, the data of monthly household consumption of electricity measured in units of energy is given below: Units of energy consumed Number of consumers 1 - 10 20 11 - 20 35 21 - 30 42 31 - 40 70 41 - 50 100 51 - 60 120 61 - 70 110 71 - 80 65 81 - 90 36 91 - 100 20 101 - above 10 The monthly rate of tax is divided into two categories: Category - I : ₹ 3 per unit for households coming 50 units or less. Category - II : ₹ 1 for every additional unit of energy above 50 units. Find the number of consumers paying the first and second categories of taxes.

Given: Units of energy consumed Number of consumers 1 - 10 20 11 - 20 35 21 - 30 42 31 - 40 70 41 - 50 100 51 - 60 120 61 - 70 110 71 - 80 65 81 - 90 36 91 - 100 20 101 - above 10 Category - I : ₹ 3 per unit for households coming 50 units or less. From the above table, the number of consumers less than 50 units as follows: For 1 - 10 : 20 units. For 11 - 20 : 35 units. For 21 - 30 : 42 units. For 31 - 40 : 70 units. For 41 - 50 : 100 units. Therefore, total number of consumptions are 20 + 35 + 42 + 70 + 100 = 267 . Category - II : ₹ 1 for every additional unit of energy above 50 units. From the table, number of consumption above 50 units: 51 - 60 : 120 units 61 - 70 : 110 units 71 - 80 : 65 units 81 - 90 : 36 units 91 - 100 : 20 units 101 - above : 10 units. Therefore, total number of consumptions are 120 + 110 + 65 + 36 + 20 + 10 = 361 .

The following is the survey report of the weekly income of the families of a ward of a municipality: Income in Rupees Number of families 80 and above 12050 150 and above 10475 180 and above 8290 250 and above 6470 370 and above 4260 500 and above 2270 750 and above 1180 1000 and above 560 1500 and above 320 2000 and above 150 2500 and above 75 3000 and above 50 3500 and above 24 4000 and above 12 4500 and above 6 From the above data construct a continuos frequency table and also find the cumulative frequency of each class. Further find the number of families whose weekly income is at the most ₹ 1000 .

Given: Frequency distribution table is the more than cumulative frequency distribution table. The continuos frequency distribution table as follows: Income in rupees Number of families 0 - 80 1575 80 - 150 2185 150 - 180 1820 180 - 250 2210 250 - 370 1990 370 - 500 1090 500 - 750 620 750 - 1000 240 1000 - 1500 170 1500 - 2000 75 2000 - 2500 25 2500 - 3000 26 3000 - 3500 12 3500 - 4000 6 4000 - 4500 6 The income of families at most ₹ 1000 is the number of families less than 1000 . 0 - 80 : 1575 80 - 150 : 2185 150 - 180 : 1820 180 - 250 : 2210 250 - 370 : 1990 370 - 500 : 1090 500 - 750 : 620 750 - 1000 : 240 So, sum of families whose income is at most ₹ 1000 is 1575 + 2185 + 1820 + 2210 + 1990 + 1090 + 620 + 240 = 11730 . Therefore, number of families, whose income at most ₹ 1000 is 11730 .

The following is the data of the number of people of a particular village having abnormal blood pressure at different age groups: Age group Number of people 10 - 15 6 15 - 20 5 20 - 25 3 25 - 30 6 30 - 35 4 35 - 40 7 40 - 45 5 45 - 50 2 Draw the histogram of the data.

The following is the data of the number of people of a particular village having abnormal blood pressure at different age groups: Age group No.of people 10 - 15 6 15 - 20 5 20 - 25 3 25 - 30 6 30 - 35 4 35 - 40 7 40 - 45 5 45 - 50 2 Histogram is a graphical display of data using bars of different heights. Here, to draw the histogram, consider age group of the people on X - axis and number of people on Y - axis . Using the bars(rectangle), mark the number of people of the corresponding age group. The histogram of the above data is given below:

The monthly expenditure of the households of a ward of municipality is given in the following data: Monthly expenditure No.of people 501 - 750 75 751 - 1000 125 1001 - 1250 200 1251 - 1500 150 1501 - 1750 230 1751 - 2000 180 2001 - 2250 120 2251 - 2500 60 2501 - 3000 55 Draw the histogram and frequency polygon of the above data.

The monthly expenditure of the households of a ward of municipality is given in the following data: Monthly expenditure No.of people 501 - 750 75 751 - 1000 125 1001 - 1250 200 1251 - 1500 150 1501 - 1750 230 1751 - 2000 180 2001 - 2250 120 2251 - 2500 60 2501 - 3000 55 Here, to draw the histogram, consider monthly expenditure on X - axis and number of households on Y - axis . Using the bars(rectangle), mark the number of households of the corresponding expenditure. To draw the frequency polygon, consider the mid-points of the histogram and join all the points starting from origin. The histogram and frequency polygon of the above data is given below:

The data occurrence of a particular disease in different age groups of a locality is given below: Age group Number of people. 15 - 25 25 26 - 35 30 36 - 40 27 41 - 50 18 51 - 55 47 56 - 60 20 61 - 75 6 76 - 90 2 Draw the histogram of the data.

The data occurrence of a particular disease in different age groups of a locality is given below: Age group No.of people 15 - 25 25 26 - 35 30 36 - 40 27 41 - 50 18 51 - 55 47 56 - 60 20 61 - 75 6 76 - 90 2 Histogram is a graphical display of data using bars of different heights. Here, to draw the histogram, consider age group of the people on X - axis and number of people on Y - axis . Using the bars(rectangle), mark the number of people of the corresponding age group. To draw a frequency polygon, draw a mid-points of the bars of the histogram and join all the points. The histogram and frequency polygon of the above data is given below:

Draw the frequency polygon of the following data: Marks Number of students. 0 - 10 6 10 - 20 14 20 - 30 25 30 - 40 35 40 - 50 46 50 - 60 51 60 - 70 32 70 - 80 24 80 - 90 7 90 - 100 2

Given: Marks No.of students 0 - 10 6 10 - 20 14 20 - 30 25 30 - 40 35 40 - 50 46 50 - 60 51 60 - 70 32 70 - 80 24 80 - 90 7 90 - 100 2 To draw the frequency polygon, first draw the histogram of the given data. Histogram is a graphical display of data using bars of different heights. Here, to draw the histogram, consider marks on X - axis and number of students on Y - axis . Using the bars(rectangle), mark the number of people of the corresponding age group. To draw a frequency polygon, draw a mid-points of the bars of the histogram and join all the points. The histogram and frequency polygon of the above data is given below:

What are the mean and median of the first elevennatural numbers Can you estimate the mode If so what is it

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.1>Q 5

The following are the weight in $kg$ of $∴ Median = 6$ pupils in a class:
$30, 37, 45, 32, 26, 40, 26, 31, 30, 35, 28, 32, 35, 41, 28, 27, 42, 36, 32, 36$

Using tally marks form an ungrouped frequency table thereby showing the frequency and cumulative frequency columns. Also find three measures of central tendency of the data.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.1>Q 6

The following are the weight in $kg$ of $20$ potatoes in a farm:
$30, 37, 45, 32, 26, 40, 26, 31, 30, 35, 28, 32, 35, 41, 28, 27, 42, 36, 32, 36$

Taking two as width if each class construct a continuous grouped frequency distribution table. Also show the mid-values of the classes and the cumulative frequencies.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.1>Q 7

For a certain locality, the data of monthly household consumption of electricity measured in units of energy is given below:

Units of energy consumed	Number of consumers
$1 - 10$	$20$
$11 - 20$	$35$
$21 - 30$	$42$
$31 - 40$	$70$
$41 - 50$	$100$
$51 - 60$	$120$
$61 - 70$	$110$
$71 - 80$	$65$
$81 - 90$	$36$
$91 - 100$	$20$
$101 - above$	$10$

The monthly rate of tax is divided into two categories:
Category $- I$ : $₹ 3$ per unit for households coming $50$ units or less.
Category $- II :$ $₹ 1$ for every additional unit of energy above $50$ units.

Find the number of consumers paying the first and second categories of taxes.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.1>Q 8

The following is the survey report of the weekly income of the families of a ward of a municipality:

Income in Rupees	Number of families
$80$ and above	$12050$
$150$ and above	$10475$
$180$ and above	$8290$
$250$ and above	$6470$
$370$ and above	$4260$
$500$ and above	$2270$
$750$ and above	$1180$
$1000$ and above	$560$
$1500$ and above	$320$
$2000$ and above	$150$
$2500$ and above	$75$
$3000$ and above	$50$
$3500$ and above	$24$
$4000$ and above	$12$
$4500$ and above	$6$

From the above data construct a continuos frequency table and also find the cumulative frequency of each class. Further find the number of families whose weekly income is at the most $₹ 1000$ .

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.2>Q 1

The following is the data of the number of people of a particular village having abnormal blood pressure at different age groups:

Age group	Number of people
$10 - 15$	$6$
$15 - 20$	$5$
$20 - 25$	$3$
$25 - 30$	$6$
$30 - 35$	$4$
$35 - 40$	$7$
$40 - 45$	$5$
$45 - 50$	$2$

Draw the histogram of the data.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.2>Q 2

The monthly expenditure of the households of a ward of municipality is given in the following data:

Monthly expenditure	No.of people
$501 - 750$	$75$
$751 - 1000$	$125$
$1001 - 1250$	$200$
$1251 - 1500$	$150$
$1501 - 1750$	$230$
$1751 - 2000$	$180$
$2001 - 2250$	$120$
$2251 - 2500$	$60$
$2501 - 3000$	$55$

Draw the histogram and frequency polygon of the above data.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.2>Q 3

The data occurrence of a particular disease in different age groups of a locality is given below:

Age group	Number of people.
$15 - 25$	$25$
$26 - 35$	$30$
$36 - 40$	$27$
$41 - 50$	$18$
$51 - 55$	$47$
$56 - 60$	$20$
$61 - 75$	$6$
$76 - 90$	$2$

Draw the histogram of the data.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 14 - Statistics>EXERCISE 14.2>Q 4

Draw the frequency polygon of the following data:

Marks	Number of students.
$0 - 10$	$6$
$10 - 20$	$14$
$20 - 30$	$25$
$30 - 40$	$35$
$40 - 50$	$46$
$50 - 60$	$51$
$60 - 70$	$32$
$70 - 80$	$24$
$80 - 90$	$7$
$90 - 100$	$2$

What are the mean and median of the first eleven natural numbers? Can you estimate the mode? If so what is it?

Important Questions on Statistics

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