## Give one example of a situation in which

[question] Question. Give one example of a situation in which (i) The mean is an appropriate measure of central tendency. (ii) The mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency. [/question] [solution] Solution: When any data has a few observations such that these are very far from the other observations in it, it is better to calculate the median than the mean of the data as median gives a better estimate of average in this ca...

## Find the mean salary of 60 workers of a factory from the following table:

[question] Question. Find the mean salary of 60 workers of a factory from the following table: [/question] [solution] Solution: We know that Mean $=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$ The value of $\sum f_{i} x_{i}$ and $\sum f_{i}$ can be calculated as follows. Mean salary $=\frac{305000}{60}$ $=5083.33$ Therefore, mean salary of 60 workers is Rs 5083.33. [/solution]...

## Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

[question] Question. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18. [/question] [solution] Solution: Arranging the data in an ascending order, 14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28 It can be observed that 14 has the highest frequency, i.e. 4, in the given data. Therefore, mode of the given data is 14. [/solution]...

## The following observations have been arranged in ascending order.

[question] Question. 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 [/question] [solution] Solution: It can be observed that the total number of observations in the given data is 10 (even number). Therefore, the median of this data will be the mean of $\frac{10}{2}$ i.e., $5^{\text {th }}$ and $\frac{10}{2}+1$ i.e., $6^{\text {th }}$ observation. Therefore, median of data $=\frac{5^{...

## In a mathematics test given to 15 students,

[question] Question. In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 Find the mean, median and mode of this data. [/question] [solution] Solution: The marks of 15 students in mathematics test are 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 Mean of data $=\frac{\text { Sum of all observation }}{\text { Total number of observation }}$ $=\frac{41+39+48+52+46+62+54+40+96+52+98+40+42+5...

## The following number of goals was scored by a team in a series of 10 matches:

[question] Question. The following number of goals was scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median and mode of these scores. [/question] [solution] Solution: The number of goals scored by the team is 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Mean of data $=\frac{\text { Sum of all observations }}{\text { Total number of observations }}$ Mean score $=\frac{2+3+4+5+0+1+3+3+4+3}{10}$ $=\frac{28}{10}=2.8$ $=2.8 \mathrm{goals}$ Arranging the number of goals in as...

## 100 surnames were randomly picked up from

[question] Question. 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: (i) Draw a histogram to depict the given information. (ii) Write the class interval in which the maximum number of surname lie. [/question] [solution] Solution: (i) Here, it can be observed that the data has class intervals of varying width. The proportion of the number of surnames per 2 lett...

## A random survey of the number of children of various age groups playing in park was found as follows:

[question] Question. A random survey of the number of children of various age groups playing in park was found as follows: Draw a histogram to represent the data above. [/question] [solution] Solution: Here, it can be observed that the data has class intervals of varying width. The proportion of children per 1 year interval can be calculated as follows. Taking the age of children on x-axis and proportion of children per 1 year interval on y-axis, the histogram can be drawn as follows. [/solution...

## The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

[question] Question. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Represent the data of both the teams on the same graph by frequency polygons. [/question] [solution] Solution: It can be observed that the class intervals of the given data are not continuous. There is a gap of 1 in between them. Therefore, $\frac{1}{2}=0.5$ has to be added to the upper class limits and $0.5$ has to be subtracted from the lower class limits. Also, class mark of eac...

## The following table gives the distribution of students of two sections according to the mark obtained by them:

[question] Question. The following table gives the distribution of students of two sections according to the mark obtained by them: Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections. [/question] [solution] Solution: We can find the class marks of the given class intervals by using the following formula. Class mark $=\frac{\text { Upper class limit }+\text { Lower class limit }}{2...

## The following table gives the life times of neon lamps:

[question] Question. The following table gives the life times of neon lamps: (i) Represent the given information with the help of a histogram. (ii) How many lamps have a lifetime of more than 700 hours? [/question] [solution] Solution: (i) By taking life time (in hours) of neon lamps on x-axis and the number of lamps on y-axis, the histogram of the given information can be drawn as follows. Here, 1 unit on y-axis represents 10 lamps. (ii) It can be concluded that the number of neon lamps having ...

## The length of 40 leaves of a plant are measured correct to one millimetre,

[question] Question. The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: (i) Draw a histogram to represent the given data. (ii) Is there any other suitable graphical representation for the same data? (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why? [/question] [solution] Solution: (i) It can be observed that the length of leaves is represented in a discontinuous class interv...

## Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

[question] Question. Given below are the seats won by different political parties in the polling outcome of a state assembly elections: (i) Draw a bar graph to represent the polling results. (ii) Which political party won the maximum number of seats? [/question] [solution] Solution: (i) By taking polling results on x-axis and seats won as y-axis and choosing an appropriate scale (1 unit = 10 seats for y-axis), the required graph of the above information can be constructed as follows. Here, the r...

## The following data on the number of girls (to the nearest ten)

[question] Question. The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below. (i) Represent the information above by a bar graph. (ii) In the classroom discuss what conclusions can be arrived at from the graph. [/question] [solution] Solution: (i) By representing section (variable) on x-axis and number of girls per thousand boys on y-axis, the graph of the information given above can be constructed by choosing an app...

## A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 − 44 (in years) worldwide,

[question] Question. A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 − 44 (in years) worldwide, found the following figures (in %): (i) Represent the information given above graphically. (ii) Which condition is the major cause of women’s ill health and death worldwide? (iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause. [/question] [solution] So...

## A company manufactures car batteries of a particular type.

[question] Question. The following table gives the life times of neon lamps: 2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5 3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7 2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8 3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4 4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6 Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2 − 2.5. [/question] [solution] Solution: A grouped frequency table of class size 0.5 has to be constructed, starting from class interval...

## A company manufactures car batteries of a particular type

[question] Question. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows: 2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5 3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7 2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8 3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4 4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6 Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2 − 2.5. [/question] [solution] Solution: A grouped frequency tabl...

## Thirty children were asked about the number of hours they watched TV programmes in the previous week.

[question] Question. Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: 1 6 2 3 5 12 5 8 4 8 10 3 4 12 2 8 15 1 17 6 3 2 8 5 9 6 8 7 14 12 (i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10. (ii) How many children watched television for 15 or more hours a week? [solution] Solution: (i) Our class intervals will be 0 − 5, 5 − 10, 10 −15….. ...

## The value of π up to50 decimal places is given below:

[question] Question. The value of π up to50 decimal places is given below: 3.14159265358979323846264338327950288419716939937510 (i) Make a frequency distribution of the digits from 0 to 9 after the decimal point. (ii) What are the most and the least frequently occurring digits? The value of π up to50 decimal places is given below: [solution] Solution: (i) By observation of the digits after decimal point, the required table can be constructed as follows. (ii) It can be observed from the above tab...

## Three coins were tossed 30 times simultaneously.

[question] Question. Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows: 0 1 2 2 1 2 3 1 3 0 1 3 1 1 2 2 0 1 2 1 3 0 0 1 1 2 3 2 2 0 Prepare a frequency distribution table for the data given above. [solution] Solution: By observing the data given above, the required frequency distribution table can be constructed as follows. [/solution]...

## A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city.

[question] Question. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows: 0.03 0.08 0.08 0.09 0.04 0.17 0.16 0.05 0.02 0.06 0.18 0.20 0.11 0.08 0.12 0.13 0.22 0.07 0.08 0.01 0.10 0.06 0.09 0.18 0.11 0.07 0.05 0.07 0.01 0.04 (i) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08, and so on. (ii) For how many days, was the c...

## The heights of 50 students,

[question] Question. The heights of 50 students, measured to the nearest centimeters, have been found to be as follows: 161 150 154 165 168 161 154 162 150 151 162 164 171 165 158 154 156 172 160 170 153 159 161 170 162 165 166 168 165 164 154 152 153 156 158 162 160 161 173 166 161 159 162 167 168 159 158 153 154 159 (i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc. (ii) What can you conclude bout their heights...

## The relative humidity (in %) of a certain city for a month of 30 days was as follows:

[question] Question. The relative humidity (in %) of a certain city for a month of 30 days was as follows: 98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89 (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88 (ii) Which month or season do you think this data is about? (iii) What is the range of this data? [solution] Solution: (i) A grouped frequency distribution table ...

## The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

[question] Question. The distance (in km) of 40 engineers from their residence to their place of work were found as follows: 5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 32 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12 Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0 - 5 (5 not included). What main feature do you observe from this tabular representation? [solution] Solution: It is given that a grouped frequency d...

## The blood groups of 30 students of Class VIII are recoded as follows:

[question] Question. The blood groups of 30 students of Class VIII are recoded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students? [solution] Solution: It can be observed that 9 students have their blood group as A, 6 as B, 3 as AB, and 12 as O. Therefore, the blood group of 30 students of the ...