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**NCERT Class 12 ****Geography** Chapter 24 **Data Processing**

**Geography**Chapter 24

**Data Processing**

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**Geography****Data Processing**

**Data Processing****Chapter: 24**

PART – III PRACTICAL WORK IN GEOGRAPHY

**Very Short Type Questions Answer**

**1. What do you mean by central tendency?**

Ans: A summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.

**2. Define arithmetic mean and give its two properties.**

Ans: Algebraic sum of the deviation of the item in a series from their arithmetic mean is zero.

**3. What do you mean by median?**

Ans: The middle value of a set of numbers.

**4. What is mode? Give its merits and demerits.**

Ans: The mode is easy to understand and calculate.

**5. What is standard deviation? Give its merits and demerits.**

Ans: The standard deviation value is always fixed and well defined.

**Short Type Questions Answer**

**1. Show relationship between mean, median and mode.**

Ans: This mean median and mode relationship is known as the “empirical relationship” which is defined as Mode is equal to the difference between 3 times the median and 2 times the mean.

**2. Give merits and demerits of meaning.**

Ans: Merits refer to the advantages or favourable significance of something. Demerits refer to the unfavourable points of something that has some of the other adverse effects.

**3. Discuss relative merits and demerits as a measure of central tendency.**

Ans: **Following are a few merits of Median:**

(a) It is easily understandable and computable.

(b) It is well defined as an average.

**Following are some of the demerits of Median:**

(a) Since the computation of a median requires data to be arranged in ascending or descending order of value, it can be time-consuming when a data volume is large.

**4. Calculate mode if mean is 18 and median is 20.**

Ans: Students, do yourself.

**Long Type Questions Answer**

**1. Define central tendency. Why are averages called measures of central tendency?**

Ans: A measure of central tendency (also referred to as measures of centre or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution. There are three main measures of central tendency: mode. median. mean.

**Averages, such as the mean, median, and mode, are called measures of central tendency because they provide a single value that represents the central position of the data set:**

**(i) Mean:** The mean is the value obtained by adding all of the values together and dividing by the number of observations. The sum of all the data divided by the number of data sets.

**Example:** 8 + 7 + 3 + 9 + 11 + 4 = 42 ÷ 6 = Mean of 7.0.

**(ii) Median:** The median is the middle value of a set of numbers. The median is the same as the 50th percentile for the set of numbers. In other words, the median is the middle of a set of numbers with half of the values less than the median and half the values greater than the median.

**(iii) Mode:** The most frequently occurring data value in a series. The mode is the most straightforward measure. It is simply the most frequent value in the data set. If categories are used, the mode is the most common category in the data set.

**2. What are the different uses of standard deviation?**

Ans: **It’s widely used across various fields for different purposes:**

**(i) Measuring Variability:** Variability is most commonly measured with the following descriptive statistics: Range: the difference between the highest and lowest values. Interquartile range: the range of the middle half of a distribution. Standard deviation: average distance from the mean.

**(ii) Risk Assessment:** A risk assessment is simply a careful examination of anything that may cause harm to you or others during the course of your work. Once this is done, you will then be able to decide upon the most appropriate action to take to minimise the likelihood of anyone being hurt.

**(iii) Quality Control:** Quality control means how a company measures product quality and improves it if need be. Quality control can be done in many ways, from testing products, reviewing manufacturing processes, and creating benchmarks. This is all done to monitor significant variations in a product.

**(iv) Analysis of Performance: **Performance Analysis (PA) is a gathering data methodology that represents an objective observation system that is useful. information to improve performance. In this experimentation we aimed at improving students’ teaching skills, using PA.

**(v) Survey Analysis:** Survey analysis is the process of turning the raw material of your survey data into insights and answers you can use to improve things for your business.

**(vi) Signal-to-Noise Ratio:** Signal-to-noise ratio (SNR) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise.

**(vii) Process Control:** Process control is the ability to monitor and adjust a process to give a desired output. It is used in industry to maintain quality and improve performance.

**(viii) Comparison of Data Sets:** One way to compare the two sets is to calculate the average of each group. The mean is a sensible average to use here because there are no outliers (unusually high or low results) that would affect the answer.

**3. Define dispersion. Explain the characteristics of a good measure of dispersion.**

Ans: The term, ‘dispersion’, refers to the scattering of scores about the measure of central tendency. It is used to measure the extent to which individual items or numerical data tend to vary or spread about an average value.

**Characteristics of a good measure of dispersion include:**

**(i) Reflects Variability:** Climate variability refers to the climatic parameter of a region varying from its long-term mean. Every year in a specific time period, the climate of a location is different. Some years have below average rainfall, some have average or above average rainfall.

**(ii) Scale Invariance:** If you zoom into a fractal it looks the same. Scale invariance is present in many important systems in the real world, and this invariance can be used to understand how the systems evolve with time.

**(iii) Sensitivity to Extreme Values:** The mean is sensitive to all scores in a sample (every number in the data affects the mean), which makes it a more “powerful” measure than the median or mode. The mean’s sensitivity to all scores also makes it sensitive to extreme values, which is why the median is used when there are extreme values.

**(iv) Easy Interpretation:** Interpretation is the act of explaining, reframing, or otherwise showing your own understanding of something. A person who translates one language into another is called an interpreter because they are explaining what a person is saying to someone who doesn’t understand.

**(v) Efficiency:** The efficiency of a river’s channel is measured by finding its Hydraulic radius. It is the ratio between the length of wetted perimeter and cross section of a river channel. Wetted perimeter: the entire length of the riverbed bank and sides in contact with water.

**(vi) Comparability:** One important issue concerns the comparability of measures of achievement. The lack of exact comparability between these surveys is a problem.

**Numerical Questions**

**1. Marks obtained by the students in a class are shown in the following table. Calculate the arithmetic mean or average:**

S.No. of students | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Marks obtained | 60 | 65 | 54 | 72 | 81 | 87 | 45 | 49 | 58 | 70 |

Ans: To calculate the arithmetic mean or average of the marks obtained by the students, you sum up all the marks and divide by the total number of students.

**Let’s do that:**

Sun of marks = 60 + 65 + 54 + 72 + 81 + 87 + 45 + 49 + 58 + 70 = 681

Total number of students = 10

Arithmetic mean = Sum of marks / Total number of students

= 681 / 10

= 68.1

So, the arithmetic mean or average marks obtained by the students is 68.1.

**2. Find the arithmetic mean of the data given in the following frequency distribution table:**

Rainfall (in mm) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

No.of days | 2 | 7 | 10 | 15 | 20 | 16 | 6 | 4 |

Ans:

Rainfall | No of days | Midpoint |

0-10 | 2 | (0 + 10) ÷ 2 = 5 |

10-20 | 7 | (10 + 20) ÷ 2 = 15 |

20-30 | 10 | (20 + 30) ÷ 2 = 25 |

30-40 | 15 | (30 + 40) ÷ 2 = 35 |

40-50 | 20 | (40 + 50) ÷ 2 = 45 |

50-60 | 16 | (50 + 60) ÷ 2 = 55 |

60-70 | 6 | (60 + 70) ÷ 2 = 65 |

70-80 | 4 | (70 + 80) ÷ 2 = 75 |

**Multiply each midpoint by its corresponding frequency:**

(5 × 2) + (15 × 7) + (25 × 10) + (35 × 15) + (45 × 20) + (55 × 16) + (65 × 6) + (75 × 4)

= 10 + 105 + 250 + 525 + 900 + 800 + 390 + 300

= 3360

**Sum up the frequencies:**

2 + 7 + 10 + 15 + 20 + 16 + 6 + 4

= 80

**Divide the sum of the products by the total number of days:**

Arithmetic mean = Sum of products ÷ Total number of days

= 3360 ÷ 80

= 42

**3. Calculate the median of the following figures: 11, 12, 8, 9, 14, 20, 15, 13.**

Ans: **To find the median of the given figures, we first need to arrange them in ascending order:**

8, 9, 11, 12, 13, 14, 15, 20.

Since there are 8 numbers, the median will be the middle number if the count is odd, or the average of the two middle numbers if the count is even.

Here, the count is odd (8), so the median will be the middle number, which is the 4th number in the ordered list:

Median = 12

So, the median of the given figures is 12.

**4. The educational expenses of children belonging to 12 families in a locality are as follows. Calculate the median. Expenses in Rupees:**

140, 150, 130, 135, 170, 190, 500, 210, 205, 195, 290, 200.

Ans: **To calculate the median, first, arrange the expenses in ascending order:**

130, 135, 140, 150, 170, 190, 195, 200, 205, 210, 290, 500

Since there are 12 values, the median will be the average of the 6th and 7th values.

Median = (170 + 190) ÷ 2

= 360 ÷ 2

= 180

So, the median educational expenses is 180 Rupees

**5. Calculate the median from the following table:**

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

No.of Students | 5 | 10 | 15 | 10 | 6 | 4 |

Ans: **Here’s the table with the cumulative Frequency:**

Marks | No. of Students | Cumulative Frequency |

0 – 10 | 5 | 5 |

10 – 20 | 10 | 15 |

20 – 30 | 15 | 30 |

30 – 40 | 10 | 40 |

40 – 50 | 6 | 46 |

50 – 60 | 4 | 50 |

Looking at the cumulative frequency column, we see that the median falls in the third class interval (20-30), which means the median marks range from 20 to 30.

**Now, to find the exact medicine, we can use the formula:**

Median = L + (( N ÷ 2 – F) ÷ f) x w

**Where:**

L is the lower boundary of the median class (20)

N is the total number of students (50)

F is the cumulative frequency before the F is the median class (15)

F is the frequency of the median class (15)

W is the width of the median class (10)

**Plugging in the values:**

Median = 20 + ((50 ÷ 2 – 15) ÷ 15) × 10

= 20 + ((25 – 15) ÷15 ) ÷ 10

= 20 + (10 ÷ 15) x10

= 20 + (2 ÷ 3)x10

= 20 + 6.67

= 26.67

So, the median marks fall around 26.67.

**Other Textual Questions & Answers**

**1. Choose the correct answer from the four alternatives given below:**

**(i) The measure of central tendency that does not get affected by extreme values.**

(a) Mean.

(b) Mean and Mode.

(c) Mode.

(d) Median.

Ans: (a) Mean.

**(ii) The measure of central tendency always coinciding with the hump of any distribution is.**

(a) Median.

(b) Median and Mode.

(c) Mean.

(d) Mode.

Ans: (b) Median and Mode.

**(iii) A scatter plot represents negative correlation if the plotted value run from.**

(a) Upper left to lower right.

(b) Lower left to upper right.

(c) Left to right.

(d) Upper right to lower left.

Ans: (a) Upper left to lower right.

**2. Give one word answer:**

**1. What are Quartiles, Deciles and Percentiles?**

Ans: The values which divide a series into pure, ten and hundred parts are known as Quartiles, Deciles and Percentiles respectively.

**2. What is meant by mean?**

Ans: It is the average of several values.

**3. What is mode?**

Ans: It is a value of variables which occurs most frequently.

**4. Define measures of central tendency.**

Ans: The values which are representative of the various distributions are known as measures of central tendency.

**5. What is meant by partition values?**

Ans: The value which divides the series into more than two equal parts is known as the partition value.

**6. What are the characteristics of a good table?**

Ans: It should be simple, compact, complete and self explanatory.

**7. Describe the formula to calculate Median.**

Ans: M = Size of N + 1/2 th item.

Where, N = Number of values.

**8. State the purpose for which data are used.**

Ans: Maps, Reports, Scientific paper books.

**9. Describe the main measures of central tendency.**

Ans: Mean, Median and Mode.

**10. Name two types of correlation.**

Ans: Positive and negative.

**3. Answer the following questions in about 30 words:**

**(i) Define the mean.**

Ans: The mean is the value which is derived by summing all the values and dividing it by the member of observation.

**(ii) What are the advantages of using mode?**

Ans: Mode is the maximum occurrence or frequency at a particular point or value. Mode is a measure that is less widely used compared to mean and median.

**(iii) What is dispersion?**

Ans: The term dispersion refers to the

scattering of scores about the measures of central tendency. It is used to measure the extent to which individual items or numerical data tend to vary or spread about an average value. Thus the dispersion is the degree of spread or scatter or variations of measures about a central value.

**(iv) Define Correlation.**

Ans: Correlation refers to the nature and strength of correspondence or relationship between two variations. The terms nature and strength in definition refer to the direction and degree of the variables with which they vary.

**(v) What is perfect correlation?**

Ans: The maximum degree of correspondence or relationship goes up to 1 (one) in mathematical terms. On adding an element of the direction of correlation it spreads the maximum extent of -1 to + 1 through zero. It can never be more than one. Correlation of 1 is known as perfect correlation (whether positive or negative). Between the two points of divergent perfect correlation lies 0 (zero) correlation a point of no correlation or absence of any correlation between the variables.

**(v) What is the maximum extent of correlation?**

Ans: The maximum extent of correlation 1 (one) in mathematical terms. It can never be more than one.