NCERT Solutions: Statistics (Exercise 14.4)

# NCERT Solutions for Class 10 Maths Chapter 13 - Statistics (Exercise 14.4)

NCERT TEXTBOOK QUESTIONS SOLVED
Page No. 293
EXERCISE 14.4
Q 1. The following distribution gives the daily income of 50 workers of a factory

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Sol. We have the cumulative frequency distribution as:

 Daily income (in Rs ) Cumulative frequencies Less than 120 12 + 0 = 12 Less than 140 12 + 14 = 26 Less than 160 26 + 8 = 34 Less than 180 34 + 6 = 40 Less than 200 40 + 10 = 50

Now, we plot the points corresponding to the ordered pairs (120, 12), (140, 26), (160, 34), (180, 40) and (200, 50) on a graph paper and join them by a free hand smooth curve as shown below:

The curve so obtained is called the less than o give.

Q 2. During the medical check-up of 35 students of a class, their weights were recorded as follows:

 Weight (in kg) Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula
Sol. Here, the values 38, 40, 42, 44, 46, 48, 50 and 52 are the upper limits of the respective class intervals.
We plot the points (ordered pairs) (38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper and join them by a free hand smooth curve.
The curve so obtained is the less than type ogive.
∵ n = 35

The point 17.5 is on y-axis.

From this point (i.e., from 17.5) we draw a line parallel to the x-axis which cuts the curve at P. From this point (i.e., from P), draw a perpendicular to the x-axis, meeting the x-axis at Q. The point Q represents the median of the data which is 47.5.
Verification
To verify the result using the formula, let us make the following table in order to find median using the formula:

 Weight (in kg) Number of students [Cumulative frequency] 0-38 0 38-40 3 40-42 5 42-44 9 44-46 14 46-48 28 48-50 32 50-52 35

Here,

Since, this observation lies in the class 46 − 48.
∴ The median class is 46 − 48 such that l = 46, h = 2, f = 14, cf = 14

Thus, the median = 46.5 kg is approximately verified.

Q 3. The following table gives production yield per hectare of wheat of 100 farms of a village.

 Production yield (in kg/ha) 50-55 55-60 60-65 65-70 70-75 75-80 Number of farms 2 8 12 24 38 16

Change the distribution to a more than type distribution, and draw its ogive.
Sol. For ‘more than type’ distribution, we have:

 Production yield (in kg/ha) Number of farms (Cumulative frequencies) More than 50 100 More than 55 98 More than 60 90 More than 65 78 More than 70 54 More than 75 16

Now, we plot the points (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) and join the points with a free hand curve.

The curve so obtained is the ‘more than type ogive’.

The document NCERT Solutions for Class 10 Maths Chapter 13 - Statistics (Exercise 14.4) is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## FAQs on NCERT Solutions for Class 10 Maths Chapter 13 - Statistics (Exercise 14.4)

 1. What is the importance of statistics in everyday life?
Ans. Statistics plays a crucial role in everyday life as it helps in making informed decisions based on data analysis. It helps in understanding trends, patterns, and variability in various fields such as business, economics, healthcare, and social sciences. For example, statistics can be used to analyze market trends, evaluate the effectiveness of a medical treatment, or determine the impact of a social program.
 2. How is statistics used in research studies?
Ans. Statistics is an essential tool in research studies as it helps in collecting, organizing, and analyzing data. Researchers use statistical techniques to summarize and interpret their findings, identify relationships between variables, and draw meaningful conclusions. It enables researchers to make reliable inferences about a population based on a sample, ensuring the validity and generalizability of their results.
 3. What are the different types of data in statistics?
Ans. In statistics, data can be classified into two main types: numerical and categorical data. Numerical data consists of numbers and can be further divided into discrete data (countable, finite values) and continuous data (measurable, infinite values). Categorical data, on the other hand, represents characteristics or qualities and can be divided into nominal data (categories with no specific order) and ordinal data (categories with a specific order).
 4. How can statistics be used to interpret survey results?
Ans. Statistics is used to interpret survey results by analyzing the collected data. This involves calculating measures of central tendency (such as mean, median, and mode) to determine the average response or opinion. Additionally, measures of dispersion (such as range or standard deviation) are used to assess the variability or spread of the survey results. Statistical techniques like hypothesis testing can also be employed to determine the significance of observed differences or relationships within the survey data.
 5. What are the limitations of statistics?
Ans. While statistics is a powerful tool, it has certain limitations. One limitation is that statistics cannot prove causation, only correlation. In other words, statistical analysis can show a relationship between variables, but it cannot establish a cause-and-effect relationship. Additionally, statistics are dependent on the quality of the data collected, and if the data is biased or inaccurate, it can lead to erroneous conclusions. It is also important to consider the assumptions and limitations of statistical models and techniques used, as they may not always be applicable to every situation.

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