Statistics Class 10 Maths (Chapter-14) NCERT Solutions (Part-1) | CBSE Class 10 Board Exams Prep

BYJU'S - Class 9 & 10・2 minutes read

The session focuses on solving NCERT statistics problems related to calculating means through direct and assumed methods, emphasizing the importance of organized data and accurate calculations for exercises like determining mean plant counts and daily wages. Additionally, students are encouraged to join a virtual quiz, participate in an English speaking program, and attend upcoming live sessions to enhance their understanding and application of statistical concepts.

Insights

  • The session provides a focused approach to solving statistics questions from NCERT, specifically emphasizing the calculation of mean using direct and assumed methods, while excluding the step division method from the syllabus. This structured guidance helps students understand when to apply each method based on the size of their data sets, enhancing their problem-solving skills in statistics.
  • Byju's offers a two-month English speaking program led by Cambridge certified teachers, aimed at boosting students' confidence and public speaking abilities. This initiative highlights the importance of communication skills alongside academic subjects, encouraging students to develop a well-rounded skill set that is crucial for their future endeavors.
  • The session stresses the significance of accurately representing and calculating data in statistical analysis, including the conversion of discontinuous series into continuous ones and the creation of frequency distribution tables. This emphasis on precision not only aids in achieving higher marks in exams but also cultivates a deeper understanding of statistical concepts that students will encounter in real-world applications.

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Recent questions

  • What is the assumed mean method?

    The assumed mean method is a statistical technique used to estimate the mean of a dataset when the values are large or when the data is grouped. This method involves selecting a middle value, known as the assumed mean, around which the data is analyzed. By calculating deviations from this assumed mean and multiplying these deviations by their respective frequencies, one can derive a more accurate mean. This approach is particularly useful in scenarios where direct calculation of the mean is cumbersome due to the size of the data set. It simplifies the process by allowing for easier calculations and helps in minimizing errors, making it a preferred method in statistical analysis.

  • How do you calculate the mean?

    Calculating the mean involves summing all the values in a dataset and then dividing that total by the number of values. For example, if you have a set of numbers representing the number of plants in several houses, you would first add all those numbers together to get a total. Then, you would divide that total by the number of houses to find the mean number of plants per house. In cases where the data is grouped, such as with frequency distributions, you may use methods like the direct mean or the assumed mean to facilitate the calculation. Each method has its own steps, but the core principle remains the same: total values divided by the count of values.

  • What is frequency distribution?

    Frequency distribution is a statistical tool that organizes data into classes or intervals, showing how often each value or range of values occurs within a dataset. This method allows for a clearer understanding of the data by summarizing it in a table format, where each class is associated with a frequency count. For instance, if you were analyzing the daily pocket allowance of children, you would categorize the allowances into ranges (like $0-$5, $6-$10, etc.) and count how many children fall into each range. This visual representation helps in identifying patterns, trends, and outliers in the data, making it easier to analyze and interpret.

  • Why is practicing statistics important?

    Practicing statistics is crucial for students as it enhances their understanding of mathematical concepts and improves their problem-solving skills. Mastery of statistical methods, such as calculating means and understanding frequency distributions, can lead to better performance in exams, as these topics are often heavily tested. Regular practice helps students avoid common mistakes and reinforces their ability to apply theoretical knowledge to practical situations. Furthermore, a solid grasp of statistics is essential not only for academic success but also for making informed decisions in real-life scenarios, such as interpreting data in various fields like economics, health, and social sciences.

  • What is a continuous series in statistics?

    A continuous series in statistics refers to a data set where the values can take any number within a given range, allowing for fractional values. This type of series is characterized by the absence of gaps between the upper limit of one class and the lower limit of the next, creating a seamless flow of data. For example, if you are measuring heights, a continuous series would include all possible values within the range, such as 150.5 cm, 151.2 cm, etc. To convert a discontinuous series into a continuous one, adjustments are made to the class limits, ensuring that they align properly. Understanding continuous series is vital for accurate data representation and analysis in statistical studies.

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Summary

00:00

Statistics Session on Mean Calculation Methods

  • The session focuses on solving NCERT statistics questions, specifically targeting exercises from chapter 14.1, which covers the concept of mean using two methods: direct mean and assumed mean. The step division method is excluded from the syllabus.
  • Students are encouraged to participate in a virtual life quiz happening today, with a registration link provided in the description box for those interested in joining.
  • A two-month English speaking program is available through Byju's, featuring Cambridge certified teachers who will assist students in gaining confidence and improving public speaking skills. Registration details are also provided in the description box.
  • The first exercise involves calculating the mean number of plants per house based on data collected from 20 houses, where students must organize the data vertically in a table format for clarity.
  • Students are instructed to determine which method to use for calculating the mean, with the direct mean method preferred when frequency values are small, as demonstrated with the provided data.
  • The calculation process includes determining class marks, multiplying frequency values by class marks, and summing these products to find the total, which is then divided by the total number of houses (20) to find the mean.
  • The second exercise requires finding the mean of daily wages for 50 factory workers, emphasizing the use of the assumed mean method due to larger wage values, with the middle value selected as the assumed mean.
  • Students must calculate deviations from the assumed mean, multiply these deviations by their respective frequencies, and sum the results to apply the mean formula accurately.
  • The importance of practicing these statistical methods is highlighted, as they can lead to full marks in exams, and students are encouraged to avoid mistakes by carefully following the steps outlined.
  • The session concludes with a focus on a question regarding the daily pocket allowance of children, emphasizing the need to calculate missing frequencies, which is deemed an important type of question for students to master.

19:58

Statistical Analysis of Frequency Distribution

  • The process begins with identifying missing frequency types and calculating mid-values between given ranges, such as 12 for the range 11-13, 14 for 13-15, and so on, up to 24 for the range 22-24.
  • Next, the calculation involves multiplying 13 by 18 and then by 4, emphasizing the importance of accuracy in calculations using the assumed mean method to minimize errors.
  • The subtraction of values from 18 is performed, yielding results like -6 for 12, -4 for 14, -2 for 16, 0 for 18, 2 for 20, 4 for 22, and 6 for 24, which helps in determining the frequency distribution.
  • The frequency values are multiplied with the corresponding differences, such as 6 multiplied by 4 resulting in 24, simplifying the calculations by canceling out equal positive and negative values.
  • The total of positive values is calculated, resulting in 20, while the negative values sum to -60, leading to a final calculation of 2f - 40 = 0, which simplifies to f = 20.
  • The next question involves calculating the number of heartbeats per minute for women in a hospital, requiring the conversion of data into a vertical table format for clarity.
  • The middle value for heartbeats is calculated as 66.5, with subsequent values following a pattern, leading to the identification of values like 69.5, 72.5, and so forth.
  • The D values are calculated by subtracting the middle value from the given heart rates, resulting in negative and positive values that help in forming a frequency distribution.
  • The method of adjusting the upper and lower limits of a distribution is explained, where the difference between limits is halved and added or subtracted from the respective limits to create a continuous series.
  • Finally, the middle value of the adjusted limits is calculated, demonstrating the importance of accurate data representation and calculation in statistical analysis.

41:01

Calculating Values and Frequency Distribution Techniques

  • The discussion begins with a calculation exercise where the first value is determined to be 51, derived from the average of the lower limit (49.5) and upper limit (52.5) of a data set, calculated as (49.5 + 52.5) / 2 = 51.
  • Following the established pattern, subsequent values are calculated as 54, 57, 60, and 63, indicating a consistent increment of 3 between each value.
  • Students are advised to avoid using any activation methods not included in their syllabus, as examiners reference a syllabus booklet to verify the correctness of answers, which can affect grading.
  • The importance of understanding continuous and discontinuous series is emphasized, with a specific example given where the upper limit of one class does not match the lower limit of the next, necessitating a change to a continuous series.
  • To convert a discontinuous series into a continuous one, the method of difference is applied, where the difference between the upper limit of one class and the lower limit of the next is halved and adjusted accordingly.
  • The session includes a calculation of frequency distribution, where students are instructed to subtract a minimum value from all calculated values to derive new values for further analysis.
  • The final step involves creating a frequency distribution table (FIDI) by multiplying the frequency of each class by the corresponding values, leading to a summation of these products.
  • The overall sum of frequencies is calculated to be 400, and the final value derived from the formula is approximately 57.19, which is rounded off for clarity.
  • Students are encouraged to utilize NCERT solutions and exemplar materials for their studies, with a reminder to focus on specific chapters relevant to their syllabus.
  • The session concludes with a brief mention of a practical exercise involving the calculation of sulfur dioxide concentration in air, where values are derived from a dataset of 30 localities, emphasizing the importance of accurate data handling and calculation methods.

01:01:57

Live Session on NCERT Questions This Weekend

  • An important announcement states that a live session will occur on Saturday and Sunday at 4:00 PM, where Khushboo will cover 100 NCERT Exemplar Questions; viewers are encouraged to subscribe to the channel, like the video, and press the bell icon to receive notifications and not miss any classes, ensuring they can participate fully and benefit from the session.
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