The NCERT Solutions for Class 11 Statistics Chapter 5 provides an excellent knowledge of Statistics to the students. They provide updated and revised solutions for which well-experienced subject experts prepare the content. These are available in three different languages, namely Urdu, English, and Hindi. Students can gain knowledge along with good marks with the help of NCERT solutions.
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Class 11 Statistics NCERT Solutions ch 5 is available in a PDF format on the official website of Vedantu for free of cost. The students should avail of this opportunity to get more knowledge. Using a soft copy or hard copy is up to the student. If they are willing to take a hard copy, then it can be easy for them to study without worrying about the internet connection. It also helps to prepare for the competitive exams and other board exams.
1. IntroductionÂ
NCERT Solutions Class 11 Statistics Chapter 5 wants to introduce the measures available for the central tendency in Statistics as the students have learned the collection of data and the representation of data. The next one is analyzing and interpreting the data. To analyze the data, we have three different measures of central tendencies, such as arithmetic means, median, and mode.
2. Arithmetic Mean
The arithmetic mean is a broadly used measure to calculate the average of the given data. NCERT Solutions for Class 11 Statistics Chapter 5 also explains two different variations called, mean for grouped data and mean for ungrouped data. For any kind of method, the arithmetic mean is the sum of all observations divided by the number of observations. A formula can represent it, and the students can proceed to calculate the mean for given data.
Statistics Class 11 NCERT Solutions' Measures of Central Tendency specify that the calculation of mean for ungrouped data and grouped data has three different kinds of methods. They are a direct method, assumed method, step division method. Each method may differ from grouped data and ungrouped data.
The NCERT Solutions Class 11 Statistics Chapter 5 clearly explains available on the official website of Vedantu with an illustration. Again the grouped data has two kinds of series namely-discrete series and continuous series.
3. Median
In this section, the students are advised to learn another measure of central tendency, median. The NCERT Class 11 Statistics Chapter 5 Measures of Central Tendency explains that the median is a simple concept. It can be calculated as taking the middle value, which separates both sides of the values will be equal. But it is possible only if the size of the series is an odd number. If the students are asked to find out the median for a set of even number values, then we need to take the two middle terms and find out the average for those two terms.
Quartiles are another topic explained to the students. If the whole size is divided into four equal parts, then it is called quartile. It can be calculated separately for both series by themselves.
Percentiles are aÂ topic for which the whole size is divided into 99 Parts which reaches the cent.Â
4. ModeÂ
Class 11 of Statistics Chapter 5 is explained by our NCERT solutions that specifies the students to understand each measure of central tendency. Because if the students can understand the meaning and formula, it is difficult to forget. Even though the mode is the last measure of central tendency, it has a lot of significance. The mode is a French word that means the fashionable or frequent value which occurred in the set. In simple words, we can say that the mode is the value which has the highest occurrences. For the direct method, we can calculate directly by seeing itself. For the continuous method, there is a particular formula to find out the value of mode.
5. Relative position of arithmetic mean, median, and mode
The NCERT solutions of Class 11 Statistics Chapter 5 have also explained the students about the positions of three measures of central tendency. If we can stir the magnitude of three measures in any direction, the median should be in the middle. Mode and the arithmetic mean will be at either of the extreme positions.
6. Conclusion
Thus the Chapter 5 of measures of central tendency has been explained very well by professional teachers to the students. The material is provided with different examples of all six concepts.
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It allows students to enrich their conceptual knowledge and to boost their scores.Â
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1. Find the mean, median, and mode for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
Ans. The mean is the usual average is,Â
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) Ã· 9 = 15
The median is the middle value, so first, we have to rewrite the list in numerical order:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the size is an odd number.Â
13, 13, 13, 13, 14, 14, 16, 18, 21
Hence, the median is 14.
A mode is a number that is repeated more times.
Hence, 13 is the mode.
2. What is the difference between Mean and Median?
Ans. Mean is the average of all the values given in the set. On the contrary, the median is the exact middle number when a list of values will be written in order. So both are completely different and how they have unique advantages in the field of Statistics.
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