Question:
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :
Show Hint
To easily remember the empirical formula, write the terms in alphabetical order: Mean, Median, Mode.
The coefficient of Median is 3 (longer word) and Mean is 2 (shorter word):
\[ \text{Mode} = 3\ \text{Median} - 2\ \text{Mean} \]
This alphabetical-length connection serves as an excellent memory aid!
The coefficient of Median is 3 (longer word) and Mean is 2 (shorter word):
\[ \text{Mode} = 3\ \text{Median} - 2\ \text{Mean} \]
This alphabetical-length connection serves as an excellent memory aid!
Updated On: Jul 7, 2026
- 43.4
- 42.4
- 44.2
- 49.3
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The mean and the median of a statistical frequency distribution are given as 43 and 43.4, respectively. We need to determine the mode of this distribution.
Step 2: Key Formula or Approach:
We will use the standard empirical relationship between the three measures of central tendency (Mean, Median, and Mode):
\[ \text{Mode} = 3\ \text{Median} - 2\ \text{Mean} \]
Step 3: Detailed Explanation:
1. Identify the given parameters:
- \(\text{Mean} = 43\)
- \(\text{Median} = 43.4\)
2. Substitute these values into the empirical formula:
\[ \text{Mode} = 3(43.4) - 2(43) \]
3. Perform the calculations:
- Calculate \(3 \times 43.4\):
\[ 3 \times 43.4 = 130.2 \]
- Calculate \(2 \times 43\):
\[ 2 \times 43 = 86 \]
4. Subtract the two values to find the Mode:
\[ \text{Mode} = 130.2 - 86 = 44.2 \]
This gives the value of the mode as 44.2.
Step 4: Final Answer:
The mode of the distribution is 44.2, which corresponds to option (C).
The mean and the median of a statistical frequency distribution are given as 43 and 43.4, respectively. We need to determine the mode of this distribution.
Step 2: Key Formula or Approach:
We will use the standard empirical relationship between the three measures of central tendency (Mean, Median, and Mode):
\[ \text{Mode} = 3\ \text{Median} - 2\ \text{Mean} \]
Step 3: Detailed Explanation:
1. Identify the given parameters:
- \(\text{Mean} = 43\)
- \(\text{Median} = 43.4\)
2. Substitute these values into the empirical formula:
\[ \text{Mode} = 3(43.4) - 2(43) \]
3. Perform the calculations:
- Calculate \(3 \times 43.4\):
\[ 3 \times 43.4 = 130.2 \]
- Calculate \(2 \times 43\):
\[ 2 \times 43 = 86 \]
4. Subtract the two values to find the Mode:
\[ \text{Mode} = 130.2 - 86 = 44.2 \]
This gives the value of the mode as 44.2.
Step 4: Final Answer:
The mode of the distribution is 44.2, which corresponds to option (C).
Was this answer helpful?
0
0
Top CBSE X Mathematics Questions
- Express each number as a product of its prime factors:
- \(140\)
- \(156\)
- \(3825\)
- \(5005\)
- \(7429\)
- Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
- \(26\) and \(91\)
- \(510\) \(\)and \(92\)
- \(336\) and \(54\)
- Find the LCM and HCF of the following integers by applying the prime factorisation method.
- \(12, 15\) and
- \(17, 23\) and
- \(8, 9\) and \(25\)
- Given that HCF \((306, 657) = 9\) , find LCM \((306, 657)\).
- Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).
View More Questions
Top CBSE X Statistics Questions
- Gurpreet is very fond of doing research on plants. She collected some leaves from different plants and measured their lengths in mm.
The length of the leaves from different plants are recorded in the following table.Based on the above information, answer the following questions :\(\text{Length (in mm)}\) 70-80 80-90 90-100 100-110 110-120 120-130 130-140 \(\text{Number of leaves}\) 3 5 9 12 5 4 2 - If a certain variable \(x\) divides a statistical data arranged in order into two equal parts; then the value of \(x\) is called the:
- The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is:
- For the above distribution, the modal class is :
Marks : Below 10 Below 20 Below 30 Below 40 Below 50 Number of Students : 3 12 27 57 75 - Calculate the mean of the following data :
Class : 4 – 6 7 – 9 10 – 12 13 – 15 Frequency : 5 4 9 10
View More Questions
Top CBSE X Questions
- Read the following source carefully and answer the questions that follow:
Print Comes to India
From 1780, James Augustus Hickey began to edit the Bengal Gazette, a weekly maga zine that described itself as ‘a commercial paper open to all, but influenced by none’. So it was private English enterprise, proud of its independence from colonial influence, that began English printing in India. Hickey published a lot of advertisements, including those that related to the import and sale of slaves. But he also published a lot of gossip about the Company’s senior officials in India. Enraged by this, Governor-General War ren Hastings persecuted Hickey, and encouraged the publication of officially sanctioned newspapers that could counter the flow of information that damaged the image of the colonial government. By the close of the eighteenth century, a number of newspapers and journals appeared in print. There were Indians, too, who began to publish Indian news papers. The first to appear was the weekly Bengal Gazette, brought out by Gangadhar Bhattacharya, who was close to Raja Rammohan Roy. - Read the following source carefully and answer the questions that follow:
Loans from Cooperatives
Besides banks, the other major source of cheap credit in rural areas are the cooperative societies (or cooperatives). Members of a cooperative pool their resources for coopera tion in certain areas. There are several types of cooperatives possible such as farmers cooperatives, weavers cooperatives, industrial workers cooperatives, etc. Krishak Coop erative functions in a village not very far away from Sonpur. It has 2300 farmers as members. It accepts deposits from its members. With these deposits as collateral, the Cooperative has obtained a large loan from the bank. These funds are used to provide loans to members. Once these loans are repaid, another round of lending can take place. Krishak Cooperative provides loans for the purchase of agricultural implements, loans for cultivation and agricultural trade, fishery loans, loans for construction of houses and for a variety of other expenses. - More than three million carbon compounds have been discovered in the field of chemistry. The diversity of these compounds is due to the capacity of carbon atoms for bonding with one another as well as with other atoms. Most of the carbon compounds are poor conductors of electricity and have low melting and boiling points.
- Human digestive system is a tube running from mouth to anus. Its main function is to breakdown complex molecules present in the food which cannot be absorbed as such into smaller molecules. These molecules are absorbed across the walls of the tube and the absorbed food reaches each and every cell of the body where it is utilised for obtaining energy.
- A student has three convex lenses A, B, and C of different focal lengths. He wants to observe the images formed by these lenses on a screen by placing a candle flame at different distances as given in the following table:
Case No. Lens Focal Length Object Distance 1 \(A\) 50 cm 25 cm 2 B 20 cm 60 cm 3 C 15 cm 30 cm
View More Questions