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If the mode of the following data is 7, then the value of k in the data set 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k + 5, 9, 7, and 13 is:
- a)3
- b)7
- c)4
- d)1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the mode of the following data is 7, then the value of k in the dat...
Concept:
Mode is the value that occurs most often in the data set of values.
Calculation:
Given data values are 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k + 5, 9, 7, and 13
In the above data set, values 6, and 7 have occurred more times i.e., 3 times
But given that mode is 7.
So, 7 should occur more times than 6.
Hence the variable 2k + 5 must be 7
⇒ 2k + 5 = 7
⇒ 2k = 2
∴ k = 1
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Community Answer
If the mode of the following data is 7, then the value of k in the dat...
To find the value of k in the given data set, we need to determine the value that would make the mode of the data set equal to 7. The mode is the value that appears most frequently in the data set.
Let's analyze the given data set step by step:
Step 1: Arrange the data set in ascending order:
1, 2k, 3, 5, 6, 6, 7, 7, 7, 8, 9, 10, 13
Step 2: Count the frequency of each value in the data set:
1 appears once
2k appears once
3 appears once
5 appears once
6 appears twice
7 appears three times
8 appears once
9 appears once
10 appears once
13 appears once
Step 3: Identify the value with the highest frequency:
In this case, the value with the highest frequency is 7, as it appears three times.
Step 4: Substitute the mode value into the data set:
Since the mode is 7, we can replace one of the 7s in the data set with the value of k.
The data set becomes: 1, 2k, 3, 5, 6, 6, 7, 7, 8, 9, 10, 13
Step 5: Find the value of k:
Since the mode is 7, we need to replace one of the 7s in the data set with the value of k. Therefore, k = 7.
Hence, the value of k in the given data set is 7, which corresponds to option D.
Let's analyze the given data set step by step:
Step 1: Arrange the data set in ascending order:
1, 2k, 3, 5, 6, 6, 7, 7, 7, 8, 9, 10, 13
Step 2: Count the frequency of each value in the data set:
1 appears once
2k appears once
3 appears once
5 appears once
6 appears twice
7 appears three times
8 appears once
9 appears once
10 appears once
13 appears once
Step 3: Identify the value with the highest frequency:
In this case, the value with the highest frequency is 7, as it appears three times.
Step 4: Substitute the mode value into the data set:
Since the mode is 7, we can replace one of the 7s in the data set with the value of k.
The data set becomes: 1, 2k, 3, 5, 6, 6, 7, 7, 8, 9, 10, 13
Step 5: Find the value of k:
Since the mode is 7, we need to replace one of the 7s in the data set with the value of k. Therefore, k = 7.
Hence, the value of k in the given data set is 7, which corresponds to option D.
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If the mode of the following data is 7, then the value of k in the data set 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k + 5, 9, 7, and 13 is:a)3b)7c)4d)1Correct answer is option 'D'. Can you explain this answer?
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