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If the mode of the following data is 7, then find the value of k. 2,4,6,7,5,6,10,6,7,2k+1,9,7,13
3
6
2
4
3
Count the frequency of each given number. Since the mode is 7 and 6 appears 3 times while 7 appears 3 times, the term containing k must equal 7 to make 7 the unique maximum frequency mode.
Data given: 2, 4, 6, 7, 5, 6, 10, 6, 7, 2k + 1, 9, 7, 13; Mode = 7
Mode=most┬аfrequently┬аoccurring┬аvalue┬аin┬аa┬аdataset
Count the frequency of each given number. Since the mode is 7 and 6 appears 3 times while 7 appears 3 times, the term containing k must equal 7 to make 7 the unique maximum frequency mode.
Students often assume 6 and 7 already tie with 3 frequencies each, and forget that the unknown term 2k+1 must equal 7 so that 7 has a frequency of 4.
Analyze the given dataset
The given data is: 2,4,6,7,5,6,10,6,7,2k+1,9,7,13. Counting the frequencies of each observed number: 2 appears 1 time, 4 appears 1 time, 5 appears 1 time, 6 appears 3 times, 7 appears 3 times, 9 appears 1 time, 10 appears 1 time, and 13 appears 1 time.
Frequency┬аof┬а6=3,Frequency┬аof┬а7=3
Apply the condition for Mode
We are given that the mode of the dataset is 7. For 7 to be the unique mode with the highest frequency, its frequency must exceed that of all other numbers (including 6). Therefore, the unknown term 2k+1 must be equal to 7 so that the frequency of 7 becomes 3+1=4.
2k+1=7
Calculate the value of k
Solving the linear equation for k: subtract 1 from both sides to get 2k=6, then divide by 2 to get k=3.
k=27тИТ1тАЛ=3
A is correct because equating the unknown term 2k+1 to the mode 7 gives 2k+1=7, which yields k=3.
In statistics problems involving unknown variables in datasets, always test whether making the unknown equal to the stated mode satisfies the frequency condition uniquely.
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