The table above shows a frequency chart for the scores on a certain

Question

Score  
  Frequency  
 
  k-4 
 1 
 
  k-2 
 4 
 
  k 
 8 
 
  k+2 
 n

The table above shows a frequency chart for the scores on a certain accounting quiz, where k and n are positive integers. What is the standard deviation of the scores on the accounting quiz?

(1) k = 5
(2) n =12

Score  Frequency 
k-4  1 
k-2   4 
k  8 
k+2  n

Bunuel · Accepted Answer

An important property to note is that  if we add or subtract a constant to each term in a set, the standard deviation does not change .

Thus, knowing the value of n alone would be enough to determine the standard deviation of the set. The value of k is irrelevant because it simply shifts each score by k, keeping the distribution shape unchanged.

This means we can analyze the scores as if they were:

Score  
  Frequency  
 
  -4 
 1 
 
  -2 
 4 
 
  0 
 8 
 
  2 
 n

Since the standard deviation remains the same regardless of k, we only need the value of n to calculate it. Therefore, the answer is B.

gmatophobia · Answer

Standard deviation denotes how much individual values in a data set differ from the mean (average) of the set. Put otherwise, standard deviation is a measure of the amount of variation or dispersion in a set of values.

Statement 1

1) k=5

This statement provides the value of  k , however, the information is not relevant as we do not know the frequency i.e. how many terms are present with the given value. We therefore cannot obtain the mean and find the standard deviation. Hence, this statement is not sufficient. We can eliminate A and D.

Statement 2

2) n =12 
 
   Score    Frequency   
  k-4  1  
  k-2  4  
  k  8  
  k+2  12

The mean of the quiz =  \frac{k - 4 + 4k - 8 + 8k + 12k + 24}{25} = \frac{25k + 12}{25} = k + \frac{12}{25}

We can find the distance each of the score elements is from the mean as each of the scores is given in terms of k. Hence, knowing the number of terms (frequency) of each element we can determine the standard deviation of the quiz.

This statement is sufficient.

Option B

ankitmba95 · Answer

how can you write mean of set without taking into account the freqency?

gmatophobia · Answer

My bad. I had overlooked that fact. Have updated the solution to reflect the details.

lavanya.18 · Answer

Can someone explain it better??

bumpbot · Answer

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