Frequency tables

Question

The table shows the number of correct answers that students gave on a recent 5 question quiz if the mean number of correct answers is 4 determine the value of K

Number correct: 1 2 3 4 5

Frequency: 1 2 k 5 12

Answer 1

Mean of a Frequency Distribution = [sum of x(i) * frequency (x(i))]/sum of frequency(x(i))

x(i) frequency(x(i)) x(i) * frequency(x(i))

1 1 1

2 2 4

3 K 3K

4 5 20

5 12 60

20 + K 85 + 3K

sum of x(i) * frequency (x(i)) = 85 + 3K

sum of frequency(x(i)) = 20 + K

(85 + 3K)/ (20 + K) = 4

85 + 3K = 4 (20+k)

85 + 3K = 80 + 4K

5 = K

Answer 2

1 + 4 + 3k + 20 + 60 = 85 + 3k

(85 + 3k) / (20 + k) = 4

85 + 3k = 80 +4k

5 = k