Calculate the mode of the following using empirical formula:
17, 10, 12, 11, 10, 15, 14, 11, 12, 13
By arranging the given data in ascending form we get;
10, 10, 11, 11, 12, 12, 13, 14, 15, 17
Draw the table;
X | f | Cumulative frequency | f × x |
10 | 2 | 2 | 20 |
11 | 2 | 4 | 22 |
12 | 2 | 6 | 24 |
13 | 1 | 7 | 13 |
14 | 1 | 8 | 14 |
15 | 1 | 9 | 15 |
17 | 1 | 10 | 17 |
∑f = 10 | ∑fx = 125 |
∑f = N = 10 (even)
Median = 1/2 [value of (n/2)th term + value of (n/2 + 1)th term]
= 1/2 [value of 5th term + value of 6th term]
= 1/2 [12 + 12] = 24/2 = 12
Now,
Mean = (∑fx)/(∑f) = 125/10 = 12.5
Mode = 3(median) – 2(mean)
= 3 × 12 – 2 × 12.5
= 36 – 25 = 11