QQuestion
Find the mode from the following data.
| Class Interval | Frequency |
| 0 – 5 | 2 |
| 5 – 10 | 6 |
| 10 – 15 | 10 |
| 15 – 20 | 16 |
| 20 – 25 | 22 |
| 25 – 30 | 11 |
| 30 – 35 | 8 |
| 35 – 40 | 5 |
✓Answer
The class with the highest frequency is 20 – 25, so it is the modal class.
Let
- l = lower limit of modal class = 20
- h = class width = 5
- f₀ = frequency of the class before the modal class = 16
- f₁ = frequency of the modal class = 22
- f₂ = frequency of the class after the modal class = 11
Formula: Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
Mode = 20 + 22 − 16 \over 2 × 22 − 16 − 11 × 5
= 20 + 6 \over 44 − 27 × 5
= 20 + 6 \over 17 × 5
= 20 + 30 \over 17
= 20 + 1.76
= 21.76
Therefore, the mode is 21.76.
Related Questions
More WBBSE Moderate level questions
Find the median of the data from the following distribution. Marks Obtained No. of Students Less than 10 8 Less than 20 15 Less than 30 29 Less than 40 42 Less than 50 60 Less than 60 70
Draw an ogive on the graph paper after calculating the cumulative frequency (less than type) of the following data: Class Interval Frequency 0 - 10 1 10 - 20 5 20 - 30 15 30 - 40 20 40 - 50 15 50 - 60 6 60 - 70 1
The median of following data is 32. Find the value of x and y if x + y = 100. Class Interval Frequency 0 - 10 10 10 - 20 x 20 - 30 25 30 - 40 30 40 - 50 y 50 - 60 10
Find the mode of the following frequency distribution : Class Frequency 50 - 59 5 60 - 69 20 70 - 79 40 80 - 89 50 90 - 99 30 100 - 109 6
If the arithmetic mean and total frequency of the following distribution are 50 and 120 respectively, then find the value of f1 and f2: Class Frequency 0 - 20 17 20 - 40 f1 40 - 60 32 60 - 80 f2 80 - 100 19
Find the mean by any suitable method from the following frequency distribution table Class Interval Frequency 85 - 105 3 105 - 125 12 125 - 145 18 145 - 165 10 165 - 185 5 185 - 205 2
27, 31, 46, 52, x, y + 2, 71, 79, 85, 90 are in increasing order. If the median is 64, then the value of x + y is (a) 125 (b) 127 (c) 128 (d) 126
The mean of a frequency distribution is 7 and Σfx = 140, then find the value of Σf
State True or False: The average of n numbers is x̄. If the sum of first (n−1) numbers is K, then nth number is (n−1) x̄ + K.
If A and M be the arithmetic mean and median of first ten natural numbers, then relation between them will be - (a) A > M (b) A < M (c) A = (d) A = M
The age of 100 persons present in a workshop is given in the following table. Find the average age of 100 people (by any method): Age Group Number of People 10 - 20 8 20 - 30 12 30 - 40 20 40 - 50 22 50 - 60 18 60 - 70 20
Construct the table of cumulative frequency (greater than type) and draw the ogive from the following frequency distribution : Class Frequency 0 - 10 7 10 - 20 10 20 - 30 23 30 - 40 50 40 - 50 6 50 - 60 4