Frequency distribution

A frequency distribution is a table that shows how many times a certain value or range of values appears in a dataset.

Given frequency distribution

Class interval: 350–369 370–389 390–409 410–429 430–449 450–469
Frequency: 5 7 13 9 6 3

Calculating mean

The mean of a frequency distribution is calculated by multiplying each class midpoint by its corresponding frequency, adding up these products, and dividing the sum by the total frequency.

To calculate the mean for the given frequency distribution:
- Find the midpoint of each class interval by adding the lower and upper limits and dividing by 2.
- Multiply each midpoint by its corresponding frequency.
- Add up these products.
- Divide the sum by the total frequency (which is the sum of all the frequencies).

Midpoints: 359.5 379.5 399.5 419.5 439.5 459.5
Products: 1797.5 2656.5 5193.5 3775.5 2637.0 1378.5

Sum of products = 18438.5
Total frequency = 43

Mean = 18438.5 / 43 = 429.5

Therefore, the mean of the given frequency distribution is 429.5.

Calculating mode

The mode of a frequency distribution is the value that appears most frequently. In some cases, there may be more than one mode if two or more values have the same highest frequency.

To find the mode for the given frequency distribution:
- Identify the class with the highest frequency.
- The mode is the midpoint of that class interval.

The class with the highest frequency is the one that corresponds to the interval 390-409, which has a frequency of 13. Therefore, the mode is the midpoint of that interval, which is:

Mode = (390 + 409) / 2 = 399.5

Therefore, the mode of the given frequency distribution is 399.5.

Summary

- The mean of the given frequency distribution is 429.5.
- The mode of the given frequency distribution is 399.5.

Frequency is 15 27 31 19 13 6