STATISTICS

CONTENT

(a) Meaning and computations of mean, median and mode of ungrouped data.

(b) Determination of the mean, median and the mode of grouped frequency data.

(c) Comparison of mean, mode and median.

(d) Rate and mixtures.

Meaning and Computation of Mean of Ungrouped Data

The mean, median and the mode are called measures of central tendency or measures of location. The mean is also known as the average, the median is the middle number while the mode is the most frequent element or data.

THE ARITHMETIC MEAN:

The arithmetic mean is the sum of the ungroup of items divided by the number of it. The mean of an ungrouped data can be calculated by using the formula;

\(\bar{x} = \frac{∑x}{n}\), (when \(n\) is small)

(where the symbol \(∑\) is called sigma meaning summation of all the given data)

Also, Mean, \(\bar{x} = \frac{∑fx}{∑f}\) (when \(n\) is large)

\(∑fx =\) Sum of the product of scores and their corresponding frequencies

\(∑f =\) Sum of the frequencies

Example 1:

Find the arithmetic mean of the numbers 42, 50, 59, 38, 41, 86 and 56

Solution: Add all the numbers and divide by 7

\(\bar{x} = \frac{42 + 50 + 59 + 38 + 41 + 86 + 56}{7} \\ = \frac{378}{7} \\ ∴ \bar{x} = 54\)

Example 2:

The table below gives the frequency distribution of marks obtained by some students in a scholarship examination.