Mean, Median and Mode
Mean: The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.
It is denoted by the symbol x̄ , read as ‘x bar’.
Median: The median is that value of the given number of observations, which divides it into exactly two parts. So, when the data is arranged in ascending (or descending) order the median of ungrouped data is calculated as follows:
(i) When the number of observations $(n)$ is odd, the median is the value of the $({n+1}/2)^{th}$ observation. For example, if $n$ = 13, the value of $({13+1}/2)^{th}$ i.e., the 7th observation will be the median.
(ii) When the number of observations (n) is even, the median is the mean of the $(n/2)^{th} $ and the $(n/2 + 1)^{th}$ observations. For example, if n = 16, the mean of the values of the $(16/2)^{th} $ and the $(16/2 + 1)^{th} $ observations, i.e., the mean of the values of the 8th and 9th observations will be the median.
The Mode:The mode is that value of the observation which occurs most frequently, i.e., an observation with the maximum frequency is called the mode.
EXERCISE 14.4 1. The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median and mode of these scores. 2. In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 Find the mean, median and mode of this data. 3. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of $x$. 29, 32, 48, 50, $x$, $x + 2$, 72, 78, 84, 95 4. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18. 5. Find the mean salary of 60 workers of a factory from the following table:
| Salary | No Of Workers |
|---|---|
| 3000 | 16 |
| 4000 | 12 |
| 5000 | 10 |
| 6000 | 8 |
| 7000 | 6 |
| 8000 | 4 |
| 9000 | 3 |
| 10000 | 1 |
| Total | 60 |