A measure of centre is a value at the middle of a data set can be measured via:
Mean
Median
Mode
The measure of centre found by adding the values and dividing the total by the number of values:
Find the mean of following values:
Answer:
Use formula;n: 6 (number of samples)
Mean = (5.5+6.5+7.5+8.5+9.5+10.5)/6=8
The measure of centre that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude.
Arrange values in order and If the number of values is odd, the median is the middle number; if the number of values is even, the median is found by computing the mean of the middle two numbers.
Example
Find the median of following values: 7 11 5 19 21Answer
1. Arrange values in order: 5 7 11 19 21
2. Odd number, so median is 11.
The mode of a data set is the value that occurs most frequently.
When two numbers occur most frequently, they are both the mode and the data set is bimodal
When more than two numbers occur most frequently, they are all the mode and the data set is multimodal
If no value is repeated, there is no mode
Example
Find the mean, median, and mode of the following data set:
10 12 14 8 18 22 26 28
Answer
Median (ordered)
8 10 12 14 18 22 26 18
even number of values
thus median is mean of 14 and 18 =(14+18)/2= 16
Mode : no value is repeated, thus there is no mode.
Since in a frequency distribution we don’t know the exact values falling in a particular class, we pretend that all values of a particular class are = class midpoint. Mean of a Frequency Distribution (shown below with x-bar )
Example
Find the mean of the Frequency Distribution of Pulse Rates for Women
| Pulse Rate | Frequency (f) |
|---|---|
| 60-69 | 12 |
| 70-79 | 14 |
| 80-89 | 11 |
| 90-99 | 1 |
| 100-109 | 1 |
| 110-119 | 0 |
| 120-129 | 1 |
| Total (Σf) | 40 |
answer:
| Pulse Rate | Frequency (f) | Class Midpoint (x) | f · x |
|---|---|---|---|
| 60-69 | 12 | 64.5 | 774 |
| 70-79 | 14 | 74.5 | 1043 |
| 80-89 | 11 | 84.5 | 929.5 |
| 90-99 | 1 | 94.5 | 94.5 |
| 100-109 | 1 | 104.5 | 104.5 |
| 110-119 | 0 | 114.5 | 0 |
| 120-129 | 1 | 124.5 | 124.5 |
| Total (Σf) | 40 | 3070 |
Standard deviation is a measure of how spread out or dispersed the values in a dataset are from the mean.
A low standard deviation means values are close to the mean (less variation).
A high standard deviation means values are spread out over a wider range (more variation).
Standard deviation of population of a frequency distribution
Standard Deviation of a population from a sample
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